Quantum system and method of operation

Abstract

The quantum system may have a quantum signal source configured to generate a first signal and a second signal, the first signal and the second signal being in a frequency domain between 4 GHz and 300 GHz; the first signal and the second signal have quantum correlation; the quantum signal source is provided with a first port operable to output a first signal and a second port operable to output a second signal; a first transmission line coupled between the quantum signal source and a transmitter operable to transmit a first signal to a target; a receiver coupled to the target and operable to receive the first signal after interaction between the first signal and the target; a second transmission line coupled between the second port and the receiver; and a first amplifier coupled between the first port and the transmitter, the first amplifier operable to induce a gain of at least 10 times that of the first signal, where an amplification degree of the first mode between the quantum signal source and the receiver is at least twice that of the second mode, and the receiver is sensitive to a quantum correlation between the first signal and the second signal.

Description

Background Art

[0001] Electromagnetic field oscillations (such as those associated with electromagnetic waves) have been used to transmit signals for decades. Radar, metrology, and telecommunications are common examples of potential applications. In radar applications, a signal is transmitted by an operator in the direction of a potential target, travels through a medium (such as air), and when the target is within range, the signal is reflected back by the target. The operator's reception of the reflected signal can result in the detection of the target and can provide certain information about the target, such as the distance between the target and the transmitter. Some non-destructive testing techniques operate according to a similar principle, and the associated electromagnetic field oscillations can travel within a part of the inspected component that serves as the medium. In telecommunications, a signal can be transmitted by a first operator, received and encoded by a target (such as a second operator), and returned to the first operator. Receiving the returned signal can allow for the decoding of the communication. Electromagnetic waves propagate in free space and can also be used in aerospace applications where free space serves as the medium.

[0002] Although there are various possible ways to use and transmit signals based on electromagnetic oscillations, there is always room for improvement. For example, sensitivity and reliability can pose problems, and such problems may be easier to solve in some parts of the electromagnetic spectrum than in others. For example, the way electromagnetic waves are generated, the way they interact with matter, and thus the scope of their practical applications depend on the frequency (which is inversely correlated with the wavelength). When the size of the transmitting antenna is a function of the wavelength, its efficiency may be higher. In addition, the travel of different wavelengths in various media (such as the Earth's atmosphere) may be easier or more difficult. In fact, radio waves in the kHz to MHz range can more easily bypass obstacles such as mountains and follow the contour of the Earth through diffraction and refraction, and interact very little with air, so they can travel far in the atmosphere, while microwaves in the GHz range or optical frequencies in the THz range and higher (such as infrared or visible light) may bend or diffract less and are limited to line of sight, some wavelengths are absorbed by air, and the power rapidly decreases with distance. Therefore, devices used in association with radio waves generally cannot be used for microwave frequencies, and vice versa; devices used in association with light generally cannot be used for microwave and radio frequencies, and so on. For these reasons, many specific applications, such as those related to devices, interactions, or propagation, can benefit from selecting a specific frequency band from the entire electromagnetic oscillation spectrum. Summary of the Invention

[0003] Quantum physics has seen remarkable growth in the past few decades and has paved the way for generating new quantum states, such as pairs of electromagnetic field waves that can have quantum correlations with each other. In one example, a pair of elements can be entangled with each other and thus highly correlated, but in another example, there may be other quantum correlations between the pair of elements besides entanglement, such as quantum discord. Entanglement is a quantum property where the individual quantum state of each element in the pair is undefined until measured, and the act of measuring one element determines the outcome of the other. More generally, quantum discord is a measure of non-classical correlations between two elements in a quantum pair, including correlations due to quantum physical effects, but not necessarily involving entanglement. Entanglement and quantum discord can be consumed to encode information that can only be accessed through coherent quantum interactions. Quantum discord is considered to be more robust to losses and noise. It has been found that some applications, such as radar and secure communication, can benefit from using signal pairs with quantum correlations, particularly in the microwave part of the electromagnetic spectrum.

[0004] In one example, a process called spontaneous parametric down-conversion (SPDC) can be used as a quantum resource to generate two entangled pairs of random thermal noise signals, called quantum two-mode squeezed states (QTMS). Given the recent significant progress in microwave quantum superconducting circuits, particularly Josephson parametric amplifiers (JPA), it has been found that QTMS can be generated in the microwave part of the electromagnetic spectrum. In some cases, even though entanglement may be lost, for example due to signal loss and / or increased noise, a certain degree of quantum correlation (such as quantum discord) can still be retained. In fact, in a process that will be referred to herein as quantum-enhanced noise radar, in a radar application using JPA to interrogate a target (such as microwave quantum illumination), quantum correlations can be obtained from post-processing the heterodyne measurement records that are orthogonal to two signals. However, the source of QTMS (such as JPA in the microwave domain) can have a relatively low output power and needs to be amplified in order to be suitable for use in practical applications. For example, in the case of quantum-enhanced noise radar, higher power may be required to increase the detectable range or speed up the detection process. Power can be increased by amplification, but amplification inevitably brings additional uncorrelated noise. It has been found that symmetrically amplifying two correlated signals may lead to a rapid collapse of the quantum correlation characteristics (such as entanglement). However, it has been found that in some applications, using asymmetric amplification can address these challenges and allow for practical feasibility. In fact, some applications do not require the same level of amplification between the two signals.

[0005] According to one aspect, a method for interrogating a target is provided, the method comprising: generating a first signal and a second signal at a quantum signal source, the first signal and the second signal having a quantum correlation; propagating the second signal to a receiver; propagating the first signal to the receiver via the target, the target altering the first signal, wherein the propagating of the first signal includes amplifying the first signal between the quantum signal source and the target by at least twice as much as the amplification of the second signal between the quantum signal source and the receiver; receiving the second signal and the altered first signal at the receiver; and performing a correlation measurement between the received second signal and the received altered first signal.

[0006] The signal can be embodied as an electromagnetic field oscillation having a frequency between 1 GHz and 300 GHz, such as between 4 GHz and 100 GHz, and perhaps more typically between 4 GHz and 12 GHz. The signal is typically loaded in a controlled manner by a transmission line (such as a conductor trace, a cable, etc.), however, the signal (especially the first signal) can also be emitted by a suitable device (such as an antenna) so as to propagate more freely at a point in a medium (such as free space, air, or the material of the component being nondestructively tested), in which case it can also be received by an antenna after a free propagation segment. Alternatively, the signal can be emitted in a manner that propagates within a telecommunications network that may have 2 or more nodes.

[0007] Performing the correlation measurement can be achieved in a variety of ways, such as by measuring the cross-correlation or cross-covariance between the received second signal and the received altered first signal.

[0008] According to another aspect, a quantum system is provided, comprising: a quantum signal source configured to generate a first signal and a second signal, the first signal and the second signal being in a frequency domain between 4 GHz and 300 GHz; the first signal and the second signal having a quantum correlation; the quantum signal source having a first port operable to output the first signal and a second port operable to output the second signal; a first transmission line coupled between the quantum signal source and a transmitter, the transmitter operable to convey the first signal to a target; a receiver coupled to the target and operable to receive the first signal after interaction between the first signal and the target; a second transmission line coupled between the second port and the receiver; a first amplifier coupled between the first port and the transmitter, the first amplifier operable to cause a gain of at least 10 times the first signal, wherein, between the quantum signal source and the receiver, the degree of amplification of the first signal is at least twice that of the second signal, and the receiver is sensitive to the quantum correlation between the first signal and the second signal.

[0009] After reading the present instant disclosure, those skilled in the art will appreciate many further features and their combinations related to this improvement. Description of the Drawings

[0010] In the figures,

[0011] Figure 1 is a schematic diagram of an example of a quantum system;

[0012] Figure 2 is a schematic diagram of an example of a quantum two-mode squeezed state (QTMS) source of a quantum system that can be used for Figure 1 ;

[0013] Figure 3A is a graph depicting the entanglement measurement (symplectic eigenvalues of the partial transpose covariance matrix) ν - versus the power gain GB and the amplifier noise NB for a fixed value of r = 0.5 in an asymmetric case; the entanglement bound is 1, with entanglement shown in red and no entanglement shown in blue;

[0014] Figure 3B is for depicting the symplectic eigenvalue v for a fixed value of r = 0.5 in an asymmetric loss case - versus dBη = 10 -loss / 10 in the loss and the increase in noise due to the loss; in the left figure, the increased noise is parameterized as the physical temperature; in the right figure, it is parameterized as N l (where 1 corresponds to T = 0); according to the PPT criterion, the entanglement bound is v - = 1, with entanglement shown in red and no entanglement shown in blue. Similar to the case of asymmetric gain, we see that for T = 0, entanglement asymptotically disappears only when the loss approaches infinity;

[0015] Figure 4 is a graph demonstrating the enhancement of quantum correlations in the case of having the same power limit as the classical source, where the left side of equation (23) is plotted as a function of the channel transmission rate η and the amplifier gain, and the squeezing and noise values are shown in the inset; the contour lines indicate the upper limit of the quantum enhancement achievable relative to the classical source, and the contour levels of each graph indicate the noise value N C ;

[0016] Figure 5 is a graph depicting the symplectic eigenvalue in the case of a cascade amplifier gain and loss with a fixed value of r = 0.5 and a loss temperature of T = 1K, where the cascade amplifier gain and loss are both applied asymmetrically to one channel, and the symplectic eigenvalue is a function of the loss (in dB) (η = 10 - loss / 10) and the increased noise due to the loss; in the upper figure, we assume the amplifier is quantum-limited (NA = 1); in the lower figure, we assume the amplifier has a small amount of excess noise (NA = 1.1); according to the PPT criterion, the entanglement bound is 1, with entanglement shown in red and no entanglement shown in blue;

[0017] Figure 6 is a block diagram providing a general representation of an amplified source quantum two-mode squeezed state (A-QTMS source);

[0018] Figure 7 is in the limit case of quantum-limited amplification with N A = N B = 1 and infinite squeezing r → ∞, the entanglement bound v of the PPT criterion for QTMS under bilateral amplification - < 1 for G A , G B graphical representation;

[0019] Figure 8 is a phase diagram of the bilateral amplification domain in the diagram {GA, GB}, where quantum enhancement can be achieved even in the presence of amplification noise, transmission loss, and additive noise, and the system parameters are: r = 0.5, η = 0.3, NI = 100, NA = 10, NB = 50, NcA = 1000, NcB = 1000;

[0020] Figure 9 is a schematic representation of a communication system employing an A-QTMS source;

[0021] Figure 10 is a schematic representation of a bistatic remote sensing system employing an A-QTMS source;

[0022] Figure 11 is a schematic representation of three different example receiver / decoder schemes. Detailed implementation mode

[0023] Figure 1 shows an example of a quantum system 10 with a quantum signal source 12, the quantum signal source 12 being configured to generate two signals 14, 16 having quantum correlations, such as two quantum entangled signals, referred to herein as signal A 14 and signal B 16. A first amplifier 20 (referred to herein as amplifier B) is configured to amplify signal B 16 before transmitting it via a transmitting antenna 22. Signal B travels as an electromagnetic wave, interacts with a "target" 24 (to name a few potential examples, the "target" 24 can be a radar target, a component to be analyzed by non-destructive testing, or a telecommunications encoder), and then returns to the quantum system 10, is received by a receiving antenna 26, and is transmitted via the receiving antenna 26 to a receiver 28. Signal A 14 is transmitted more directly to the receiver 28, optionally after being amplified by a second amplifier 18 (referred to herein as amplifier A), but without interacting with the target 24.

[0024] In one example, the quantum signal source 12 can be a quantum two-mode squeezed state (QTMS) source 30, where one example exists in Figure 2A as Figure 2AAs shown, in this embodiment, the QTMS source 30 can be embodied by a Josephson parametric amplifier (JPA) 32. More specifically, the JPA 32 can be embodied using a superconducting quantum interference device (SQUID) 34 that operates at low temperature. A pump 36 operating at a pump frequency (f pump ) can be used to drive a coil 38 that drives an AC magnetic flux (which may or may not have a DC component) at the pump frequency. Between the input and output of the transmission line 44, a resonator 40 and a coupling capacitor 42 are coupled to the SQUID 34. The JPA 32 can have multiple resonant or normal modes, many of which are represented by Gaussian curves in Figure 2B . The pump frequency can be selected in a way that excites two resonant frequencies, which will be referred to herein as f A and f B . From the perspective of energy conservation, the activated resonant frequencies f A and f B have a sum equal to f pump . In a way that occupies a relatively limited "detection band" (which can be covered by a receiver), the activated resonant frequencies f A and f B can be selected to be "close" to each other. f A can be used as the first signal output, f B can be used as the second signal output, and vice versa. In some embodiments, although some practical considerations may prompt the selection of one or the other as the first signal. To operate in the QTMS mode, the input of the transmission can be left as the quantum vacuum.

[0025] Now let's model this scenario in a way that provides a more detailed example embodiment.

[0026] As an introduction, and as a way to introduce notation, we will first derive the quantum enhancement of a quantum noise radar based on an ideal two-mode squeezed state.

[0027] By measuring the covariance matrix of the corresponding in-phase I and quadrature Q voltages, the quantum state of the microwave field generated by the QTMS source can be fully characterized. This is a general property of so-called Gaussian states, which include classical thermal states, coherent states, and squeezed states. I and Q are common concepts in modern wireless and radar technologies. In the quantum realm, they are the canonical conjugate variables of the electromagnetic field, similar to position and momentum in a mechanical system. If we consider signals A and B, the form of the covariance matrix is V′ = E[xx T , where x = [I A , Q A , I B , Q BT And E[.] represents the expected value. Generally, the signal orthogonality of two signals depends on time, so the covariance matrix of the signals measured at different times can be calculated.

[0028] To quantify quantum properties (such as entanglement), the measured covariance matrix V′ must be calibrated and normalized in units of the absolute photon number, resulting in a scaled covariance matrix V. QTMS is a zero-mean Gaussian random signal whose covariance matrix has the general form

[0029]

[0030] where P A and P B represent the signal power, C Q represents the quantum correlation between signal A and signal B, and φ represents the relative phase between signal A and signal B.

[0031] The QTMS source can be characterized by immediately measuring and calibrating the covariance matrix at its output. Among them, signals A and B have the same power P A = P B = P Q and the phase φ = 0. In this case, it is characterized by a single parameter, namely the squeezing parameter r, such that the total output power (variance) in each quadrature is P Q = cosh(2r), and the quantum correlation is C Q = sinh(2r).

[0032] To determine the existence of entanglement in V, we can use a test called positive partial transpose (PPT), where the degree of entanglement can be quantified by the minimum symplectic eigenvalue v min of the partial transpose of V. If v min < 1, the two-mode Gaussian state is an entangled state (and thus a quantum state), and if v min ≥ 1, it is called a classical state.

[0033] A suitable reference is an ideal classical correlated state that reaches the positive partial transpose (PPT) bound and v min = 1. The best classical correlation (C c ) in this state corresponds to the output power P of one of the signals minus one unit of vacuum noise, or C c = P - 1. For a classical source with the same output power as the QTMS source, the best classical source will have C c = cosh(2r) - 1. Considering data fitting, we define the differential output power P D′ ​= cosh(2r) - 1 and the measured differential power P D , where P D / P 0 = cosh(2r) - 1, where P 0 is a scaling factor that includes the system gain. Thus, we can express the correlation as a function of the measured power and find the squeezing parameter r as:

[0034]

[0035] Conversely, we can then use this identity to write the quantum correlation as:

[0036]

[0037] and the best classical correlation as:

[0038]

[0039] Finally, this allows us to define the enhancement of the quantum correlation relative to its classical analogue as:

[0040]

[0041] It is known that the quantum enhancement of the correlation relative to its classical analogue is a direct consequence of a source that can generate quantum discord in its output in the case of Q_E > 1.

[0042] Here, we want to consider the effect of amplifying a quantum signal on its entanglement. We will consider the case of symmetric amplification (where both signals are amplified equally) and the case of fully asymmetric amplification (where only one signal is amplified). In both cases, we will assume that the signals are generated by an ideal symmetric parametric amplifier where the variances of the orthogonal parts of the output modes are all equal and have the value P Q , and the covariances are all equal and have the value C Q .

[0043] Symmetric amplification

[0044] In the symmetric case, we consider the same amplifier with a power gain G for both signals emitted by a quantum two-mode squeezing source. We model the amplifier using the standard operator equation, for example, for mode a of A amp ,

[0045]

[0046] where a o is the output mode of the parametric amplifier (quantum source) to be amplified, and h is the noise operator of the amplifier. This form ensures that A outFollowing the usual commutation relations, but the result does not depend on the details of the amplifier model. Thus, we obtain a simple relation between the power at the output of the amplifier and the correlation, namely

[0047]

[0048] where, is the amplifier noise figure, and T N is the noise temperature. Recall that the entanglement bound in the PPT test is P - C < 1, then we calculate

[0049] P amp - C amp = G exp(2r) + (G - 1)N A (7)

[0050] where we assume that the quantum source is ideal, and r is the squeezing parameter. As a bound, we can assume infinite squeezing, then this gives us a simple entanglement condition:

[0051] (G - 1)N A < 1 (8)

[0052] Then we see that for a quantum-limited amplifier with N A = 1, we break the entanglement for G > 2.

[0053] Even if amplifying the quantum signal breaks the entanglement, we can still ask whether there might be an advantage based on the fact of using quantum-limited amplification. As our classical benchmark, we will use the state proposed above, namely the coherent state with added thermal noise. In the case of our noisy radar protocol, a pair of coherent states will be classically modulated to produce a classically correlated pseudorandom signal. We write the classical quadrature output power as P C = C C + N C ≥ N C , where C C is the classical correlation, and N C is the noise figure of the source. To compare our classical benchmark with our amplified quantum source, we will set the two output powers equal to the power of the classical source, i.e., P C = P amp . Again approaching the infinite squeezing result P Q = C Q , we can express the classical covariance as:

[0054] C C = GC Q + (G - 1)N A - N C = C amp + (G - 1)N A - NC (9)

[0055] From this, we obtain that when the following is satisfied, when the quantum covariance of the amplified quantum source exceeds the classical covariance, there is a result of quantum enhancement, that is, C amp > C C ,

[0056] (G - 1)N A < N C (10)

[0057] That is, if the output noise of the amplifier is lower than the noise of the classical source, quantum enhancement can be achieved.

[0058] Asymmetric amplification

[0059] Starting from the symmetric output of the parametric amplifier, we now assume that only the second signal, i.e., signal B, is amplified by an amplifier with the same form as before (i.e., amplifier A does not exist in this simulation), but now with a gain G B and noise N B . After this amplification, we now have an asymmetric covariance matrix (still in the canonical form), described as:

[0060]

[0061] To test for entanglement, we will calculate the symplectic eigenvalues v - , that is

[0062]

[0063] where and δP = (P A - P B ) / 2. Writing these out we find:

[0064]

[0065] and

[0066]

[0067] Putting it all together, we get

[0068]

[0069] The PPT criterion states that if v - < 1, the state is entangled.

[0070] An important element of this result is that for a quantum-limited amplifier with N B = 1, the system for any amplification gain GB The values all remain entangled. That is, in principle, if we only put out one output mode of the large quantum two-mode squeezed state (using a quantum-limited amplifier), we can make it arbitrarily bright while still maintaining entanglement. In Figure 3A , we plotted this function.

[0071] Effect of Loss

[0072] Now let's consider the effect of asymmetric channel loss, which we model as an unbalanced beam splitter that inserts a power transmission rate η into the path of the signal or the idler light. Then the beam splitter transformation is

[0073]

[0074] where v is the annihilation operator of the additional noise of the amplifier (port 4) imposed by the fluctuation-dissipation theorem and the preservation of the commutation relation. We assume here that the loss is inserted into path B and find that

[0075]

[0076] where N l is the noise number of the loss, given by where T is now the physical temperature of the loss medium. Substituting these values into Equation (12), we find that

[0077]

[0078] and

[0079]

[0080] Putting them all together, we get the symplectic eigenvalues

[0081]

[0082] In Figure 3B , we plotted the functions of loss and temperature. We can make some comments. First, similar to the case of asymmetric gain, we see that for T → 0, entanglement only asymptotically vanishes when the loss goes to infinity. At finite temperatures, entanglement vanishes faster. Nevertheless, we can observe that losses at sub-Kelvin temperatures are tolerable to a considerable extent.

[0083] The next question is how amplifier gain and external loss interact. Specifically, we can ask whether asymmetric amplification of a quantum signal before it suffers loss can increase the loss threshold. Simply cascading the two models above, we find that:

[0084]

[0085] The definition of the operator is the same as above. Applying this gain and loss to the channel again, we find that:

[0086]

[0087] Writing down the explicit expression for v - is cumbersome, but these results can be directly used to numerically calculate the symplectic eigenvalues from equation (12). In Figure 5 , we plot some sample results showing v - as a function of the gain and loss. For both plots, we use a fixed value of r = 0.5 and a physical loss temperature of T = 1K. Due to the interesting numerical results, we see that for the case of a quantum-limited amplifier with N A = 1, the gain does not affect the loss value of the lost entanglement. For a finite excess amplifier noise (N A > 1), we instead see that the amplifier gain typically makes the situation worse. That is, as we increase the gain, the loss bound moves to lower loss values.

[0088] Even when entanglement is lost, within some parameter ranges of the amplifier gain and channel loss, the quantum correlations can still be practically enhanced relative to a comparable classical signal source. As before, we consider an asymmetrically amplified quantum source with loss having the same transmission power as a comparable classical source with P C = C C + N C = P B , and if C asy > C C , then we determine that there is a quantum enhancement. Considering the effects of amplification and channel loss on the quantum source, if P B - C asy < N C , more specifically, if the following is satisfied, then a quantum enhancement can be achieved

[0089]

[0090] In Figure 4 , for different parameter values of the squeezing parameter r, the amplifier noise N A and the loss noise N l , we plot the left-hand side of equation 23 as a function of the amplifier gain G and the channel transmission rate η. The contour lines indicate the classical noise number N CThe added value, and represents the upper limit that can achieve quantum enhancement. First, we can see that quantum enhancement can be achieved for a wide range of parameter values. Second, the loss temperature has little effect on the reduction of the enhancement. We evaluate that when the loss noise becomes comparable to the classical noise temperature (not shown), the effect of the loss temperature becomes significant. Third, the enhancement is very sensitive to the amplifier noise. Finally, we find that reducing the quantum squeezing parameter r relative to the classical case will improve the overall enhancement effect.

[0091] That is to say, the classical source only generates correlated signals to transmit power higher than its background noise N C . Therefore, the quantum source can be used as a correlated signal source for signals with power far lower than the background noise.

[0092] Generalized two-sided amplification model

[0093] As Figure 6 represented in, here we generalize the model to consider the limitations of having two amplifiers acting on a two-mode squeezed state. We extend the previous model by adding an amplifier 118 with noise to the signal A114, such that:

[0094]

[0095] Note that for clarity, some symbol changes are made: G A(B) and N A(B) refer to the amplifier gain and the noise added to the signal A(B). To keep the discussion more concise, we do not include loss and additive noise in channel A.

[0096] Since additive noise is not conducive to correlation, the effect of the second amplifier (on signal A) is to reduce the maximum gain on signal B before the entanglement is destroyed. To simply show this, we first consider the ideal case of a quantum-limited amplifier, where N A = N B = 1 without channel loss and added noise. The PPT criterion states that there is entanglement for v - <1. From equation (12), we obtain the following inequality for two-sided amplification of the state that maintains entanglement:

[0097]

[0098] Note that inverting G A and G B gives the maximum gain of G B constrained by G A . The result of this equation is plotted in Figure 8In it, we can see that it is a very steep function of the amplifier gain. Additionally, if the amplification is unidirectional, there is no limit to the amplification (i.e., if G B →1, then G A →∞, and vice versa), and in the symmetric amplification scheme, the maximum gain is indeed G A =G B =2.

[0099] We require that the quantum power and the classical power be the same, where P A =C c +N cA and P B =C c +N cB , and at the same time C asy >C c , which means that the following inequalities must be satisfied simultaneously:

[0100] P A -C asy <N cA and P B -C asy <N cB (26)

[0101] That is to say, depending on the classical noise amounts on the two channels, for a given value of the squeezing parameter r, there is at least one combination of the amplifier gain and noise on the two channels that satisfies the two inequalities simultaneously. In Figure 8 , we illustrate the amplification domain {G A ,G B} that can achieve quantum enhancement for the selection of system parameters. As we can see, the amplification domain can be quite large and provides a great deal of freedom for optimization.

[0102] Therefore, amplification can be used to increase the transmitted power in order to compensate for channel losses and noise, i.e., to achieve the minimum signal-to-noise ratio at the receiver required for the application.

[0103] For applications using correlated signals, a balance can be achieved between the transmission power and the correlation quantity. The optimal parameters depend on the application requirements, the environment, and the technological limitations.

[0104] The amplification gain here is at least G>1, and for a JPA operating at or near the quantum limit, it is typically found to be in the range of G~20 - 40 dB. The ideal or maximum gain value depends on (but is not limited to) the amplification scheme (unidirectional or bidirectional), the amplifier noise, the source power, the channel losses, and the added noise. The gain should be set according to the application specifications as well as the minimum quantum requirements corresponding to entanglement preservation or quantum enhancement.

[0105] Quantum microwave devices such as JPA typically operate at center frequencies in the GHz range, typically in the 2 to 12 GHz band. Depending on the device configuration and materials, the operating frequency can extend to the hundreds of GHz range. Depending on the embodiment, the amplification bandwidth can be narrow (<1 MHz) or wide (>1 GHz).

[0106] The amplifier stage may consist of one or more amplifiers placed in a chain. In the latter, it is preferred that the first amplifier in the chain has the least amount of added noise, since the first amplifier stage sets the effective noise characteristics of the chain.

[0107] application

[0108] Asymmetric amplification of signals with quantum correlations may be desirable in various applications. In particular, in the two example applications presented below, the use of entangled states of microwave signals, particularly in the form of quantum two-mode squeezed states, is beneficial despite signal losses and additive noise. As mentioned above, given the low power that QTMS sources may have, amplification that preserves entanglement (or minimally preserves correlations) may be desirable to offset channel losses and improve performance, efficiency, practical distance, etc.

[0109] One possible application is secure communication between two users in a covert manner, i.e. the transmitted messages have a low probability of being detected, intercepted and thus decoded, an example of which is found in Figure 9 middle. Figure 9 In the embodiment presented in FIG. 1 , an A-QTMS source 212 is used as a shared resource between two operators. A first operator generates a QTMS state and shares signal B 216 with a second operator over a common communication channel while retaining signal A 214. Via encoder 252, the second operator encodes the message on the received signal and transmits the encoded signal back to the first operator. The first operator then performs a correlation measurement of the appropriate type between the encoded signal B and signal A to extract the encoded message.

[0110] This application can have different embodiments. Due to entanglement and quantum correlation, QTMS has been shown to saturate the secret key rate capacity on lossy and noisy communication channels. Amplification using QTMS can compensate for channel losses, thereby improving communication performance over a given distance. Conversely, it may allow longer distances between users for the same communication performance.

[0111] Another possible application is remote sensing. Figure 10As depicted, the amplified signal B 316 can be sent towards a distant object (target 324), while the signal A 314 is retained in the system. The object affects the incident signal by changing one or more of its characteristics: its amplitude, frequency, and / or phase. The signal that has been transformed and reflected is then referred to as an echo. At least part of the echo is sent back to the receiving antenna 326. The collected echo and signal A are then processed in the receiver to extract information about the object. Various information about the object can be extracted through the analysis of the echo, such as but not limited to: presence or absence, distance, speed, size, shape, or composition. The type and structure of the receiver will vary depending on the information about the object to be obtained, but at least a correlation type measurement between the echo and signal A will be performed. Repeated measurements can be made several times and averaged to increase the accuracy of the system.

[0112] It should be noted that the system can use one (monostatic), two (bistatic, as shown), or multiple (multistatic) antennas to make the measurements.

[0113] By way of a few examples, this general framework describes radar type measurements that can be used for non-destructive testing and evaluation (NDT-E) of materials, target detection, and ranging (radar) or radar imaging.

[0114] Other potential applications can include, for example, sensing applications (such as non-destructive testing, imaging, radar); communication (such as exchanging data, exchanging voice, short-range, long-range, via a network, via an antenna, via a wire); and quantum computing (such as improving performance, using the technology for qubit readout), etc.

[0115] For example, in the case of a communication application, the quantum system can include a device that allows a modulation source to convey information in the signal. The modulation can be, for example, amplitude, frequency, and / or phase modulation. In some embodiments, an encoding layer can be applied on top of the basic information in the signal, but this may not be required in some applications.

[0116] Correlation Receiver

[0117] Various types of receivers can be used to perform the type of correlation measurements associated with a given application. In many applications, the goal at the receiver may be to search for a correlation. More specifically, a first signal can be compared with a second signal, and a peak in the similarity between the signals can be an indication of the presence of a correlation. Several examples thereof will now be presented in order to provide a detailed description of potential embodiments. In some examples, for instance, the comparison can be performed digitally on a computer by calculating the cross-correlation of the quadrature voltage of signal A measured at time tA with the quadrature voltage of signal B measured at time tB. The computer can calculate the cross-correlation over a wide range of time delays τ = tA - tB and store the magnitude of the cross-correlation as a function of the delay time in memory. This process is referred to as matched filtering. Prior to calculating the cross-correlation, a phase transformation / compensation of the measurement record of pattern B can be performed digitally. The measurement process can be repeated a certain number of times under the same conditions, and then the results of these repeated measurements can be averaged. When the cross-correlation magnitude reaches a certain threshold set by the user, a successful detection of the return signal is obtained. In such an example, signal B can be digitized directly at the output of the QTMS source, while signal A can be digitized after being received by the receiving antenna, for example, or after interacting with the target.

[0118] In Figure 11A In the first example shown, a digital matched filter receiver 428 is used. This type of receiver 428 can be referred to as a heterodyne receiver. In one embodiment, the receiver 428 has two separate and independent digitizers 460, 462, each digitizer measuring two quadratures of the voltage pattern and storing the digital measurement records in memory. Ideally, pattern B is digitized directly at the output of the QTMS source, while pattern A is digitized after being received by the receiving antenna. The correlation can be performed digitally on a computer 464 by calculating the cross-correlation of the quadrature voltage of pattern A measured at time tA with the quadrature voltage of pattern B measured at time tB. The computer 464 calculates the cross-correlation over a wide range of time delays τ = tA - tB and stores the magnitude of the cross-correlation as a function of the delay time in memory. This process can be referred to as matched filtering. Prior to calculating the cross-correlation, a phase transformation / compensation of the measurement record of pattern B can be performed digitally. The measurement process can be repeated a certain number of times under the same conditions, and then the results of these repeated measurements can be averaged. When the cross-correlation magnitude reaches a certain threshold set by the user, a successful detection of the return signal is obtained.

[0119] Such a receiver can be easily implemented and allows for digital control of the signal phase and time delay without the need for imperfect and lossy components.

[0120] In Figure 11BIn the second example shown, a parametric amplifier (PA) receiver 528 is used. This type of receiver 528 can be interpreted as an analog version of a matched filter receiver and can rely on recombining mode A and mode B on a second parametric amplifier at exactly the same time, essentially producing an interference-type measurement. The second parametric amplifier effectively mixes mode A and mode B through a correlation product. The second parametric amplifier produces two independent noise signals at two outputs. The variance of each output mode corresponds to the magnitude of the cross-correlation of mode A and mode B. The variance of the modes can be measured by measuring a single voltage quadrature using a digitizer.

[0121] The second parametric amplifier can be ideally matched in frequency and bandwidth to the parametric amplifier used as the QTMS source. The second parametric amplifier 570 can use a pump signal to perform a non-linear mixing process. The phase of the pump signal sets the magnitude of the cross-correlation relative to the phase of the mode A signal, thus setting the variance of the output signal. Mode B can travel to the receiver through a delay line 572, and the length of the delay line 572 can be selected such that mode B arrives at the receiver at the same time as mode A. Delay line losses, phase mismatches, and perhaps more critically, time delay mismatches, can severely degrade the performance and practicality of this analog matched filter receiver.

[0122] In Figure 11C In the third example shown, a sum-frequency generation (SFG) receiver 628 can be used. This type of receiver 628 can operate in a similar manner to the PA receiver 528. It can recombine mode A with a delayed mode B on a non-linear quantum device 680 that performs a sum-frequency generation (SFG) process. That is, the SFG 680 is exactly the opposite of the process that occurs in the QTMS source. In the SFG 680, photons from A and B that arrive at the quantum device simultaneously can spontaneously recombine to create photons in mode C at the output. The frequency of mode C corresponds to the sum of the frequencies of mode A and mode B, i.e., fC = fA + fB. At the output, the signal in mode C corresponds to a coherent state, whose amplitude and phase depend on the amplitudes and relative phases of mode A and mode B at the input.

[0123] The SFG process can be somewhat random and have relatively low efficiency. Additionally, the SFG process is not selective and does not directly rely on the correlation between pattern A and pattern B, but rather on the probability of having simultaneously arriving A and B photons. Thus, random events that occur, for example, under non-ideal conditions (external signal sources from other devices) and thermal noise may still be recorded. To compensate, the SFG receiver can be provided with multiple SFG units in series, which incorporate measurement and feedforward loops to filter out those spurious events. As a result, the SFG receiver may be more complex and difficult to implement in practice, and non-idealities may severely inhibit the overall performance.

[0124] It is noted that the embodiments in Figure 11A are digital, i.e., the signals are digitized and generally compared at the receiver based on the digital representation of the signals stored in a computer-readable memory that can be either temporary or non-temporary, while the embodiments in Figure 11B and Figure 11C are more analog in nature, utilize interference phenomena, and in some embodiments may require adjustment of the hardware to have the signals arrive at the receiver simultaneously, whereas in the Figure 11A non-temporary memory variant of

[0125] It will be understood that the examples described and illustrated above are for illustrative purposes only. As disclosed above, various modifications and adaptations can be made to the existing and described embodiments. Additionally, when a broader interpretation consistent with the knowledge of those skilled in the art is possible, the expressions should not be construed in a limiting manner. For example, in this specification, the expression "receiver" is used to refer to the equipment for receiving the first signal and the second signal, but this expression is not intended to imply that the same piece of hardware will receive both signals. In fact, separate hardware blocks can be used to digitize each of the two signals, and then a computer can be used to perform calculations on the digitized signals to evaluate whether there is an association. Similarly, the expression "computer" is not intended to be construed in a limiting manner, but rather is interpreted in a general sense to mean, for example, a device having a processor and a memory accessible to the processor, where instructions for performing functions and other data can be stored in the memory and accessed by the processor to perform functions on other data. In practice, by way of example, a desktop computer, a laptop computer, or a smartphone can be used as a "computer". Various types of transmitters can be used to transmit signals as needed. In some embodiments, the transmitter can be located inside the cryocooler, while in other embodiments, the transmitter can be located outside the cryocooler. In some embodiments, the transmitter and the receiver can have corresponding antennas, or in other embodiments, they can share the same antenna. In some alternative examples, the target can be a sample located inside the cryocooler rather than outside the cryocooler, and a quantum system can be used to characterize the sample at low temperatures. Its scope is indicated by the appended claims.

Claims

1. A quantum system, comprising: a quantum signal source configured to generate a first signal and a second signal, the first signal and the second signal being in a frequency domain between 4 GHz and 300 GHz; the first signal and the second signal having a quantum correlation; the quantum signal source having a first port operable to output the first signal and a second port operable to output the second signal; a first transmission line coupled between the quantum signal source and a transmitter, the transmitter operable to transmit the first signal to a target; a receiver operable to receive the first signal after interaction between the first signal and the target, the receiver being sensitive to the quantum correlation between the first signal and the second signal; a second transmission line coupled between the second port and the receiver; and a first amplifier coupled between the first port and the transmitter, the first amplifier operable to cause a gain of at least 10 times the first signal; wherein, between the quantum signal source and the receiver, the amplification degree of the first mode is at least twice that of the second mode.

2. The quantum system according to claim 1, further comprising a cryogenic refrigerator enclosing the quantum signal source, the cryogenic refrigerator operable to maintain a temperature between 50 K and 5 mK.

3. The quantum system according to claim 2, wherein, the target is located outside the cryogenic refrigerator.

4. The quantum system according to claim 3, wherein, the transmitter is located outside the cryogenic refrigerator.

5. The quantum system according to claim 1, wherein, the quantum signal source is a quantum two-mode squeezed state source, the first signal is the first mode of the QTMS source, the second signal is the second mode of the QTMS source, and the QTMS source has a first mode port operable to output the first mode and a second mode port operable to output the second mode.

6. The quantum system according to claim 5, wherein, the QTMS source further comprises two input ports.

7. The quantum system according to claim 5, wherein, the first amplifier is coupled to the QTMS source via a circulator.

8. The quantum system according to claim 1, wherein, the first signal and the second signal are in a frequency domain between 4 GHz and 100 GHz.

9. The quantum system according to claim 1, wherein, the first signal and the second signal are in a frequency domain between 4 GHz and 12 GHz.

10. The quantum system according to claim 1, wherein, the gain of the first amplifier is at least 100, preferably at least 1000, preferably at least 100000.

11. The quantum system according to claim 1, wherein, the first amplifier is configured to provide an amplification of at least 20 dB, preferably at least 30 dB, preferably at least 50 dB.

12. The quantum system according to claim 1 further includes a second amplifier, and the second amplifier is coupled between the first amplifier and the transmitter.

13. The quantum system according to claim 1 further includes a second amplifier, and the second amplifier is coupled between the second mode port and the receiver. The second amplifier has a gain of at least half of the gain of the first amplifier, preferably less than 1 / 10 of the gain.

14. The quantum system according to claim 1 wherein, the receiver is a heterodyne digital matched filter receiver, which has a first digitizer coupled to the first signal and a second digitizer coupled to the second signal. The first digitizer and the second digitizer are configured to measure two orthogonal voltages of the corresponding signals and store the digital measurement records in a computer-readable memory.

15. The quantum system according to claim 14 further includes a computer, and the computer is configured to calculate the cross-correlation between the orthogonal voltage of the first signal measured at time tA and the orthogonal voltage of the second signal measured at time tB.

16. The quantum system according to claim 1 further includes a computer, and the computer is configured to perform digital correlation of the first signal and the second signal.

17. A method for interrogating a target, the method comprising: generating a first signal and a second signal at a quantum signal source, the first signal and the second signal having a quantum correlation; propagating the second signal to a receiver, propagating the first signal to the receiver via the target, including that the amplification of the first signal between the quantum signal source and the target is at least 2 times the amplification of the second signal between the quantum signal source and the receiver, and including that the target changes the first signal; digitizing the second signal and the changed first signal at the receiver; and performing a correlation measurement between the received second signal and the received changed first signal.

18. The method according to claim 17 wherein, the performing the correlation measurement includes measuring one of the cross-correlation and the cross-covariance between the received second signal and the received changed first signal.

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