Linear optical qubit amplifier under time mode coding

Abstract

The invention provides a linear optical quantum amplifier based on coding in time modes, which comprises a first photon detector and a second photon detector in two time modes, and an input end beam splitter, a first beam splitter, a second beam splitter and an output end beam splitter, the first photon detector is used for detecting photons appearing in a first time window of the upper path, and the second photon detector is used for detecting photons appearing in a second time window of the lower path; the input end beam splitter and the output end beam splitter completely transmit photons emitted in a first time window and completely reflect photons emitted in a second time window at the same time, the first beam splitter completely reflects the photons emitted in the first time window and reflects the photons emitted in the second time window with the reflectivity of gamma, and the second beam splitter completely reflects the photons emitted in the second time window with the reflectivity of gamma. And the first beam splitter completely reflects the incident photons in the first time window and transmits the incident photons in the second time window by a transmission coefficient of 1-gamma, the second beam splitter completely reflects the incident photons in the second time window and reflects the incident photons in the first window by a reflectivity of gamma, and the first beam splitter transmits the incident photons in the first time window by a transmission coefficient of 1-gamma. The method is more concise, easy to operate and better in amplification effect, and a large number of sub-state amplification protocols are achieved.

Description

Technical Field

[0001] The present invention belongs to the field of quantum amplification and relates to a linear optical quantum amplifier based on encoding in a time mode. Background Art

[0002] Quantum amplification is a crucial concept in quantum information science and technology. It refers to the process of enhancing weak quantum signals or quantum effects while preserving their quantum properties as closely as possible. Unlike classical amplification, quantum amplification must take into account fundamental principles of quantum mechanics, such as the uncertainty principle and the non-cloning of quantum states.

[0003] Quantum amplification requires design for quantum signals with different encoding modes. In quantum technology, quantum information is often encoded in optical modes, where various degrees of freedom (DOFs) of the light field can be used for encoding, such as the number of photons (single-photon sources, squeezed-state light fields); polarization (horizontal / vertical polarization, diagonal / anti-angle polarization, circular polarization, etc.); frequency (photons of different frequencies represent different quantum states); time-bin (light pulses occurring in different time windows represent different quantum states); spatial mode (Gaussian mode, Laguerre-Gaussian mode); and phase (phase information of the light field). Optical parametric amplifiers (OPAs), the primary optical quantum amplifier, can amplify quantum signals in various optical modes.

[0004] Temporal-mode qubit encoding utilizes the temporal degree of freedom of light pulses to encode quantum information. Unlike traditional polarization, path, or frequency encoding, temporal-mode encoding exploits the temporal properties of light pulses—for example, their occurrence in distinct time windows (time-bins) or their specific temporal waveforms (temporal modes)—to represent the |0> and |1> states of a qubit, as well as their superpositions. Its fundamental principle is to use the temporal degree of freedom of the light field as a carrier of quantum information. The classical temporal waveform of the light field can be quantized to form different temporal patterns or temporal wave packets. These temporal patterns can form a complete orthogonal basis set, similar to Gaussian and Laguerre-Gaussian modes in spatial patterns.

[0005] Existing quantum amplification schemes have involved quantum amplification schemes based on encoding in polarization mode, which have achieved good output results in terms of amplification gain. However, under polarization encoding, calculations are cumbersome, and the polarization detection module for the quantum state is relatively complex, resulting in the need for classified discussion of the amplification gain after quantum collapse. Therefore, the present invention proposes a scheme that replaces polarization encoding with time encoding to solve the above problems. Summary of the Invention

[0006] The purpose of the present invention is to provide a linear optical quantum amplifier based on encoding in a time mode in order to address the problems and deficiencies in the prior art.

[0007] The technical solutions for achieving the purpose of the present invention are:

[0008] A linear optical quantum amplifier based on encoding in a time mode includes a first photon detector and a second photon detector in two time modes, as well as an input beam splitter, a first beam splitter, a second beam splitter, and an output beam splitter. The first photon detector is used to detect photons appearing in a first time window t1 of an upper path, and the second photon detector is used to detect photons appearing in a second time window t2 of a lower path. The input beam splitter and the output beam splitter completely transmit photons incident in the first time window and completely reflect photons incident in the second time window. The first beam splitter completely reflects photons incident in the first time window and reflects photons incident in the second time window with a reflectivity of γ, while transmitting photons incident in the second time window with a transmission coefficient of 1-γ. The second beam splitter completely reflects photons incident in the second time window and reflects photons incident in the first window with a reflectivity of γ, while transmitting photons incident in the first time window with a transmission coefficient of 1-γ. When the first detector detects a photon in the first time window and the second detector detects a photon in the second time window, the protocol amplification operation is successful.

[0009] Furthermore, the first photon detector, the second photon detector, the input end beam splitter, the first beam splitter, the second beam splitter and the output end beam splitter are connected through optical fibers.

[0010] Furthermore, the input end beam splitter is connected to the first beam splitter and the second beam splitter respectively, and the first beam splitter, the second beam splitter and the output end beam splitter are connected; the first photon detector is connected to the first beam splitter, and the second photon detector is connected to the second beam splitter.

[0011] Furthermore, the conversion mode of the first beam splitter is specifically:

[0012]

[0013] in, represents the generation operator of the input signal photons in the first time window, represents the photon generation operator of the output signal in the first time window, represents the photon generation operator of the photon detected by the first photon detector in the first time window, represents the photon generation operator of the photon passing through the upper path a1 in the first time window, represents the photon generation operator of the photon passing through the upper path a1 in the second time window, The photon generation operator representing the photon detected by the first photon detector at the second time channel.

[0014] Furthermore, the conversion mode of the second beam splitter is specifically:

[0015]

[0016] in, represents the generation operator of the input signal photons in the second time window, represents the photon generation operator of the output signal in the second time window, represents the photon generation operator for the photons detected by the second photon detector in the second time window, represents the photon generation operator of the photon passing through the upper path a1 in the second time window, The photon generation operator representing the photon detected by the second photon detector at the first time channel.

[0017] Furthermore, the photons are encoded in the form of 0 and 1 codes, where |0> indicates that the photon detector has not detected the photon, and |1> indicates that the photon detector has detected the photon.

[0018] Furthermore, the total initial input state of the amplifier |Ψ N >For:

[0019]

[0020] Among them, α, β t1 , β t2 are the coefficients of the initial input signal, X and Y represent the encoding of the photon bit in the auxiliary photon pair, which is to distinguish it from the polarization encoding H and V; the superscripts 1 and 2 represent the upper and lower paths, |T1> is the photon generated in the first time window defined in the initial input signal, and |T2> is the photon generated in the second time window defined in the initial input signal.

[0021] Furthermore, the encoding conditions for successful protocol amplification include:

[0022]

[0023] in, Indicates that a photon is detected on the upper path in the first time window. Indicates that a photon is detected in the lower path in the second time window. Indicates that no photons are detected on the upper path in the first time window, It indicates that no photon is detected in the upper path in the second time window, and 1, 1′, 0, 0′ are the four photon positions used to distinguish the two-photon pair X and Y.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] (1) The present invention adopts time mode coding. First, the coding mode is simpler. Photons are encoded in the form of 0 and 1 codes, where 0 indicates that a photon is detected and 1 indicates that a photon is detected. Secondly, compared with polarization coding, the evolution process of the quantum state is simpler, eliminating the tedious classification discussion. Finally, the amplification gain result is significantly improved compared with polarization coding.

[0026] (2) The linear optical amplifier based on time pattern coding of the present invention constructs a simpler, easier to operate and more effective quantum state amplification protocol, which can be used for linear optical qubit amplification. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 Schematic diagram of the structure of the amplifier of the present invention.

[0028] Figure 2 A graph showing the amplification gain. DETAILED DESCRIPTION

[0029] Combine Figure 1 A linear optical quantum amplifier based on encoding in a time mode comprises a first photon detector U1 and a second photon detector U2 in two time modes, as well as an input beam splitter BSin, a first beam splitter BS1, a second beam splitter BS2, and an output beam splitter BSout. The first photon detector U1 detects photons on the upper path appearing in the first time window t1, while the second photon detector U2 detects photons on the lower path appearing in the second time window t2. After the initial state is input from the input port, the input beam splitter BSin and the output beam splitter BSout completely transmit photons incident in the first time window and completely reflect photons incident in the second time window. The first beam splitter BS1 completely reflects photons entering the first time window and reflects photons entering the second time window with a reflectivity of γ, while transmitting photons entering the second time window with a transmission coefficient of 1-γ. The second beam splitter BS2 completely reflects photons entering the second time window and reflects photons entering the first time window with a reflectivity of γ, while transmitting photons entering the first time window with a transmission coefficient of 1-γ. The optical components are connected by optical fibers. When the first photon detector U1 detects a photon in the first time window and the second photon detector U2 detects a photon in the second time window, the protocol amplification operation is successful.

[0030] The first beam splitter BS1 completely reflects the photons incident in the first time window, reflects the photons incident in the second time window with a reflectivity of γ, and transmits the photons incident in the second time window with a transmission coefficient of 1-γ. This conversion can be expressed as follows:

[0031]

[0032] The second beam splitter BS2 completely reflects the photons incident in the second time window, reflects the photons incident in the first window with a reflectivity of γ, and transmits the photons incident in the first time window with a transmission coefficient of 1-γ. This conversion mode can be expressed as follows:

[0033]

[0034] When the detector T1 detects a photon in the first time window and the detector T2 detects a photon in the second time window, the protocol is amplified and runs successfully. For the auxiliary two-photon state, this application still uses the maximum entangled Bell state.

[0035]

[0036] However, polarization encoding is not used, and the auxiliary photon state is written as follows:

[0037]

[0038] The initial total state consists of the input signal and the auxiliary photon, which is expressed as:

[0039]

[0040] Through post-selection, according to the effect of the beam splitter on the photons, we can get:

[0041]

[0042] After the above series of transformations, the total initial input state |Ψ N >Written as:

[0043]

[0044] Next, when detecting photons, we use 0, 1 encoding, which is relatively concise:

[0045] |0>→ means the photon detector did not detect any photons

[0046] |1>→ indicates that the photon detector detects a photon

[0047] Then, the auxiliary photon state is encoded in the above way, and the four photon positions of the auxiliary photon state will have the following 16 situations:

[0048]

[0049] The corresponding output state |Ψ N The form of > may eventually have the following 16 situations:

[0050]

[0051]

[0052] This application selects the situation where the first photon detector U1 detects photons in the first time window t1, and the second photon detector U2 detects photons in the second time window t2. Since the photon detector can only detect the presence or absence of photons in a time window, but cannot identify the number of photons, the following situations all indicate that the amplification operation is successful:

[0053]

[0054] In the above case, |Ψ N >will collapse to:

[0055]

[0056] In the above formula, the parameters α and β are the coefficients of the initial input signal. α represents the coefficient of the vacuum state in the initial input signal that interacts with the auxiliary photon pair, and β represents the coefficient of the non-vacuum state in the initial signal. Both α and β can be set in advance as long as they meet the normalization conditions. The parameter γ represents the reflectivity of the beam splitter, which is determined by the beam splitter itself. This application defines the amplification gain G as the square of the ratio of the signal to the vacuum probability:

[0057]

[0058] Results of working with polar coding:

[0059]

[0060] By comparing the G of the present invention with other coding methods, it can be shown that the linear optical quantum amplifier implemented by the time pattern coding adopted in this work has a significant improvement in amplification efficiency.

[0061] Figure 2 is a curve diagram of the amplification gain of the amplifier of the present invention, through Figure 2 It can be seen that when α 2=0.3, when γ is less than 0.42 or greater than 0.78, G is greater than 1, indicating that the system is successfully amplified. Similarly, when α 2 = 0.5, to make G greater than 1, then γ should be less than 0.38 or greater than 0.85. 2 =0.9, in order to make G greater than 1, γ should be less than 0.34 or greater than 0.97. Therefore, in practical applications, the appropriate parameter value should be selected according to the actual situation.

[0062] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.

Claims

1. A linear optical quantum amplifier based on temporal mode encoding, characterized in that: The invention comprises a first photon detector (U1) and a second photon detector (U2) in two time modes, as well as an input end beam splitter (BSin), a first beam splitter (BS1), a second beam splitter (BS2) and an output end beam splitter (BSout), wherein the first photon detector (U1) is used to detect photons appearing in a first time window t1 on an upper path, and the second photon detector (U2) is used to detect photons appearing in a second time window t2 on a lower path; the input end beam splitter (BSin) and the output end beam splitter (BSout) completely transmit photons incident in the first time window and completely reflect photons incident in the second time window. The first beam splitter (BS1) completely reflects the photons incident in the first time window, and reflects the photons incident in the second time window with a reflectivity of γ, while transmitting the photons incident in the second time window with a transmission coefficient of 1-γ. The second beam splitter (BS2) completely reflects the photons incident in the second time window, and reflects the photons incident in the first window with a reflectivity of γ, while transmitting the photons incident in the first time window with a transmission coefficient of 1-γ. When the first photon detector (U1) detects a photon in the first time window and the second photon detector (U2) detects a photon in the second time window, the protocol amplification operation is successful.

2. A linear optical quantum amplifier based on encoding in a time mode according to claim 1, characterized in that: The first photon detector (U1), the second photon detector (U2), the input end beam splitter (BSin), the first beam splitter (BS1), the second beam splitter (BS2) and the output end beam splitter (BSout) are connected via optical fibers.

3. A linear optical quantum amplifier based on encoding in a time mode according to claim 1, characterized in that: The input end beam splitter (BSin) is connected to the first beam splitter (BS1) and the second beam splitter (BS2) respectively, and the first beam splitter (BS1), the second beam splitter (BS2) and the output end beam splitter (BSout) are connected; the first photon detector is connected to the first beam splitter (BS1), and the second photon detector (U2) is connected to the second beam splitter (BS2).

4. The linear optical quantum amplifier based on encoding in time mode according to claim 1, characterized in that: The conversion mode of the first beam splitter (BS1) is specifically: in, represents the generation operator of the input signal photons in the first time window, represents the photon generation operator of the output signal in the first time window, represents the photon generation operator of the photons detected by the first photon detector (U1) in the first time window, represents the photon generation operator of the photon passing through the upper path a1 in the first time window, represents the photon generation operator of the photon passing through the upper path a1 in the second time window, The photon generation operator represents the photon detected by the first photon detector (U1) at the second time channel.

5. The linear optical quantum amplifier based on encoding in time mode according to claim 1, characterized in that: The conversion mode of the second beam splitter (BS2) is specifically: in, represents the generation operator of the input signal photons in the second time window, represents the photon generation operator of the output signal in the second time window, represents the photon generation operator for the photons detected by the second photon detector (U2) in the second time window, represents the photon generation operator of the photon passing through the upper path a1 in the second time window, The photon generation operator represents the photon detected by the second photon detector (U2) at the first time channel.

6. The linear optical quantum amplifier based on encoding in time mode according to claim 1, characterized in that: Photons are encoded in the form of 0 and 1, where |0> means that the photon detector has not detected a photon, and |1> means that the photon detector has detected a photon.

7. The linear optical quantum amplifier based on encoding in time mode according to claim 1, characterized in that: The total initial input state of the amplifier |Ψ N >For: Among them, α, β t1 , β t2 are the coefficients of the initial input signal, X and Y represent the encoding of the photon bit in the auxiliary photon pair, which is to distinguish it from the polarization encoding H and V; the superscripts 1 and 2 represent the upper and lower paths, |T1> is the photon generated in the first time window defined in the initial input signal, and |T2> is the photon generated in the second time window defined in the initial input signal.

8. The linear optical quantum amplifier based on encoding in time mode according to claim 6, characterized in that: The encoding conditions for successful protocol amplification include: in, Indicates that a photon is detected on the upper path in the first time window. Indicates that a photon is detected in the lower path in the second time window. Indicates that no photons are detected on the upper path in the first time window, It indicates that no photon is detected in the upper path in the second time window, and 1, 1′, 0, 0′ are the four photon positions used to distinguish the two-photon pair X and Y.

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