CN114430299A - Indication amplification method of three-degree-of-freedom coded single photon - Google Patents

Indication amplification method of three-degree-of-freedom coded single photon Download PDF

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CN114430299A
CN114430299A CN202011177879.9A CN202011177879A CN114430299A CN 114430299 A CN114430299 A CN 114430299A CN 202011177879 A CN202011177879 A CN 202011177879A CN 114430299 A CN114430299 A CN 114430299A
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周澜
徐保文
盛宇波
钟伟
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Nanjing University of Posts and Telecommunications
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Abstract

The invention provides an indication amplification method of three-degree-of-freedom coded single photons, wherein amplifier equipment is arranged on four spatial modes, and each amplifier equipment uses an imperfect single photon state generated by a single photon source under the current realization condition as an assistant. The signal photons and the auxiliary photons on each spatial mode are operated by an amplifier, and finally a new mixed state is extracted. The method can effectively improve the fidelity of single photons in an output mixed state and perfectly protect the coding information of the output mixed state on three degrees of freedom. The method can be realized under the current experimental condition by using an imperfect photon source and other linear optical devices which are commonly used under the current experimental condition, and has stronger practicability.

Description

Indication amplification method of three-degree-of-freedom coded single photon
Technical Field
The invention belongs to the technical field of quantum communication, particularly relates to an indication amplification method of a three-degree-of-freedom coded single photon, and particularly relates to an indication amplification method for a single photon coded in three degrees of freedom with polarization and double longitudinal momentums at the same time.
Background
In the field of quantum communication, the multi-freedom simultaneous coding of single photons can effectively improve the channel capacity of the single photons, thereby improving the communication efficiency of quantum communication. At present, researchers have experimented with the realization of simultaneous encoding of three degrees of freedom, namely polarization of single photons, dual longitudinal momentum and the like. The single photon with three degrees of freedom coding has important application prospect in the field of long-distance quantum communication. However, photon transmission loss is an important technical problem in long-distance quantum communication. When photons are transmitted in an actual quantum channel, the photon transmission loss causes the propagation of photons in the fiber to exhibit exponential attenuation as the channel length increases. Photon loss not only seriously affects the success rate fidelity of quantum communication, but also affects its security. Quantum instruction amplification is an effective method for solving the problem of photon transmission loss in quantum communication, which is firstly proposed by Ralph and Lund in 2009. In device independent quantum key distribution (DI-QKD), quantum-indicative amplification is widely used to protect single-photon qubits and entanglement.
The information capacity of the single photon can be effectively improved by simultaneously encoding the multiple degrees of freedom of the single photon, so that the efficiency of quantum communication can be effectively improved. At present, single photons coded in three degrees of freedom such as polarization, double longitudinal momentum and the like are successfully prepared in a laboratory, and the coded photons with the three degrees of freedom have important application prospects in the field of remote quantum communication. However, when photons are transmitted in an actual noise quantum channel, transmission loss may occur, the communication distance is greatly limited, and the security of communication is threatened, and the prior art has not yet realized indication and amplification of single photons which are simultaneously encoded on polarization and dual longitudinal momentum degrees of freedom.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide an indication amplification method of three-degree-of-freedom coded single photons. Since the single photons encoded in the polarization degrees of freedom are distributed with different probabilities to the four spatial modes, it is necessary to simultaneously prepare the amplifier devices and provide auxiliary states in the four spatial modes. Each amplifier unit consists of two Polarization Beam Splitters (PBS), two 50:50 Beam Splitters (BS), two Variable Beam Splitters (VBS) and four single-photon detectors, and can judge whether the amplification process is successful according to the response condition of the single-photon detector of each amplifier unit and calculate the success probability and the fidelity of the scheme. Under the condition that the amplification scheme is successful, the fidelity of the single photon can be effectively improved, and the coding information of the single photon on three degrees of freedom can be perfectly kept. The amplification scheme only needs some common optical elements, and the imperfect single photon state generated by the imperfect single photon source commonly used under the current experimental condition is used as an auxiliary state, so that the amplification scheme can be realized under the current experimental technology, has strong practicability and has important application prospect in the field of remote quantum communication.
The invention provides an indication amplification method of three-degree-of-freedom coded single photons, which comprises the following steps:
the method comprises the following steps: a user 1 prepares a single photon with coding information on polarization and double longitudinal momentum degrees of freedom at the same time to form a signal photon and sends the signal photon to a user 2;
step two: user 2 uses the imperfect single photon state generated by the single photon source under the current experimental conditions as an auxiliary state of each amplifier unit (amplifier);
step three: the user 2 leads the signal photons and the auxiliary state photons in each space mode into the amplifier unit, the user 2 carries out a series of operations on the signal photons and the auxiliary state photons entering the amplifier, and because the amplification probability is not one hundred percent, a plurality of output states can be generated, and different output states can lead a detector in each amplifier unit to obtain different response effects;
step four: according to calculation, the output state corresponding to the response result of the four types of detectors in each amplifier unit is obtained as a required state and needs to be reserved; the output states corresponding to the response conditions of other detectors are not required states and must be discarded; therefore, states which are needed to be reserved can be selected according to the response condition of the detector, states which do not meet the condition are abandoned, and the success probability of the scheme and the fidelity of the signal state are calculated according to the result.
Firstly, in the first step, a single photon with coded information on polarization and double longitudinal momentum degrees of freedom is prepared by using a polarization modulator (POL-M).
The further improvement lies in that: in the first step, a user 1 prepares a single photon which is coded on polarization and double longitudinal momentum freedom degrees at the same time to form a single photon four-mode space entangled state, and the form of the entangled state is as follows:
Figure BDA0002749216570000031
wherein, | H>And | V>Are defined as horizontal polarization and vertical polarization, |>，|r>，|I>And | E>Defined as left, right internal and external modes, respectively, the coefficients α, β, δ, η, ε, ν in each degree of freedom satisfying | α2+|β|2＝1，|δ|2+|η|2＝1，|ε|2+|ν|21 is ═ 1; in which single photon alpha | H with polarization characteristic>+β|V>Distributed in four spatial modes | lI with different probabilities>，|lE>，|rI>，|rE>The following steps of (1); the user 1 sends the coded single photon to the user 2 through the quantum channel, the information content is composed of the polarization and the double longitudinal momentum single photon state coding, but in reality, environmental noise in the quantum channel can cause photon transmission loss, so that the original super-entangled state is degraded into a mixed state.
The further improvement lies in that: in the second step, in order to improve the fidelity of the single photon space entangled state in the mixed state, the user 2 uses a single photon source under the current experimental condition to prepare an imperfect auxiliary state, wherein the auxiliary state is in the form of
Figure BDA0002749216570000041
Figure BDA0002749216570000042
Wherein | vac>Indicating a null state.
The further improvement lies in that: in the third step, signal photons and auxiliary photons in four spatial modes are simultaneously introduced into an amplifier, an amplification scheme is operated on the four spatial modes, each amplifier unit mainly comprises two Polarization Beam Splitters (PBS), two 50:50 Beam Splitters (BS), two Variable Beam Splitters (VBS) and four single photon detectors, each photon can reach each detector and an output port with different probabilities, and one PBS is arranged in front of the output port and can recombine polarization states separated in the process of entering into polarization state single photons with an initial form.
The further improvement lies in that: in the fourth step, according to calculation, the output states corresponding to the response conditions of the four types of detectors are required states and are reserved; the output states corresponding to the response conditions of other detectors are not required states and are abandoned; d1、D2、D3And D4Representing four detection modules in each amplifier unit, the four types of detector responses are respectively:
the first type is only D1、D3Each detecting a photon, i.e.
Figure BDA0002749216570000043
Figure BDA0002749216570000044
And
Figure BDA0002749216570000045
the second type is only D2、D4Each detecting a photon, i.e.
Figure BDA0002749216570000046
Figure BDA0002749216570000047
And
Figure BDA0002749216570000048
the third type is only D1、D4Each detecting a photon, i.e.
Figure BDA0002749216570000049
Figure BDA00027492165700000410
And
Figure BDA00027492165700000411
the fourth type is only D2、D3Each detecting a photon, i.e.
Figure BDA0002749216570000051
Figure BDA0002749216570000052
And
Figure BDA0002749216570000053
the further improvement lies in that: in the fourth step, when the amplifier units in the four spatial modes | l >, | lE >, | rI >, | rE > all obtain one of the four successful detection results, the whole amplification scheme is successful, the finally retained output state perfectly retains the encoded information of the input signal state in three degrees of freedom, and the user 2 can improve the fidelity of single photons in the output state by adjusting the transmittance of VBS in each amplifier.
The invention has the beneficial effects that: in the scheme, amplifier equipment is arranged on four space modes such as | ll >, | lE >, | rI >, | rE > and the like, an imperfect single photon state generated by a single photon source under the current realization condition is used as assistance, and signal photons and auxiliary photons on each space mode are operated through the amplifier; if the amplification processes in the four amplifiers are successful at the same time, the overall amplification scheme is successful, and a new mixed state is output from the output port; by adjusting the transmittance of VBS in each amplifier, the user 2 can effectively improve the fidelity of single photon in an output state, reduce the photon transmission loss and perfectly keep the coded information of the single photon in three degrees of freedom such as polarization, double longitudinal momentum and the like; the amplifying equipment adopts common optical devices, and particularly adopts an imperfect single photon state generated by an imperfect single photon source under the current experimental condition as an auxiliary state instead of an ideal single photon state under the current experimental condition to realize the amplification of the target single photon under the existing experimental condition, so that the technical scheme of the invention has stronger practicability and experimental operability.
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FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a schematic diagram of the present invention for encoding single photons in three degrees of freedom including polarization, dual longitudinal momentum, etc.;
FIG. 3 is a schematic diagram of the single photon amplification scheme of the polarization, dual longitudinal momentum three degree of freedom encoding of the present invention;
fig. 4 is a schematic diagram of the structure of an amplifier device unit (amplifier) of the present invention.
Detailed Description
In order to further enhance the understanding of the present invention, the following detailed description of the present invention is provided in connection with examples, which are provided for illustration only and are not intended to limit the scope of the present invention.
This example provides a specific embodiment of a three-degree-of-freedom coded single-photon bit indication amplification method, as shown in fig. 1, in this example, it is specifically assumed that a communication party Alice, i.e., a user 1, and an information sender prepare a single photon having coded information on both polarization and dual longitudinal momentum degrees of freedom by using a photon source S and a polarization modulator (Pol-M), and a coding schematic diagram is shown in fig. 2, that is, the single photon is equivalent to a single-photon four-mode space entangled state, and the form thereof is expressed by a formula:
Figure BDA0002749216570000061
Figure BDA0002749216570000062
wherein, | H>And | V>Are defined as horizontal polarization and vertical polarization, |>，|r>，|I>And | E>Defined as left, right, inner and outer modes, respectively, and the entanglement coefficients satisfy | α2+|β|2＝1，|δ|2+|η|2＝1，|ε|2+|ν|21 is ═ 1; in which single photon alpha | H with polarization characteristic>+β|V>In four spatial modes | lI with different probability distributions>，|lE>，|rI>，|rE>In (1).
And the single-photon four-mode space entangled state is sent to a remote Bob, namely a user 2 and an information receiver by Alice through a quantum channel. In the process of photon transmission, channel noise can cause photon loss, and the probability of the loss is assumed to be 1-F, so that the original single photon entangled state is degraded into a mixed state, wherein the mixed state is expressed as:
ρin＝F|Ψin><Ψin|+(1-F)|vac><vac|，
wherein, | vac > represents a vacuum state.
The schematic diagram of this amplification scheme is shown in fig. 3. Bob's goal is to increase | Ψ in the output mixture by operating on the signal photons and the assist photons in the four amplifier units by letting the signal photons and assist photons in each spatial mode enter a pre-prepared amplifierin>Fidelity of the states. Within each amplifier cell in the protocol, the user 2 uses as an auxiliary state an imperfect single photon state generated by an imperfect single photon source under the current experimental conditions, in the form of
Figure BDA0002749216570000071
Bob then passes the received signal photons and the auxiliary photons into each amplifier cell.
The amplifier cell structure employed here is shown in fig. 4. The amplifier unit consists of two Polarization Beam Splitters (PBS), two 50:50 Beam Splitters (BS), two Variable Beam Splitters (VBS) and four single photon detectors. The PBS may transmit fully horizontally polarized light and reflect fully vertically polarized light. The BS transmits photons with 50% probability and reflects photons with 50% probability. VBS transmits photons with probability of t and reflects photons with probability of 1-t. Here D1、D2、D3And D4Is 4 photon detection modules. Let us assume that a single photon detector in the detection module can distinguish the number of incident photons, and judge whether to keep the output state according to the measurement result.
Taking the amplification of polarized photons in a spatial mode as an example, consider the case where an auxiliary single photon source produces an ideal single photon, and assume that in a1The input state in the mode is not lost with a probability of F. Bob messengerInitial photon passing through PBS1. After passing through PBS1Then, state | Ψin>Is changed into
Figure BDA0002749216570000072
Next, Bob passes the assist photon through VBSs, and the assist photon state becomes:
Figure BDA0002749216570000073
Figure BDA0002749216570000081
thus, the entire photon state is written as:
Figure BDA0002749216570000082
in the above equation, Bob selects the case where each BS has only one output containing a photon, and the other output does not, in which case the equation would collapse to
Figure BDA0002749216570000083
Bob make
Figure BDA0002749216570000084
By means of the BSs, the data is transmitted,
Figure BDA0002749216570000085
will become:
Figure BDA0002749216570000086
next, Bob enters D1、D2、D3And D4Photons in the detection module are detected. All successful probe results are classified here into four categories:
the first type:D1、D3each detecting a photon, D2、D4When no photons are detected, i.e.
Figure BDA0002749216570000087
And
Figure BDA0002749216570000088
the second type: d2、D4Each detecting a photon, D1、D3When no photons are detected, i.e.
Figure BDA0002749216570000089
And
Figure BDA00027492165700000810
in the third category: d1、D4Each detecting a photon, D2、D3When no photons are detected, i.e.
Figure BDA00027492165700000811
And
Figure BDA00027492165700000812
the fourth type: d2、D3Each detecting a photon, D1、D4When no photons are detected, i.e.
Figure BDA0002749216570000091
And
Figure BDA0002749216570000092
suppose the detection result is D1D3One photon each is detected, after which the entire state collapses into:
Figure BDA0002749216570000093
then, a9And a6Photon flux on the pathPerPBS (Per PBS)2And (4) post-outputting, wherein the final output state is as follows:
Figure BDA0002749216570000094
it can be seen that the output state has the same form as the original input state, and if the detection result is one of the other three successful detection results, the same output state as the above expression can be finally obtained by means of the phase flip operation.
From the above description, the success probability can be calculated as: p00＝t(1-t)。
On the other hand, if the spatial pattern is a1Is lost with a probability of 1-F in transmission, the only states entering the amplification system are the auxiliary states, and the total photon state is:
Figure BDA0002749216570000095
will be provided with
Figure BDA0002749216570000096
By means of the amplifier, then selecting the case where one output of each BS contains only one photon, while the other output does not, the success state selected is:
Figure BDA0002749216570000097
bob will
Figure BDA0002749216570000098
After passing through the BSs, states are obtained:
Figure BDA0002749216570000099
after probing, state
Figure BDA00027492165700000910
Will collapse into an empty state. In this case, the success probability is:
P01＝(1-t)2。
in summary, in the case that only signal photons are considered in one spatial mode and the assist state is an ideal single photon, the total work probability of the scheme is:
P1t＝FP00+(1-F)P01＝Ft(1-t)+(1-F)(1-t)2
when the scheme is successful, a new mixed state can be obtained as follows:
ρout＝F′|Ψout><Ψout|+(1-F′)|vac><vac|，
wherein the target state | Ψout>The fidelity of (a) is:
Figure BDA0002749216570000101
the resulting amplification factor was:
Figure BDA0002749216570000102
to achieve fidelity amplification, G > 1 is guaranteed. As can be seen from the calculation, the transmittance when VBS is used
Figure BDA0002749216570000103
G is more than 1, so that the amplification of the original incident state can be realized only by adjusting the coefficient t of VBS.
When single photon coding is performed in three degrees of freedom, such as polarization, dual longitudinal momentum and the like, if a photon is not lost, the photon can appear in any one of four spatial modes with a certain probability, and then Bob must simultaneously operate the amplification scheme on the four spatial modes. For example, if a single photon is at | rI>On spatial mode, then at | rI>The probability of success of operating the amplification scheme in mode is P00And in the other three spatial modes (| rE)>，|lE>，|lI>) On the upper partThe success probabilities of running the amplification schemes are all P01. Therefore, if we consider that a single photon is encoded in three degrees of freedom simultaneously, the total work probability of the resulting scheme is
Figure BDA0002749216570000104
When the scheme is successful, the obtained final output state is as follows:
Figure BDA0002749216570000105
in the same form as the original input state.
On the other hand, if an input photon is lost, then there are no photons on any of the four spatial modes, and the probability of success of the amplification protocol is
Figure BDA0002749216570000111
After detection, the output state will finally collapse into a vacuum state. Therefore, the total power probability of the entire amplification protocol is:
Figure BDA0002749216570000112
when the scheme is successful, the corresponding output states are as follows:
ρout2＝F*|Ψout2><Ψout2|+(1-F*)|vac><vac|，|Ψout2>the fidelity of (a) is:
Figure BDA0002749216570000113
the amplification factor is:
Figure BDA0002749216570000114
it follows that the amplification factor of this amplification scheme is the same for amplifying single photons encoded in three degrees of freedom simultaneously as for amplifying single photons encoded in only one degree of freedom of polarization.
Consider next the case where an auxiliary single photon source produces an imperfect auxiliary photon state. Firstly, the condition that two auxiliary single photon sources respectively generate a two-photon and a single photon is considered, and the generated auxiliary state is assumed to be
Figure BDA0002749216570000115
The probability of this occurring is
Figure BDA0002749216570000116
Then after the VBS, the auxiliary state becomes:
Figure BDA0002749216570000117
Figure BDA0002749216570000118
the incident photon is analyzed in one spatial degree of freedom, and if the input photon is not lost, the whole photon state is represented as:
Figure BDA0002749216570000119
Figure BDA0002749216570000121
after the signal photons and the auxiliary photons enter the amplifier, the condition that one output end of each BS only contains one photon and the other output end does not contain the photon is selected, and the selected state is as follows:
Figure BDA0002749216570000122
bob make
Figure BDA0002749216570000123
By means of the BSs, the data is transmitted,
Figure BDA0002749216570000124
will become:
Figure BDA0002749216570000125
Figure BDA0002749216570000126
may lead to the four successful detector response cases described above. Suppose the detection result is D1D3One photon each, after detection, the entire state collapses into:
Figure BDA0002749216570000127
then let a9And a6Photons on the path pass through the PBS2And then outputting, so as to obtain a final output state:
Figure BDA0002749216570000128
the success probability for this case is:
P10＝α2t2(1-t)+2β2t2(1-t)＝(1+β2)t2(1-t)。
if input photons are lost during transmission and one auxiliary single photon source produces a couple and the other auxiliary source produces a single photon, the total photon state becomes
Figure BDA0002749216570000131
If the successful detector response is obtained, the final states that can be selected are:
Figure BDA0002749216570000132
bob make
Figure BDA0002749216570000133
Through the BSS, the mobile station (ms),
Figure BDA0002749216570000134
will become:
Figure BDA0002749216570000135
then let aqAnd a6Photons on the path pass through the PBS2Output to obtain final output state
Figure BDA0002749216570000136
The probability of success for this case is P11＝2t(1-t)2。
From the above discussion, we consider that single photons occur in four spatial modes with different probabilities when they are encoded in three degrees of freedom, polarization, dual longitudinal momentum, etc. In the case where the auxiliary states are one single photon and the other two photon, the overall work probability of the amplification scheme is:
Figure BDA0002749216570000137
if the auxiliary photon state generated by a spontaneous parametric down-conversion (SPDC) source is
Figure BDA0002749216570000138
Then, similar to the previous derivation, the probability of success for this amplification scheme is:
Figure BDA0002749216570000141
thus, in the case of one auxiliary source producing two photons and one auxiliary source producing a single photon, the probability of success of the amplification scheme is:
Figure BDA0002749216570000142
next, we consider the case where the auxiliary photon states generated by the auxiliary photon source are both two photons, i.e., the auxiliary photon states are
Figure BDA0002749216570000143
The probability of this case is
Figure BDA0002749216570000144
Then after passing through the VBSs, the auxiliary photon state becomes:
Figure BDA0002749216570000145
Figure BDA0002749216570000146
considering first that the initial photon is not lost, the whole mixed state becomes:
Figure BDA0002749216570000147
the output states chosen based on successful detector response are:
Figure BDA0002749216570000148
bob make
Figure BDA0002749216570000151
By means of the BSs, the data is transmitted,
Figure BDA0002749216570000152
will become:
Figure BDA0002749216570000153
suppose the detection result is D1D3One photon each, after detection, the entire state collapses into:
Figure BDA0002749216570000154
then let a9And a6Photons on the path pass through the PBS2Output, the final output state will be obtained:
Figure BDA0002749216570000155
the success probability in this case is:
P20＝2t3(1-t)。
if the input photons are lost during transmission and the auxiliary single photon source generates two photons, then the entire state is only the auxiliary state:
Figure BDA0002749216570000156
when the scheme is successful, the selected states are as follows:
Figure BDA0002749216570000157
bob make
Figure BDA0002749216570000158
By means of the BSs, the data is transmitted,
Figure BDA0002749216570000159
will become:
Figure BDA00027492165700001510
then let a9And a6Photons on the path pass through the PBS2Output, the final output state will be obtained:
Figure BDA00027492165700001511
in this case, the success probability is:
P21＝4t2(1-t)2。
the auxiliary state is under the condition that both are two-photon, the total work probability is as follows:
Figure BDA0002749216570000161
in summary, if an imperfect auxiliary photon source is considered, the total work probability of a polarized single photon scheme in only one spatial mode is considered as follows:
Ptm＝P1t+P″1+P″2+P″3
when considering single photon encoding in three degrees of freedom, polarization, dual longitudinal momentum, etc., if no loss of a photon occurs (probability F), it will be in any of the four spatial modes. Bob runs the amplification scheme simultaneously on four spatial modes. If the single photon is on | rI > spatial mode, then the probability of success of the amplification on | rI > is:
Figure BDA0002749216570000162
while the success probability of amplification on other spatial modes is:
Figure BDA0002749216570000163
therefore, the total power probability of amplification of a single photon in four spatial modes is
Figure BDA0002749216570000164
On the other hand, if the input photon is lost (probability (1-F)), then there are no photons on any of the four spatial modes, and the probability of success for the entire amplification scheme is
Figure BDA0002749216570000165
Therefore, for the case of single photons encoded in 3 degrees of freedom simultaneously, the total work probability of the whole amplification protocol is:
Figure BDA0002749216570000166
the fidelity of the target output state is:
Figure BDA0002749216570000171
thus, the scale-up factor for the scheme is:
Figure BDA0002749216570000172
as can be seen by calculation, is G'*With > 1, the resulting minimum value of t is still very close to 0.5, about 0.505. In summary, by operating the amplification scheme, the communication party 2 can significantly improve the fidelity of the incident target state and perfectly retain the information of the original incident state in three degrees of freedom. The amplification scheme uses common optical devices under the current experimental conditions, so the scheme has strong practicability.

Claims (7)

1. A three-degree-of-freedom coded single photon indicating amplification method is characterized by comprising the following steps:
the method comprises the following steps: a user 1 prepares a single photon with coding information on polarization and double longitudinal momentum degrees of freedom at the same time to form a signal photon and sends the signal photon to a user 2;
step two: user 2 uses an imperfect single photon source under current experimental conditions to generate auxiliary photons as an auxiliary state for each amplifier unit;
step three: the user 2 leads the signal photons and the auxiliary state photons in each space mode into the amplifier unit, the user 2 carries out a series of operations on the signal photons and the auxiliary state photons which enter the amplifier unit, and because the amplification probability is not one hundred percent, a plurality of output states can be generated, and different output states can lead a detector in each amplifier unit to obtain different response effects;
step four: according to the response effect of the detector, selecting the state which is required to be reserved, discarding the state which does not meet the condition, and calculating the success probability of the scheme and the fidelity of the signal state.
2. The three-degree-of-freedom coded single photon indicating amplification method according to claim 1, wherein in the first step, single photons having coded information on both polarization and dual longitudinal momentum degrees of freedom are prepared in the following form:
Figure FDA0002749216560000011
wherein, | H>And | V>Are defined as horizontal polarization and vertical polarization, |>，|r>，|I>And | E>Defined as left, right, inner and outer modes, respectively, the coefficients α, β, δ, η, ε, v in each degree of freedom satisfying | α2+|β|2＝1，|δ|2+|η|2＝1，|ε|2+|v|21 is ═ 1; the above formula is equivalent to a single-photon four-mode space entangled state in which the single-photon α | H with polarization characteristic>+β|V>Distributed in four spatial modes | lI with different probabilities>，|lE>，|rI>，|rE>The following steps.
3. The three-degree-of-freedom coded single photon indication amplification method according to claim 1, wherein a user 1 sends the single photon to a user 2 through a quantum channel; photon transmission loss may occur due to the presence of channel noise, and the single photon state degrades into a mixed state.
4. The three-degree-of-freedom coded single photon indication amplification method according to claim 1, wherein in the second step, the user 2 prepares an imperfect auxiliary state by using a single photon source under the current experimental conditions.
5. The three-degree-of-freedom coded single photon indicating and amplifying method according to claim 1, wherein the amplifier unit is arranged in four spatial modes of | lI >, | lE >, | rI >, | rE > in the step three, the signal photons and the auxiliary photons in each spatial mode are simultaneously introduced into the amplifier unit, and the amplification scheme is simultaneously operated in the four spatial modes; the main components of each amplifier unit are two Polarization Beam Splitters (PBS), two 50:50 Beam Splitters (BS), two Variable Beam Splitters (VBS) and four single photon detectors, each photon arriving at a different probability at each detector and at the output port, which is preceded by a PBS capable of recombining the polarization states separated on entry into a polarized single photon state having the original form.
6. The three-degree-of-freedom coded single photon indication amplification method according to claim 5, wherein in the fourth step, the output states corresponding to the response conditions of the four types of detectors in each amplifier unit are obtained according to calculation and are required states, and are reserved; and the output states corresponding to the response conditions of other detectors are not required states and are discarded.
7. The three-degree-of-freedom coded single photon indication amplification method according to claim 6, wherein in the fourth step, when the amplifier units in the four spatial modes | lI >, | lE >, | rI >, | rE > all obtain one of the four successful detection results, the whole indication amplification scheme is successful, the finally retained output state perfectly retains the coding information of the input signal state in three degrees of freedom, and the user 2 can improve the fidelity of single photon in the output state by adjusting the transmittance of VBS in each amplifier.
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