CN111181633B - Time-polarization super-entangled state entanglement auxiliary noiseless linear amplification method - Google Patents

Time-polarization super-entangled state entanglement auxiliary noiseless linear amplification method Download PDF

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CN111181633B
CN111181633B CN202010074990.9A CN202010074990A CN111181633B CN 111181633 B CN111181633 B CN 111181633B CN 202010074990 A CN202010074990 A CN 202010074990A CN 111181633 B CN111181633 B CN 111181633B
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周澜
李宇鹏
盛宇波
钟伟
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Nanjing University of Posts and Telecommunications
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Abstract

The invention provides an entanglement-assisted noiseless linear amplification method of a time-polarization super-entangled state, which comprises the following steps: user 2 prepares a pair of time-polarized two-photon super-entangled states containing information data and sends one photon in the super-entangled state to user 1; a user 1 prepares a pair of maximum entangled polarization entangled states, and adds time entanglement to the pair of polarization entangled states to form a maximum entangled time-polarization super-entangled state, wherein the super-entangled state is used as an auxiliary state of an amplification system; the user 1 carries out a series of operations on the photon state and the auxiliary state of the signal 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 cause different response effects of the detector; and calculating to obtain output states corresponding to different detector response results, selecting and reserving a needed state according to the response condition of the detector, discarding a state which does not meet the condition, and calculating the success probability of the scheme and the fidelity of the signal state according to the result.

Description

Time-polarization super-entangled state entanglement auxiliary noiseless linear amplification method
Technical Field
The invention relates to the technical field of quantum communication, in particular to an entanglement-assisted noiseless linear amplification method for a time-polarization super-entangled state.
Background
The super-entangled state plays an important role in quantum communication schemes, such as quantum invisible state transfer, quantum key distribution, quantum secure direct communication and quantum secret sharing. The super-entanglement is the entanglement of a quantum system on a plurality of degrees of freedom at the same time, and has attracted wide attention in the field of quantum communication. Previous studies have demonstrated that super-entanglement can improve channel capacity. In addition, the Bell inequality of the super-entangled quantum system can effectively improve the security of quantum communication. Therefore, the super-entangled quantum system is an important resource in the field of quantum communication.
The noiseless linear 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), noise-free linear amplification is widely used to protect single-photon qubits and entanglement. In long-distance quantum communication, the distribution of quantum entanglement is a major technical problem. Environmental channel noise in actual quantum channels can cause photon transmission loss, reduce communication efficiency, and even threaten the safety of quantum communication.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide an entanglement-assisted noiseless linear amplification method of a time-polarization super-entangled state, which needs to use a pair of polarized photons in the maximum entangled state, and then adds the prepared entangled state into time entanglement through a time delay system to finally form the super-entangled assisted quantum state. The auxiliary photon state and the signal photon enter the amplifier simultaneously. The amplifier mainly comprises four Polarization Beam Splitters (PBS), two Partial Polarization Beam Splitters (PPBS) and four detectors. Finally, according to the response type of the detector, whether an output state is reserved or not can be judged, and success probability and fidelity are calculated according to the result. Only some common optical elements are needed, and the method can be realized under the current experimental technology and has strong practicability.
The invention provides an entanglement-assisted noiseless linear amplification method for a time-polarization super-entangled state, which comprises the following steps:
the method comprises the following steps: user 2 prepares a pair of time-polarized two-photon super-entangled states containing information data and sends one photon in the super-entangled state to user 1;
step two: a user 1 prepares a pair of maximum entangled polarization entangled states, and adds time entanglement to the pair of polarization entangled states to form a maximum entangled time-polarization super-entangled state, wherein the super-entangled state is used as an auxiliary state of an amplification system;
step three: the user 1 carries out a series of operations on the photon state and the auxiliary state of the signal 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 cause different response effects of the detector;
step four: according to the calculation, the output states corresponding to different detector response results are obtained, the states required to be reserved are selected according to the response condition of the detector, the states which do not meet the conditions are abandoned, and the success probability of the scheme and the fidelity of the signal states are calculated according to the results.
The further improvement lies in that: in the step oneUser 2 encodes information in a time-polarized super-entangled state, the form of which is written
Figure GDA0003391009070000022
| H > and | V > are defined as horizontal polarization and vertical polarization, | S |, respectively>And | L>Respectively defined as short path and long path in time slice entanglement, alpha, beta, delta, eta are four entanglement coefficients requiring | alpha | < u >2+|β|2＝1、|δ|2+|η|21 is ═ 1; the user 2 sends the coded information to the user 1 through the quantum channel, the information content is composed of the time-polarization super-entangled state code, but the original super-entangled state is degraded into a mixed state due to photon transmission loss caused by environmental noise in the quantum channel in reality.
The further improvement lies in that: in the second step, in order to improve the fidelity of the super-entangled state in the mixed state, the user 1 prepares a pair of maximally-entangled two-photon polarization entangled states
Figure GDA0003391009070000031
Then, the prepared entangled state is added into a time slice for entanglement through a time delay system to form a new super-entangled state form
Figure GDA0003391009070000032
The auxiliary state required for user 1, user 1 then passes the received information photons and auxiliary state photons into the amplifier.
The further improvement lies in that: after the information state and the auxiliary state in the third step enter the amplifier, the information state passes through one PBS and is respectively amplified in each amplifier unit according to polarization characteristics, each amplifier unit mainly comprises four Polarization Beam Splitters (PBS), two Partial Polarization Beam Splitters (PPBS) and four detectors, each photon can reach each detector and an output port with different probabilities, one PBS is added before the output port, and the separated states during entering are recombined into a super-entangled state with an initial form.
The further improvement lies in that: in the fourth step, according to calculation, the fourth step is obtainedThe response condition of the class detector corresponds to a required state, while the output states obtained by the response conditions of other detectors are abandoned, and in the four types of reserved response types of the detectors: the first type is when D1、D2、D3、D4When the detectors are of the same polarity, D1、D2、D3、D4When both H or V respond, i.e. | HHHV>D1D2D3D4、|VVVV>D1D2D3D4(ii) a The second type is D1、D2Response polarity being the same, D3、D4When the response polarity is reversed, i.e. | HHHV>D1D2D3D4、|HHVH>D1D2D3D4、|VVHV>D1D2D3D4、|VVVH>D1D2D3D4(ii) a The third type is D1、D2Opposite response polarity, D3、D4With the same response polarity, | HVHH>D1D2D3D4、|VHHH〉D1D2D3D4、|HVVV〉D1D2D3D4、|VHVV〉D1D2D3D4(ii) a The fourth type is D1、D2Response polarity is opposite, while D3、D4When the response polarity is also reversed, | HVHV >D1D2D3D4、|HVVH〉D1D2D3D4、|VHHV>D1D2D3D4、|VHVH>D1D2D3D4。
The further improvement lies in that: in the first step, the loss in the photon transmission process is considered, and the super-entangled state is degraded into a mixed state.
The further improvement lies in that: in the second step, the user 1 makes the received signal photons and the auxiliary state enter an amplifier to amplify the super-entangled state containing the information.
The invention has the beneficial effects that: the method can effectively improve the fidelity of the time-polarization super-entangled state, reduce the photon transmission loss and keep the characteristics of entangled photon pairs in two degrees of freedom of time and polarization. The probability of success of the amplification device employed does not gradually decrease to zero as the fidelity amplification factor increases. The amplifying equipment adopts common optical devices, can be applied under the existing experimental conditions and has stronger applicability.
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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 structure of the amplifier unit of the present invention.
Fig. 3 is a schematic diagram of a noise-free linear amplification scheme of the present invention.
Detailed Description
In order to further understand the present invention, the following detailed description will be made with reference to the following examples, which are only used for explaining the present invention and are not to be construed as limiting the scope of the present invention. As shown in fig. 1 to 3, this embodiment provides an entanglement-assisted noiseless linear amplification method for a time-polarization super-entangled state, assuming that a communication party Bob, i.e., a user 2, an information sending party prepares an arbitrary two-photon polarization-time super-entangled state from a photon source S. This arbitrary super-entangled state is written as
Figure GDA0003391009070000051
Here, | H>And | V>Defined as horizontal polarization and vertical polarization, respectively. I S>And | L>Defined as short and long paths in the temporal entanglement, respectively. Where α, β, δ, η are four entanglement coefficients, requiring | α |. Y2+|β|2＝1、|δ|2+|η|2＝1。
Bob will B1The photons of the pattern are transmitted to a distant Alice, i.e., user 1, the receiver of the information via a quantum channel. During photon transmission, channel noise can cause photon loss, and the probability of the loss is assumed to be 1-F, which causes the super-entangled state to be degraded into a mixed state which is expressed as
Figure GDA0003391009070000052
Alice aims to increase ρ by a prepared amplifierinIn
Figure GDA0003391009070000053
Fidelity of the states. In the protocol, Alice needs to prepare two pairs of maximum entangled states as an aidState of the form
Figure GDA0003391009070000054
To generate time entanglement, Alice makes b1(c1) Mode sequencing through PBS1b(PBS1c) And PBS2b(PBS2c) B is caused to be2(c2) Mode sequencing through PBS3b(PBS3c) And PBS4b(PBS4c). The long path (L) and the short path (S) need to be precisely adjusted so that the polarized photon | H>And | V>Adding time slices | S respectively>And | L>. In this way, two auxiliary states are obtained
Figure GDA0003391009070000061
Alice then passes the received information photons and assist state photons into an amplifier.
The amplifier unit used here is shown in fig. two. The amplifier unit consists of two Polarization Beam Splitters (PBS) and two Partial Polarization Beam Splitters (PPBS). The PBS may transmit fully horizontally polarized light and reflect fully vertically polarized light. Partial polarization beam splitter PPBS1Vertically polarized light may be totally reflected and horizontally polarized light may be reflected with a reflectivity of r. This conversion is written to
Figure GDA0003391009070000062
Figure GDA0003391009070000063
α+ a1,V→-α+ D1,V
Also, a partial polarization beam splitter PPBS2It is possible to reflect the horizontally polarized light completely and the vertically polarized light with a reflectivity of r. This conversion is written to
Figure GDA0003391009070000064
Figure GDA0003391009070000065
α+ a2,H→-α+ D2,H
Here D1And D2Is a standard polarization analysis block, at D1And D2And performing two-photon composite measurement on the two detection blocks, and judging whether an output state is reserved according to a measurement result.
The schematic diagram of the time-polarization super-entangled state noise-free linear amplification scheme is shown in figure three. The first case to consider is in a1The single photon in the mode is not lost with the probability of F. Alice passes the initial single photon through the PBS1. After passing through PBS1Then, state | ψin>Is changed into
Figure GDA0003391009070000071
Next, Alice makes a2、a3The photons pass through a Purchase Box (PC) to reverse the polarity of the photons, where the PCS(PCL) Time entanglement, | ψ, acting only on S (L), respectivelyin 1>Then become
Figure GDA0003391009070000072
Thus, the entire photon state is written
Figure GDA0003391009070000073
In fig. three, the detection modules in the amplifier unit 1 are defined as D, respectively1And D2The detection modules in the amplifier unit 2 are respectively defined as D3And D4. In the above formula, Alice selects D1、D2、D3And D4In the case of only one photon response, respectively, in which case the above equation would collapse into
Figure GDA0003391009070000074
Alice to D1、D2、D3And D4The output photons in the mode are measured in the Bell state, first letting each photon of the detection module enter a quarter-wave plate. The quarter-wave plate functions as follows
Figure GDA0003391009070000081
Figure GDA0003391009070000082
Where i is 1, 2, 3, 4. Through a quarter wave plate, | ψ2>Will become into
Figure GDA0003391009070000083
Next, proceed to D1、D2、D3、D4Each photon passes through a PBS and the outgoing photons from each exit port are detected with a single photon detector. All successful probe results are classified into four categories. The first type: enter D1And D2The photon polarity detection results are the same, and enter D3And D4The photon polarity detection results are also the same; the second type: enter D1And D2The photon polarity detection result is the same, but enters D3And D4The photon polarity detection results are different; in the third category: enter D1And D2Photon polarity detection result ofAt the same time, but enter D3And D4The photon polarity detection results are the same; the fourth type: enter D1And D2The photon polarity detection results are different, and enter D3And D4The photon polarity detection results are also different.
Analyze the first success, i.e. go to D1And D2The photon polarity detection results are the same, and enter D3And D4The same applies to the photon polarity detection result from | ψ3>The required state can be selected from:
Figure GDA0003391009070000091
under the above detection result, the state of the above formula will be collapsed to
Figure GDA0003391009070000092
By the same method, successful output results of the second type, the third type and the fourth type can be obtained, the four types of results are integrated together, and finally the total output result is obtained
Figure GDA0003391009070000093
Next, the pattern b3(c3) Photon of (2) through PCL(PCS) In output state | ψout 2>Will become into
Figure GDA0003391009070000101
Finally, b4And c4Photons of the mode pass through the PBS2Output, the final output result will be obtained
Figure GDA0003391009070000102
It can be seen that the output result and the received input state are identical in both degrees of freedom for polarization and time slice.
From the above description, a success probability of
Figure GDA0003391009070000103
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. The obtained state is
Figure GDA0003391009070000104
Like before, | ψ'1>By means of amplifiers, and then selecting the case where each amplifier has only one photon response, the successful state selected being
Figure GDA0003391009070000105
Alice still lets the input photons of each detection block enter a quarter-wave plate. As above, there may be four successful probing types, each similar to the previous operation. The above equation will collapse to a vacuum state, in which case the success probability is
Figure GDA0003391009070000106
The overall probability of success for both cases is
Figure GDA0003391009070000111
The fidelity of the new mixed state is
Figure GDA0003391009070000112
To obtain an amplification factor of
Figure GDA0003391009070000113
To achieve fidelity amplification, F' > F is required, i.e., g > 1. By calculation, when
Figure GDA0003391009070000114
Or
Figure GDA0003391009070000115
In time, g is more than 1, so that the amplification of the original incident state can be realized only by adjusting the coefficient r of the PPBS.
In conclusion, by operating the scheme, the guarantee degree of the incident target state can be obviously improved, the information of two degrees of freedom of the original incident state in polarization and time segments can be perfectly kept, and the success probability of the scheme cannot be reduced to zero along with the increase of the amplification factor. The whole process is divided into four steps, wherein the first two steps are preparation of states, including an initial state and an auxiliary state. The third step is the amplifier amplification process, in which the PBSs and PPBSs in the amplifier play a critical role, determining the success probability and fidelity. The final step is the selection process, which picks the desired successfully amplified state by different responses of the detector. The optical device is common under the current experimental conditions, so that the scheme has strong practicability.

Claims (5)

1. A time-polarization super-entangled state entanglement auxiliary noiseless linear amplification method is characterized in that: the method comprises the following steps:
the method comprises the following steps: user 2 prepares a pair of time-polarized two-photon super-entangled states containing information data and transmits one photon in the super-entangled state to user 1, and in step one user 2 encodes information in one time-polarized super-entangled state in a form written as
Figure FDA0003391009060000011
And | V>Are defined as horizontal polarization and vertical polarization, | S>And | L>Respectively defined as short path and long path in time slice entanglement, alpha, beta, delta, eta are four entanglement coefficients requiring | alpha | < u >2+|β|2＝1、|δ|2+|η|21 is ═ 1; the user 2 sends the coded information to the user 1 through the quantum channel, the information content is composed of the time-polarization super-entangled state codes, but the original super-entangled state is degraded into a mixed state due to photon transmission loss caused by environmental noise in the quantum channel in reality;
step two: a user 1 prepares a pair of maximum entangled polarization entangled states, and adds time entanglement to the pair of polarization entangled states to form a maximum entangled time-polarization super-entangled state, wherein the super-entangled state is used as an auxiliary state of an amplification system;
step three: the user 1 carries out a series of operations on the signal photon state and the auxiliary state entering the amplifier, because the amplification probability is not one hundred percent, a plurality of output states can be generated, different output states can cause different response effects of the detector, in the step three, after the information state and the auxiliary state enter the amplifier, the information state passes through a PBS and is separately amplified in each amplifier unit according to polarization characteristics, each amplifier unit mainly comprises four Polarization Beam Splitters (PBS), two Partial Polarization Beam Splitters (PPBS) and four detectors, each photon can reach each detector and output port according to different probabilities, a PBS is added before the output port, and the separated states during entering are recombined into a super-entangled state with an initial form;
step four: according to the calculation, the output states corresponding to different detector response results are obtained, the states required to be reserved are selected according to the response condition of the detector, the states which do not meet the conditions are abandoned, and the success probability of the scheme and the fidelity of the signal states are calculated according to the results.
2. A time-polarization super-entangled state entanglement-assisted noiseless linear amplification method as claimed in claim 1, wherein: in the second step, in order to improve the fidelity of the super-entangled state in the mixed state, the user 1 prepares a pair of maximally-entangled two-photon polarization entangled states
Figure FDA0003391009060000021
Then, the prepared entangled state is added into a time slice for entanglement through a time delay system to form a new super-entangled state form
Figure FDA0003391009060000022
The auxiliary state required for user 1, user 1 then passes the received information photons and auxiliary state photons into the amplifier.
3. A time-polarization super-entangled state entanglement-assisted noiseless linear amplification method as claimed in claim 1, wherein: in the fourth step, states corresponding to the four types of detector response conditions are obtained according to calculation, output states obtained by the response conditions of other detectors are abandoned, and in the four types of remaining detector response types: the first type is when D1、D2、D3、D4When the detectors are of the same polarity, D1、D2、D3、D4When both H or V respond, i.e. | HHHV>D1D2D3D4、|VVVV>D1D2D3D4(ii) a The second type is D1、D2Response polarity being the same, D3、D4When the response polarity is reversed, i.e. | HHHV>D1D2D3D4、|HHVH>D1D2D3D4、|VVHV>D1D2D3D4、|VVVH>D1D2D3D4(ii) a The third type is D1、D2Opposite response polarity, D3、D4With the same response polarity, | HVHH>D1D2D3D4、|VHHH>D1D2D3D4、|HVVV>D1D2D3D4、|VHVV>D1D2D3D4(ii) a The fourth type isD1、D2Response polarity is opposite, while D3、D4When the response polarity is also opposite, i.e. | HVHV>D1D2D3D4、|HVVH>D1D2D3D4、|VHHV>D1D2D3D4、|VHVH>D1D2D3D4。
4. A time-polarization super-entangled state entanglement-assisted noiseless linear amplification method as claimed in claim 1, wherein: in the first step, the loss in the photon transmission process is considered, and the super-entangled state is degraded into a mixed state.
5. A time-polarization super-entangled state entanglement-assisted noiseless linear amplification method as claimed in claim 1, wherein: in the second step, the user 1 makes the received signal photons and the auxiliary state enter an amplifier to amplify the super-entangled state containing the information.
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