Quantum systems and methods of operation

Abstract

The quantum system 10 includes a quantum signal source 12 configured to generate a first signal 14 and a second signal 16, the first signal 14 and the second signal 16 being in the frequency range of 4 to 300 GHz, the first signal 14 having a quantum correlation with the second signal 16, the quantum signal source 12 having a first port operable to output the first signal 14 and a second port operable to output the second signal 16; a first transmission line coupled between the quantum signal source 12 and an emitter operable to transmit the first signal 14 to a target 24; The quantum signal source 12 may have a receiver 28 coupled to the target 24 and operable to receive the first signal 14 after interaction between the first signal 14 and the target 24, a second transmission line coupled between the second port and the receiver 28, and a first amplifier 20 coupled between the first port and the emitter and operable to induce a gain of at least 10 on the first signal 14, wherein the first mode is amplified at least twice as much as the second mode between the quantum signal source 12 and the receiver 28, and the receiver 28 is affected by quantum correlation between the first signal 14 and the second signal 16.

Description

[Background technology]

[0001] For the past several decades, electromagnetic field oscillations, such as electromagnetic waves, have been used to transmit signals. Radar, metrology, and telecommunications are common examples of potential applications. In radar applications, a signal is emitted by an operator in the direction of a potential target, travels through a medium such as air, and is reflected by targets within range. Reception of the reflected signal by the operator allows for target detection and can provide specific information about the target, such as the distance between the target and the emitter. Several nondestructive testing techniques operate on a similar principle, where the associated electromagnetic field oscillations can travel in a portion of the component being inspected, acting as a medium. In telecommunications, a signal is emitted by a first operator, can be received and encoded by a target (e.g., a second operator), and transmitted back to the first operator. Receipt of the returned signal can enable decoding of the communication. Electromagnetic waves propagating through space can also be used in aerospace applications, where space acts as a medium.

[0002] While the potential means for using and transmitting electromagnetic vibration-based signals are vast and numerous, there is always room for improvement. For example, sensitivity and reliability can be concerns, but such concerns are more easily addressed in some parts of the electromagnetic spectrum than in others. For example, the methods for generating electromagnetic waves, the ways they interact with matter, and thus their respective practical applications are determined by frequency, which is inversely related to wavelength. Emitting antennas can be more efficient when sized as a function of wavelength. Furthermore, different wavelengths can travel with varying degrees of ease in various media, such as the Earth's atmosphere. Indeed, radio waves in the kHz-MHz range can travel very far through the atmosphere because they can navigate around obstacles such as mountains, easily follow the contours of the Earth through diffraction and refraction, and interact very little with the air. In contrast, microwaves in the GHz range or optical frequencies in the THz range and above (e.g., infrared or visible light) bend or diffract much less, are limited to line of sight, and, depending on the wavelength, lose power rapidly over distance due to air absorption. Thus, equipment used in connection with radio waves generally cannot be used with microwave frequencies and vice versa, equipment used in connection with light generally cannot be used with microwave and radio frequencies, etc. For these reasons (e.g., equipment-, interaction-, or propagation-related), many specific applications can benefit from the selection of specific frequency bands from the full spectrum of electromagnetic oscillations. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] International Publication No. 2016 / 005737 [Patent Document 2] International Publication No. 2022 / 168079 Summary of the Invention [Problem to be solved by the invention]

[0004] Quantum physics has seen significant development over the past several decades, paving the way for the creation of new quantum states, such as electromagnetic wave pairs, that can have quantum correlations with each other. In one example, pairs can be highly correlated because they entangle with each other, while in another example, quantum correlations other than entanglement, such as quantum discord, can exist between pairs. Entanglement is a quantum property in which the individual quantum states of each pair are indeterminate until measured, and the act of measuring one determines the outcome of the other. More broadly, quantum discord is a measure of the non-classical correlation between two elements of a quantum pair, including correlations in quantum physics effects but not necessarily involving entanglement. The use of entanglement and quantum discord can encode information that is only accessible through coherent quantum interactions. Quantum discord has been recognized as being more robust to loss and noise. It has been shown that some applications, such as radar and secure communications, can benefit from the use of quantum-correlated signal pairs, particularly in the microwave portion of the electromagnetic spectrum.

[0005] In one example, a process called spontaneous parametric down-conversion (SPDC) can be used as a quantum resource to generate a pair of entangled random thermal noise signals called quantum two-mode squeezed states (QTMS). Considering recent significant advances in microwave quantum superconducting circuits, particularly Josephson parametric amplifiers (JPAs), it has been shown that QTMS can be generated in the microwave portion of the electromagnetic spectrum. In some circumstances, even when entanglement is lost due to signal loss and / or added noise, some quantum correlation, such as quantum discord, may remain. Indeed, in radar applications using JPAs, microwave quantum states can be used to identify targets (e.g., microwave quantum illumination), allowing quantum correlation to be obtained by post-processing quadrature heterodyne measurements of both signals in a process referred to herein as quantum-enhanced noise radar. However, QTMS sources such as JPAs in the microwave region can have relatively low output power and therefore require amplification for practical use. For example, quantum-enhanced noise radar may require more power to increase the detection range or speed up the detection process. Power can be increased by amplification, but amplification inevitably introduces additional uncorrelated noise. It has been shown that symmetric amplification of both correlated signals rapidly destroys quantum correlation properties such as entanglement. However, it has been shown that, for some applications, asymmetric amplification can address this challenge and enable practical workability. Indeed, some applications do not require the same level of amplification between the two signals. [Means for solving the problem]

[0006] According to one aspect, there is provided a method of identifying a target, the method comprising: generating a first signal and a second signal at a quantum signal source, the first signal having a quantum correlation with the second signal; propagating the second signal to a receiver; propagating the first signal through a target to the receiver, the target altering the first signal, wherein propagating the first signal comprises amplifying the first signal between the quantum signal source and the target by a factor of at least two greater than any 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.

[0007] The signal may be embodied as an electromagnetic field oscillation at a frequency between 1 and 300 GHz, such as 4 to 100 GHz (perhaps more commonly 4 to 12 GHz). The signal will typically be carried in a controlled manner by a transmission line such as a conductor trace, cable, etc., but in particular a first signal may be emitted by a suitable device such as an antenna and propagated more freely in a medium such as free space, air, or at some point in the material of, for example, a component undergoing non-destructive testing, in which case reception by the antenna after the free propagation segment may also occur. Alternatively, the signal may be emitted to propagate within a telecommunications network, which may have two or more nodes.

[0008] Performing a correlation measurement can be achieved in a variety of ways, such as measuring the cross-correlation or cross-covariance between the received second signal and the received altered first signal.

[0009] According to another aspect, there is provided 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 range of 4 to 300 GHz, the first signal having a quantum correlation with the second signal, 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 an emitter operable to transmit the first signal to a target; a receiver operable to receive the first signal after an 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 emitter operable to induce a gain of at least 10 on the first signal, wherein the first signal is amplified by at least twice as much as the second signal between the quantum signal source and the receiver, and the receiver is affected by the quantum correlation between the first signal and the second signal.

[0010] Many other features and combinations thereof that would improve upon this invention will become apparent to those skilled in the art upon reading this disclosure. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a schematic diagram of an example quantum system. [Figure 2] FIG. 2 is a schematic diagram of an example of a quantum two-mode squeezed state (QTMS) source that can be used in the quantum system of FIG. 1. [Figure 3A] 10 is a graph showing the entanglement measure (symplectic eigenvalue of the partially transposed covariance matrix) ν− for the asymmetric case versus the power gain GB and amplifier noise NB for a fixed value of r=0.5 (the entanglement boundary is 1, red indicates entanglement, blue indicates no entanglement). [Figure 3B]Graph showing the symplectic eigenvalue ν for the case of asymmetric loss versus the loss in dB (η=10-loss / 10) and the additive noise due to the loss at a fixed value of r=0.5. (In the left graph, the additive noise is parameterized as the physical temperature T, while in the right graph it is parameterized by Nl (1 corresponds to T=0); the entanglement boundary according to the PPT criterion is ν=1, red indicates entanglement, and blue indicates no entanglement. As in the case of asymmetric gain, we see that for T=0 the entanglement vanishes asymptotically only as the loss goes to infinity.) [Figure 4] 2A-2C are graphs showing a demonstration of quantum enhancement in correlation quantities under the same power constraints for classical quantum sources (where the LHS of equation (23) is plotted against the channel transmittance η and amplifier gain, along with the squeezing and noise values ​​found in the inserted information, and the contours indicate the upper bound on the quantum enhancement achievable for a classical quantum source with noise values ​​N C indicated by the contour levels on each graph). [Figure 5] Graph showing the symplectic eigenvalues ​​for cascaded amplifier gain and loss, both applied asymmetrically to one channel, as a function of loss in dB (η=10-loss / 10) and the additive noise due to the loss at a fixed value of r=0.5 and the loss temperature T=1K. (In the top plot, we assume the amplifier is quantum-limited (NA=1); in the bottom plot, we assume the amplifier has a small amount of extra noise (NA=1.1). The entanglement bound according to the PPT criterion is 1, with red indicating entanglement and blue indicating no entanglement.) [Figure 6] FIG. 1 is a block diagram giving a general representation of an amplified quantum two-mode squeezed-state source (A-QTMS source). [Figure 7] This is a graph representation of the entanglement boundary ν<1 in the PPT criterion for GA and GB of QTMS under double-sided amplification in the limit of quantum-limited amplification where NA=NB=1 and infinite squeezing r→∞. [Figure 8]Figure 1 shows the phase diagram of the two-sided gain region of {GA, GB} where quantum enhancement is obtained in the presence of gain noise, transmission loss, and additive noise for the system parameters r = 0.5, η = 0.3, Nl = 100, NA = 10, NB = 50, NcA = 1000, and NcB = 1000. [Figure 9] 1 is a schematic diagram of a communication system employing an amplified QTMS source. [Figure 10] FIG. 1 is a schematic diagram of a bistatic remote sensing system employing an amplified QTMS source. [Figure 11] 1 is a schematic diagram of three different exemplary receiver / decoder schemes; DETAILED DESCRIPTION OF THE INVENTION

[0012] FIG. 1 illustrates an example quantum system 10 having a quantum signal source 12 configured to generate two quantum-correlated signals 14, 16 (referred to herein as signal A 14 and signal B 16), such as two quantum-entangled signals. A first amplifier 20, referred to herein as amplifier B, is configured to amplify signal B 16 prior to emission via an emitting antenna 22. Signal B, traveling as an electromagnetic wave, interacts with a “target” 24 (which may be a radar target, a component to be analyzed by nondestructive testing, or a telecommunications encoder, to name a few potential examples), returns to the quantum system 10, is received by a receiving antenna 26, and transmitted therethrough to a receiver 28. Signal A 14 is optionally transmitted to the receiver 28 more directly via a second amplifier 18, referred to herein as amplifier A, without interacting with the target 24.

[0013] In one example, quantum signal source 12 can be a quantum two-mode squeezed state (QTMS) source 30, an example of which is shown in FIG. 2A. As seen in FIG. 2A, in this embodiment, QTMS source 30 can be embodied with a Josephson parametric amplifier (JPA) 32. More specifically, JPA 32 can be embodied using a superconducting quantum interference device (SQUID) 34 operating at cryogenic temperatures. The pump frequency (f pump ), which drives a coil 38 that drives an AC magnetic flux at the pump frequency (a DC component may or may not be present). A resonator 40 and a coupling capacitor 42 are coupled to the SQUID 34 between its input and output on a transmission line 44. The JPA 32 may have multiple resonant or normal modes, many of which are represented by Gaussian curves in FIG. 2B. The pump frequency is referred to herein as f A and f B The active resonant frequency f A and f B From the viewpoint of conservation of energy, pump The activation resonant frequency f A and f B can be chosen to be "close" to one another so as to occupy a relatively limited "detection band" that the receiver can cover. A is output as the first signal, and f B can be output as the second signal, or vice versa, but in some embodiments, one or the other may be selected as the first signal as a result of some practical considerations. Also, for operation in QTMS mode, the input of the transmission may be the quantum vacuum.

[0014] We now provide a more detailed exemplary embodiment by modeling such a scenario.

[0015] First, as a way to derive notation, we derive the quantum enhancement of quantum noise radar based on an ideal two-mode squeezed state.

[0016] The quantum state of the microwave field generated by a QTMS source can be fully characterized by measuring the covariance matrix of the corresponding in-phase I and quadrature Q voltages. This is a general property of so-called Gaussian states, which include squeezed states as well as classical thermal and coherent states. I and Q are common concepts in modern radio and radar technology. In the quantum world, these are the canonical conjugate variables of the electromagnetic field, analogous to position and momentum in a mechanical system. Considering signals A and B, the covariance matrix is ​​V'=E[xx T ] where x=[I A ,Q A ,I B ,Q B ] T where E[.] denotes the expected value. In general, the signal quadrature of both signals is time dependent, so the covariance matrix can be calculated for signals measured at different times.

[0017] To quantify quantum properties such as entanglement, the measured covariance matrix V' must be calibrated and normalized in units of the absolute photon number to obtain a scaled covariance matrix V. Because QTMS are zero-mean Gaussian random signals, the respective covariance matrices have the general form:

[0018]

number

[0019] where P A , P B denotes the signal power, and C Q denotes the quantum correlation between signals A and B, while φ is the relative phase between signals A and B.

[0020] A QTMS source can be characterized by measuring and calibrating the covariance matrix immediately at its output, where signals A and B have the same power P A =P B =P Qand phase φ=0. In such a case, the QTMS source is characterized by a single parameter (the squeezing parameter r), so that the total output power in each quadrature (dispersion) is P Q =cosh(2r), quantum correlation is C Q =sinh(2r).

[0021] To determine the presence or absence of entanglement in V, a test known as the positive partial transpose (PPT) can be used, where the degree of entanglement is the smallest symplectic eigenvalue ν of the partial transpose of V min The two-mode Gaussian state can be quantified by min < 1, it is entangled (and therefore quantum), and ν min It is said to be classical when ≥ 1.

[0022] The appropriate standard is ν min This is an ideal classical correlation state where the positive partial transpose (PPT) is saturated with the boundary of C = 1. C ) corresponds to the output power P of one of the signals minus one unit of vacuum noise (i.e., C C =P-1). For a classical quantum source with the same output power as the QTMS source, the optimal classical signal source is C C = cosh(2r)-1. Then, with the data fitting in mind, we obtain the differential output power P D’ = cosh(2r)-1 and the measured differential power P D Define P D Let / P0=cosh(2r)-1, where P0 is a scaling factor that includes the system gain. This allows us to express the correlation as a function of the measured power and find the squeezing parameter r as follows:

[0023]

number

[0024] On the other hand, the identity

number

[0025]

number

[0026] Also, the optimal classical correlation can be written as:

[0027]

number

[0028] This finally allows us to define the quantum enhancement of correlations relative to its classical analogue as follows:

[0029]

number

[0030] The quantum enhancement of correlations relative to the classical analogue is Q E >1 is known as a direct consequence of a signal source that can generate quantum discord at its output.

[0031] We now consider the effect of the amplification of quantum signals on their entanglement. We consider both 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 assume that the dispersions of the output mode quadratures are all equal and have a value P Q and all covariances are equal, with value C Q Assume that the signal is generated by an ideal symmetrical paraamplifier with

[0032] Symmetric Amplification

[0033] In the symmetric case, we consider the same amplifier with power gain G for both signals emitted by the quantum two-mode squeezing source. For example, A for mode a amp We model the amplifier by a standard operator equation for

[0034]

number

[0035] where a0 is the mode at the output of the paraamplifier (quantum source) being amplified, and h is the noise operator of the amplifier. This form is out The result does not depend on the details of the amplifier model, although we ensure that {tilde over (x)} obeys the usual commutation relations. This gives a simple relationship for power and correlation at the amplifier output:

[0036] P amp =GP Q +(G-1)N A C amp =GC Q (6)

[0037] where:

number

[0038] P amp -C amp =Gexp(2r)+(G-1)N A (7)

[0039] Here we assume that the quantum source is ideal and r is the squeezing parameter. As a boundary, we can assume infinite squeezing, which gives us a simple entanglement condition:

[0040] (G-1)N A <1 (8)

[0041] And N A In the case of a quantum-limited amplifier with G = 1, it is found that entanglement is broken when G > 2.

[0042] Even if entanglement is broken in the amplification of quantum signals, one can still argue that there may be advantages based on the fact that quantum-limited amplification is used. As a classical benchmark, we use the proposed state, which is a coherent state with added thermal noise. In the context of a noise radar protocol, we generate classically correlated pseudorandom signals by classical modulation of a pair of coherent states. Let the classical quadrature output power be P C =C C +N C ≧N C Here, C C is the classical correlation, and N C is the noise power of the source. To compare the classical benchmark with the amplified quantum source, we set the two output powers to be equal to the classical source (i.e., P C =P amp ). In this case too, P Q =C Q By approximating this with the infinite squeezing result, the classical covariance can be expressed as

[0043] C C =GC Q +(G-1)N A -N C =C amp +(G-1)N A -N C (9)

[0044] Here, when the quantum covariance of the amplified quantum source exceeds the classical covariance, i.e., C amp >C C If , then quantum enhancement exists, as follows:

[0045] (G-1)NA <N C (10)

[0046] That is, quantum enhancement is achieved when the amplifier's output noise is lower than the noise of the classical signal source.

[0047] Asymmetric Amplification

[0048] Starting from the symmetrical output of the paraamplifier, we will assume in the following that only the second signal, signal B, is amplified by the same type of amplifier as before (i.e., amplifier A is not present in this simulation), but with a gain of G B , noise is N B This amplification results in an asymmetric covariance matrix (still in canonical form) described by:

[0049]

number

[0050] To test for entanglement, we compute the symplectic eigenvalues ​​v of the asymmetric covariance matrix as follows:

[0051]

number

[0052] where:

number

[0053]

number

[0054] and

[0055]

number

[0056] To summarize, these are as follows:

[0057]

number

[0058] According to the PPT criterion, the state is entangled when ν<1.

[0059] The key factor in this result is N B In the case of a quantum-limited amplifier with .DELTA.=1, the amplification gain G B The goal is for the system to maintain entanglement for any value of . That is, in principle, if only one output mode of a quantum two-mode squeezed state is amplified (by a quantum-limited amplifier), it can be made arbitrarily bright while still maintaining entanglement. This function is plotted in Figure 3A.

[0060] Impact of losses

[0061] We now consider the effect of asymmetric channel loss, modeled as an unbalanced beam splitter with power transmission η inserted in the signal or idler path. The transformation of the beam splitter is:

[0062]

number

[0063] where v is the vanishing operator of the additive noise of the amplifier (fourth port) imposed by the fluctuation-dissipation theorem and the conservation of the commutation relation. Now, assuming that losses are inserted in the B path, we find:

[0064]

number

[0065] where N l teeth,

number

[0066]

number

[0067] and

[0068]

number

[0069] Putting this together, we get the following for the symplectic eigenvalues:

[0070]

number

[0071] This loss as a function of temperature is plotted in Fig. 3B. First, as in the case of asymmetric gain, entanglement asymptotically vanishes only as the loss tends to infinity when T → 0. At finite temperatures, entanglement vanishes more rapidly, but we can observe that the loss at sub-Kelvin temperatures can be tolerated to a large extent.

[0072] The next question is how the amplifier gain and external losses interact. In particular, we can determine that asymmetrically amplifying the quantum signal before losses can result in a higher loss threshold. By simply connecting the two models above, we find that

[0073]

number

[0074] The definition of the operators is the same as above. By reapplying this gain and loss to the B channels we find:

[0075]

number

[0076] Using these results, it is straightforward to numerically calculate the symplectic eigenvalues ​​from equation (12), although it is cumbersome to write an explicit expression for ν. Figure 5 plots some sample results, showing ν as a function of gain and loss. For both plots, we use a fixed value of r=0.5 and a physical loss temperature of T=1K. An interesting numerical result is that N A For a quantum-limited amplifier with N = 1, the gain does not affect the value of the loss at which entanglement is lost. On the other hand, the finite excess amplifier noise (N A >1), it can be seen that amplifier gain generally makes things worse: increasing the gain moves the loss boundary towards lower loss values.

[0077] Even if entanglement is lost, realistic quantum enhancement of correlations can be obtained for an equivalent classical source under certain parameter regimes of amplifier gain and channel loss. Similarly to the above, an asymmetric amplified quantum source with loss can be expressed as P C =C C +N C =P B Considering that the quantum source has the same transmitted power as an equivalent classical source with asy >C C Considering the effects of amplification and channel loss on the quantum source, we determine that quantum enhancement exists when P B -C asy <N C Quantum enhancement is obtained when:

[0078]

number

[0079] In Figure 4, the squeezing parameter r and the amplifier noise N A , and loss noise N l The LHS of Equation 23 is plotted as a function of the amplifier gain G and the channel transmittance η for various parameter values ​​consisting of the classical noise number N C The graph shows the increase in r, which represents the upper limit for which quantum enhancement can be obtained. First, it can be seen that quantum enhancement is obtained for a wide range of parameter values. Second, it can be seen that the loss temperature has little effect on the reduction of enhancement. It can also be estimated that the effect of loss temperature becomes important when the loss noise is comparable to the classical noise temperature (not shown). Third, the enhancement is significantly affected by amplifier noise. Finally, it can be seen that decreasing the quantum squeezing parameter r improves the overall enhancement relative to the classical case.

[0080] That is, a classical quantum source has a noise floor N C Therefore, the quantum source can act as a correlation signal source for signals with powers well below the noise floor.

[0081] Generalized two-sided amplification model

[0082] Here, we consider the limitations of operating two amplifiers in a two-mode squeezed state by generalizing the model, as shown in Figure 6. By adding amplifier 118 with noise in signal A 114, we extend the model as follows:

[0083]

number

[0084] However, the notation has been slightly changed to make it easier to understand. A(B) and N A(B) represents the amplifier gain and the additive noise on signal A(B). For easier discussion, the loss and additive noise on channel A are not considered.

[0085] Since additive noise is detrimental to correlation, the effect of the second amplifier (on signal A) is to reduce the maximum gain of signal B before entanglement is broken. To show this more simply, first consider the case of N A =N B Consider the ideal case of a quantum-limited amplifier with ν = 1. Starting from the PPT criterion that entanglement exists when ν<1, equation (12) gives the following inequality for the two-sided amplification required to maintain the entangled state:

[0086]

number

[0087] However, G A and G B If you reverse it, G A The maximum gain of G B The result of this equation is plotted in Figure 8, and can be seen to be a very sharp function of amplifier gain. Also, when the amplification is single-sided, there is no limit to the amplification (i.e., G B → In case of 1, G A →∞ and vice versa), in symmetric amplification, the maximum gain is actually G A =G B =2.

[0088] where P A =C c +N cA KatsP B =C c +N cB On the other hand, C asy >C cWe require that the quantum and classical powers are equal in the state . This means that the following inequalities must simultaneously hold:

[0089] P A -C asy <N cA and P B -C asy <N cB (26)

[0090] That is, depending on the amount of classical noise on both channels, there exists at least one combination of amplifier gain and noise on both channels for which, for a given value of the squeezing parameter r, both inequalities hold simultaneously. In Figure 8, we show the amplification regime {G A ,G B As can be seen, the amplification region can be quite large, giving a lot of freedom for optimization.

[0091] Therefore, by increasing the transmit power through amplification, it is possible to compensate for channel loss and noise, i.e. to achieve the minimum signal-to-noise ratio at the receiver required for the application.

[0092] In applications using correlated signals, a balance between transmit power and amount of correlation can be achieved, with the optimal parameters depending on the application requirements, environment, and technical constraints.

[0093] Here, the amplification gain is a minimum G>1, and is typically found to be in the range of G≈20-40 dB for JPAs operating at or near the quantum limit. The ideal or maximum gain value depends on, but is not limited to, the amplification scheme (single-sided or double-sided), amplifier noise, quantum source power, channel loss, and additive noise. The gain should be set according to the application specifications and the minimum quantum requirements corresponding to entanglement preservation or quantum enhancement.

[0094] Quantum microwave devices such as JPAs typically operate at center frequencies in the GHz range (typically the 2-12 GHz frequency band). Depending on the device configuration and materials, the operating frequency can extend into the hundreds of GHz range. Also, depending on the implementation, the amplification bandwidth can be narrow (<1 MHz) or wide (>1 GHz).

[0095] The amplification stage can consist of a single amplifier, or it can consist of many amplifiers arranged in a chain. In the latter case, it is best to minimize the amount of additive noise in the first amplifier in the chain, as this sets the effective noise characteristic of the chain.

[0096] Purpose

[0097] In a variety of applications, asymmetric amplification of signals with quantum correlations may be desirable. In particular, in two exemplary applications presented below, the use of entangled states of microwave signals, particularly in the form of quantum two-mode squeezed states, may be beneficial despite signal loss and the presence of additive noise. As mentioned above, given that QTMS sources may have low power, entanglement-preserving (or minimum correlation-preserving) amplification may be desirable to offset channel loss and improve performance, efficiency, practical range, etc.

[0098] One possible application is secure communication between two users in a covert manner, i.e., the transmitted message has a low probability of being detected, intercepted, and therefore decoded. An example is shown in FIG. 9. In the embodiment presented in FIG. 9, 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 public networks while maintaining signal A 214. The second operator encodes a message on the received signal via encoder 252 and relays this encoded signal back to the first operator. The first operator then performs a suitable type of correlation measurement between encoded signal B and signal A to extract the encoded message.

[0099] This application can have various implementations. QTMS saturates the secret key rate capacity over lossy and noisy communication channels due to entanglement and quantum correlation. Using QTMS amplification can compensate for channel losses and thus improve communication performance over a given distance. Conversely, for the same communication performance, it can be possible to increase the distance between users.

[0100] Another possible application is remote sensing. As shown in FIG. 10, while signal A 314 is maintained in the system, amplified signal B 316 can be transmitted toward a distant object (target 324). The object affects the incident signal by changing one or more of its characteristics (amplitude, frequency, and / or phase). The transformed and reflected signal is then referred to as an echo. At least a portion of the echo returns to the receiving antenna 326. The collected echo and signal A are then processed in a receiver to extract information about the object. Analysis of the echo can extract multiple pieces of information about the object, including, but not limited to, presence / absence, distance, measure, size, shape, or composition. The type and architecture of the receiver will vary depending on the object information to be obtained, but at least a correlation-type measurement between the echo and signal A is performed. To improve the accuracy of the system, multiple repeated measurements may be performed consecutively and averaged.

[0101] It should be noted that the system can use one antenna (monostatic), two antennas (bistatic as shown), or many antennas (multistatic) to perform the measurements.

[0102] This general framework represents radar-type measurements that can be used for non-destructive testing and evaluation of materials (NDT-E), target detection and ranging (radar), or radar imaging, to name a few.

[0103] Other potential applications may include sensing applications such as non-destructive testing, imaging, radar, etc.; data exchange, voice exchange, communications over short distances, long distances, via networks, via antennas, via wires, etc.; and quantum computing, such as improving the performance and performing qubit readout using the present technology.

[0104] For example, in communications applications, a quantum system may comprise a device that allows the transmission of information as a signal by modulation of a quantum source. This modulation can be, for example, in amplitude, frequency, and / or phase. In some embodiments, a coding layer may be applied on top of the basic information in the signal, although this may not be necessary depending on the application.

[0105] Correlation Receiver

[0106] Various types of receivers can be used to perform correlation measurements of the type relevant to a given application. In many applications, the receiver's objective can be to search for correlation. More specifically, a first signal can be compared to a second signal, and peaks of similarity between the signals can indicate whether a correlation exists. Several examples of these are presented below for the purpose of detailed description of potential embodiments. For example, in some examples, the comparison can be performed digitally on a computer by calculating the cross-correlation between the quadrature voltage of signal A measured at time tA and the quadrature voltage of signal B at time tB. The computer can calculate the cross-correlation over a wide range of time delays, τ = tA - tB, and the amplitude of this cross-correlation is stored in memory as a function of the delay time. This process is known as matched filtering. Prior to calculating the cross-correlation, phase translation / compensation of the Mode B measurement record can be performed digitally. The measurement process can be repeated a predetermined number of times under the same conditions, and the results are then averaged over these repeated measurements. Successful detection of a return signal occurs when the cross-correlation amplitude reaches a certain user-configurable threshold. In such an example, signal B may be digitized directly at the output of the QTMS, while signal A may be digitized, for example, after reception by a receive antenna or after interaction with a target.

[0107] In the first example shown in FIG. 11A, a digital matched filter receiver 428 is used. This type of receiver 428 may be referred to as a heterodyne receiver. In one embodiment, the receiver 428 has two separate and independent digitizers 460, 462, each measuring two quadrature phases of the mode voltage and storing the digital measurement records in memory. Ideally, Mode B is digitized directly at the output of the QTMS source, while Mode A is digitized after reception by the receive antenna. Correlation can be performed digitally on a computer 464 by calculating the cross-correlation between the quadrature voltage of Mode A measured at time tA and the quadrature voltage of Mode B at time tB. The computer 464 calculates the cross-correlation over a wide range of time delays, τ=tA-tB, and the amplitude of this cross-correlation is stored in memory as a function of the delay time. This process may be referred to as matched filtering. Prior to calculating the cross-correlation, phase translation / compensation of the Mode B measurement record may be performed digitally. The measurement process can be repeated a predetermined number of times under the same conditions, and the results of these repeated measurements are then averaged. Successful detection of the return signal occurs when the amplitude of the cross-correlation reaches a certain user-configurable threshold.

[0108] Such a receiver may be easily implemented and may allow digital control of signal phase and time delay without the need for imperfect and lossy components.

[0109] In a second example, shown in FIG. 11B, 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 may rely on the recombination of Modes A and B on a second parametric amplifier at exactly the same time, producing an essentially interferometric measurement. The second parametric amplifier effectively mixes Modes A and B together through a correlation product. The second parametric amplifier also generates two separate noise signals at the two outputs. The variance of each output mode corresponds to the amplitude of the cross-correlation of Modes A and B. The variance of the mode can be measured using a digitizer that measures a single voltage quadrature.

[0110] The second parametric amplifier 570 can ideally be frequency and bandwidth matched to the parametric amplifier used as the QTMS source. The second parametric amplifier 570 can use the pump signal to perform a nonlinear mixing process. The phase of the pump signal relative to the phase of the Mode A signal sets the amplitude of the cross-correlation and therefore dispersion of the output signals. Mode B can travel to the receiver through a delay line 572, the length of which can be selected so that Mode B arrives at the receiver at the same time as Mode A. Delay line losses, phase mismatch, and, potentially more importantly, time delay mismatch can significantly degrade the performance and practicality of such analog matched filter receivers.

[0111] In a third example, shown in FIG. 11C, a sum frequency generation (SFG) receiver 628 can be used. This type of receiver 628 can operate similarly to PA receiver 528. It can recombine Mode A with delayed Mode B on a nonlinear quantum device 680 that performs a sum frequency generation (SFG) process. That is, SFG 680 is the opposite process that occurs in a QTMS source. In SFG 680, spontaneous recombination of photons arriving at the quantum device from A and B simultaneously generates Mode C photons at the output. The frequency of Mode C corresponds to the sum of the frequencies of Modes A and B. That is, f C =f A +f BAt the output, the signal in Mode C corresponds to a coherent state whose amplitude and phase are determined by the amplitudes and relative phases of Modes A and B at the input.

[0112] The SFG process may be somewhat random and relatively inefficient. Furthermore, the SFG process is not selective and does not directly rely on the correlation between modes A and B, but rather on the probability of A and B photons arriving simultaneously. Therefore, random events, such as those occurring under non-ideal conditions (external signal sources from other devices) and thermal noise, can still be detected. To compensate, an SFG receiver may have multiple SFG units in series, incorporating a measurement-feedforward loop to filter out these spurious events. Thus, SFG receivers are considered more complex and difficult to implement, and non-idealities can strongly hinder overall performance.

[0113] It should be noted that the embodiment shown in Figure 11A is digital, i.e., the signals are digitized and the comparison is performed at the receiver based on a digital representation of the signal typically stored in computer-readable memory (which may be temporary or non-temporary). In contrast, the embodiments shown in Figures 11B and 11C are more analog in nature and utilize interference phenomena, which may require hardware adaptation in some embodiments to ensure that the signals arrive at the receiver simultaneously. In contrast, in non-temporary memory variants of Figure 11A, the signals may arrive with a delay.

[0114] As will be understood, the examples described above and shown in the drawings are intended to be illustrative only. As noted above, various modifications and adaptations to the embodiments shown and shown are possible. Furthermore, terms should not be construed as limiting when broader interpretations consistent with the knowledge of those skilled in the art are possible. For example, while the term "receiver" is used herein to refer to equipment used to receive the first and second signals, this term is not intended to imply that the same hardware receives both signals. In fact, separate hardware can be used to digitize each of the two signals, and a computer can be used to perform calculations on the digitized signals and evaluate whether there is a correlation. Similarly, the term "computer" is not intended to be limiting, but rather encompasses any device, e.g., having a processor and memory accessible to the processor, where instructions for performing functions and other data are stored in the memory, and where the processor can access the instructions to perform functions on other data. In practice, a desktop computer, a laptop computer, or a smartphone, to name a few, may be used as a "computer." Furthermore, various types of emitters can be used to transmit signals as needed. In some embodiments, the emitter may be located inside the cryogenic refrigerator, while in other embodiments the emitter may be located outside the cryogenic refrigerator. The emitter and receiver may each have a corresponding antenna in some embodiments, or may share the same antenna in other embodiments. In some alternatives, the target may be a sample located inside the cryogenic refrigerator rather than outside, and the quantum system may be used to characterize the sample at cryogenic temperatures. The scope is indicated by the appended claims.

Claims

1. 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 range of 4 to 300 GHz, the first signal having a quantum correlation with the second signal, 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 an emitter operable to transmit the first signal to a target; a receiver operable to receive the first signal after an interaction between the first signal and the target, the receiver being subject to the quantum correlation between the first signal and the second signal; a second transmission line coupled between the second port and the receiver; a first amplifier coupled between the first port and the emitter, the first amplifier operable to induce a gain of at least 10 on the first signal; Equipped with the first signal is amplified at least twice as much as the second signal between the quantum signal source and the receiver; A quantum system characterized by:

2. 10. The quantum system of claim 1, a cryogenic refrigerator surrounding the quantum signal source and operable to maintain a temperature between 50K and 5mK; A quantum system characterized by:

3. 3. The quantum system of claim 2, the target is located outside the cryogenic refrigerator; A quantum system characterized by:

4. 4. The quantum system of claim 3, The emitter is disposed outside the cryogenic refrigerator. A quantum system characterized by:

5. 10. The quantum system of claim 1, the quantum signal source is a quantum two-mode squeezed state (QTMS) source; the first signal is a first mode of the QTMS source; the second signal is a second mode of the QTMS source; the QTMS source having a first mode port operable to output the first mode and a second mode port operable to output the second mode; A quantum system characterized by:

6. 6. A quantum system according to claim 5, the QTMS source further comprises two input ports; A quantum system characterized by:

7. 6. A quantum system according to claim 5, the first amplifier is coupled to the QTMS source via a circulator; A quantum system characterized by:

8. 10. The quantum system of claim 1, the first signal and the second signal are in a frequency range of 4 to 100 GHz; A quantum system characterized by:

9. 10. The quantum system of claim 1, the first signal and the second signal are in a frequency range of 4 to 12 GHz; A quantum system characterized by:

10. 10. The quantum system of claim 1, the gain of the first amplifier is at least 100, preferably at least 1000, preferably at least 100,000; A quantum system characterized by:

11. 10. The quantum system of claim 1, the first amplifier is configured to provide an amplification of at least 20 dB, preferably at least 30 dB, preferably at least 50 dB; A quantum system characterized by:

12. 10. The quantum system of claim 1, a second amplifier coupled between the first amplifier and the emitter; A quantum system characterized by:

13. 10. The quantum system of claim 1, a second amplifier coupled between the second port and the receiver, the second amplifier having a gain that is at least half, preferably less than 1 / 10, of the gain of the first amplifier; A quantum system characterized by:

14. 10. The quantum system of claim 1, the receiver is a heterodyne digital matched filter receiver having 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 quadrature phases of voltages of corresponding signals and store digital measurement records in computer readable memory; A quantum system characterized by:

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

16. 10. The quantum system of claim 1, further comprising a computer configured to perform a digital correlation of the first signal and the second signal. A quantum system characterized by:

17. 1. A method for target confirmation, comprising: generating a first signal and a second signal in a quantum signal source, the first signal having a quantum correlation with the second signal; Propagating the second signal to a receiver; propagating the first signal through the target to the receiver, the first signal being amplified between the quantum signal source and the target by at least two times greater than any amplification of the second signal between the quantum signal source and the receiver; and the target modifying the first signal; digitizing the second signal and the modified first signal at the receiver; performing a correlation measurement between the received second signal and the received altered first signal; A method comprising:

18. 18. The method of claim 17, performing the correlation measurement includes measuring one of a cross-correlation and a cross-covariance between the received second signal and the received altered first signal; A method characterized by:

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