Continuous variable quantum relay method and system based on all-optical entanglement swapping

Abstract

The invention discloses a continuous variable quantum relay method and system based on all-optical entanglement swapping. According to the disclosed scheme, a transmitting end prepares a hyper-entangled photon pair with continuous variable entanglement association on orthogonal amplitude-phase degree of freedom and time-energy degree of freedom at the same time, keeps one group of photons, and transmits the other group of photons to a relay node; at a relay node, quantum purification is firstly implemented based on T-E degree of freedom; then, all-optical entanglement exchange is carried out on the purified photons and photons locally prepared by a relay, and transfer of the X-P degree-of-freedom continuous variable entanglement relation is achieved; reconstructing T-E degree-of-freedom entanglement for the photons after entanglement exchange through a non-degenerate spontaneous parametric down-conversion process; and the plurality of relay nodes are repeatedly executed until the Bob end receives the photon sequence. Probabilistic non-Gaussian measurement is not needed, the structure is simple, the problems that a traditional continuous variable quantum relay is low in generation rate and poor in cascading performance are solved, and the continuous variable quantum relay is suitable for a long-distance continuous variable quantum communication network.

Description

Technical Field

[0001] This invention belongs to the field of quantum communication and quantum network technology, specifically relating to a continuous variable quantum repeater method based on all-optical entanglement swapping. Background Technology

[0002] Quantum repeaters, as an important technical means to realize long-distance quantum communication and quantum networks, have received widespread attention in recent years. Existing technical literature 1 Zhang Y, Bian Y, Li Z, et al. Continuous-variable quantumkey distribution system: Past, present, and future[J]. Applied PhysicsReviews, 2024, 11(1).” From the perspective of system implementation and network evolution, it is pointed out that the field of quantum communication has long developed two parallel technical routes: discrete variable and continuous variable. The discrete variable scheme, based on discrete quantum events such as single photons, shows advantages in long-distance transmission, but its signal form, timing organization, and control logic have structural differences from existing classical optical fiber networks. The continuous variable scheme, based on coherent state modulation and coherent detection, is relatively limited in transmission distance, but has advantages in information carrying capacity and compatibility with classical coherent optical communication systems. Therefore, the two schemes complement each other for different application constraints, jointly constituting an important branch of the quantum communication technology system.

[0003] Reference 2 " Li X, Zhou R, Cai Y, et al. A continuous-variable quantumrepeater protocol enhanced with multiplexing and thermal noise: X. Li et al[J]. Quantum Information Processing, 2025, 24(8): 237. ” A quantum repeater protocol for continuous-variable quantum communication is proposed. By introducing mode multiplexing and thermal noise optimization into the error correction module based on noiseless linear amplification, the reachability and success probability of continuous-variable quantum key distribution in multi-segment links are improved. However, this type of scheme still relies on probabilistic operations and multi-stage cascaded structures. Its overall generation rate is limited by the amplification success probability, multiplexing resources, and the number of cascaded nodes. Further optimization is still possible in large-scale network deployments and high-throughput applications. Summary of the Invention

[0004] To address the shortcomings or deficiencies of existing technologies, this invention provides a continuous-variable quantum repeater method based on all-optical entanglement swapping. The provided method utilizes hyper-entangled quantum purification to improve entanglement fidelity and employs all-optical entanglement swapping to construct long-distance continuous-variable quantum repeater links, comprising the following steps:

[0005] Step 1: Alice at the transmitting end prepares a set of photon sequence pairs. The photon sequence pair exhibits continuous variable entanglement in both orthogonal amplitude-phase (X–P) and time-energy (T–E) degrees of freedom, where the photon sequence The photon sequence is retained at the Alice end. Send to the relay node adjacent to the sender Alice. ; This represents the j-th signal photon from the transmitting end, Alice. This represents the j-th idle photon sent to Bob at the receiving end, and k represents the total number of photons in the photon sequence. ; Step 2: Relay Node Received photon sequence contaminated by channel noise relay node Photon sequences were filtered using frequency domain and gated using time domain. The T–E degrees of freedom were purified and screened to obtain the purified photon sequence. ; Step 3: Relay Node Prepare a pair of photon sequence pairs The photon sequence pair and the photon sequence They have the same entangled structure in the X–P degrees of freedom; relay nodes The purified photon sequence and photon sequence Perform an all-optical entanglement swap operation to obtain the entangled photon sequence. ; Step 4: Relay Node Photon sequence Reconstruction yields the reconstructed photon sequence. The reconstruction is performed without destroying the photon sequence. Reconstructing photon sequences under the premise of existing X–P continuous variable entanglement structure T–E degree of freedom entanglement to generate photon sequences Reconstructed photon sequences with the same entanglement structure in both the X–P and T–E degrees of freedom ; Step 5: Relay Node Reconstructing the photon sequence Send it to the next relay node, repeating steps 2 through 4 until the receiver Bob receives the photon sequence transmitted via the quantum channel.

[0006] An alternative approach is that the entanglement of continuous variables on the X–P degrees of freedom in step 1 is a two-mode compressed state, and the entanglement correlation is characterized by an EPR-type correlation between amplitude and phase orthogonality quantities.

[0007] An alternative approach is to constrain the photon sequence by limiting the filtering range of the frequency domain filtering. The short-time narrow-band fidelity of the T–E degrees of freedom is greater than 0.5; the time-domain gating restricts the photon sequence selection range. The fidelity of the short-time narrow-band T–E degree of freedom is greater than 0.5.

[0008] An alternative approach is that the frequency domain filtering in step 2 is performed on the photon sequence. Apply a window function to the frequency variable ω ,

[0009] in, express frequency, This indicates the filtering range for frequency filtering, as detailed in the specific scheme. The value is determined based on the actual noise conditions of the channel, thereby achieving selective retention of photons that meet the preset spectral range conditions; The time-domain gating is for photon sequences Applying a window function to the time variable t ,

[0010] in, Indicates the preparation of photon sequences The corresponding time, This indicates the filtering range for time-domain gating, as specified in the specific scheme. The value is determined based on the actual noise conditions of the channel, thereby achieving selective retention of photons that meet the preset arrival time window conditions.

[0011] An alternative approach is that the all-optical entanglement swapping operation in step 3 includes the relay node using a high-efficiency amplifier to switch the photon sequence. and photon sequence A dual-mode parametric amplification operation is applied, followed by an optical correction operation on the photon sequence after the dual-mode parametric amplification operation is performed through a linear optical coupler to obtain entangled photons. Optionally, the linear optical coupler is a 3 dB optical coupler.

[0012] An alternative approach is to perform the reconstruction using non-degenerate spontaneous parametric down-conversion. The reconstruction employs non-degenerate spontaneous parametric down-conversion and local Gaussian modulation.

[0013] An alternative approach is to implement the non-degenerate spontaneous parametric downconversion process in step 4 in a periodically polarized lithium niobate waveguide or an equivalent nonlinear optical medium.

[0014] The present invention also provides a related quantum communication system, including a transmitter Alice, a receiver Bob, multiple relay nodes, and a quantum relay protocol, wherein the quantum relay protocol adopts the relay method described above.

[0015] This invention significantly optimizes the low cascading capability of continuous-variable quantum repeaters, specifically addressing the exponential decrease in generation rate over short to medium distances with limited repeater node deployment. Simultaneously, it features high-end end-to-end generation rates, making it suitable for long-distance, multi-node quantum network scenarios. Compared to discrete-variable schemes, this approach is highly compatible with coherent optical communication networks at both the physical and signal processing levels, facilitating integration and large-scale application on existing fiber optic communication infrastructure.

[0016] This invention, based on a continuous-variable quantum communication framework, provides a holistic design for the construction of quantum repeater communication links. Without relying on probabilistic non-Gaussian operations, it achieves a quantum repeater mechanism suitable for multi-node cascading, effectively improving the end-to-end entanglement generation rate and cascading stability in long-distance quantum networks. Compared to the latest continuous-variable quantum repeater scheme in Reference 2, this scheme has a significant advantage in generation rate and can effectively optimize the cascading type difference problem of traditional continuous-variable quantum repeater schemes. Through the above design, this scheme improves engineering feasibility and scalability potential while ensuring quantum repeater functionality, making it suitable for practical applications of long-distance, multi-node quantum networks. Attached Figure Description

[0017] Figure 1 This is a flowchart of the present invention (taking the first relay node as an example).

[0018] Figure 2 This is a performance comparison chart between the present invention and Reference 2. Detailed Implementation

[0019] Unless otherwise specified, the scientific and technical terms used in this article are intended for understanding by those skilled in the art.

[0020] See Figure 1 As shown, the photon pair sequence prepared by Alice at the transmitting end in this invention ( j Represents the first photon in the sequence j One photon, kRepresents the total number of photons in the photon sequence and In the context of entanglement, the orthogonal amplitude-phase (X–P) degree of freedom serves as the information-carrying degree of freedom for continuous variable entanglement, while the time-energy (T–E) degree of freedom serves as the channel noise-sensing degree of freedom for continuous variable entanglement. The photon sequence... The photon sequence is retained at the Alice end. The sequence of photons was sent to a neighboring relay node, which then received the photon sequence contaminated by noise. Then, firstly, at the relay node, the photon sequence... Perform quantum purification operations, that is, only on the photon sequence Selective screening of the T–E degrees of freedom is performed to improve the entanglement fidelity of the X–P degrees of freedom. Then, a set of photon sequences is locally prepared at the relay. Photon pairs with the same X–P structure Photon sequences after purification and screening With relay to prepare photon sequences Perform a full optical entanglement swap across the X–P degrees of freedom. Finally, obtain the photon after the full optical entanglement swap. Photon sequences that generate X–P entanglement By reconstructing the T–E degrees of freedom, continuous variable quantum entanglement can be transmitted step by step in the quantum channel, thereby constructing a communication link suitable for multi-node quantum relay cascading.

[0021] In this invention, at each relay node, the received photon sequence contaminated by channel noise is processed. Perform quantum purification operations, i.e., only on the photon sequence. The T–E degrees of freedom perform selective screening operations, including frequency domain screening and time domain gating, to distinguish photons under different channel noise conditions, thereby retaining photons that meet the screening criteria and discarding those that do not. After discarding photons affected by noise, the X–P fidelity increases, resulting in a photon sequence purified by quantum screening. of Degrees of freedom compared to the photon sequence before purification of Degrees of freedom and Alice-end photon sequences prepared without any noise contamination purity The degree of freedom is more similar.

[0022] After the operation in step 3 of this invention, the photon pair sequence originally distributed... and The entangled correlations of the X–P continuous variables in the sequence are swapped to a sequence of photon pairs that have never directly interacted. This allows for the transfer of continuous variable entanglement at the first relay node. Specifically, for the X–P degrees of freedom, the photon sequence... of After the degrees of freedom are entangled and swapped, the photons retained at the Alice end... of Degrees of freedom generate entangled relationships.

[0023] Step 4 of this invention reconstructs the photons because the photon sequence in step 2... Due to quantum purification operation Degrees of freedom disappear, including the purified photon sequence participating in the all-optical entanglement swapping operation. , , and the photon sequence output after entanglement swap None of them contain T–E degrees of freedom, and the next relay node needs to undergo quantum purification operations, so the entangled photon sequence must be... Reconstruct the X–P–T–E degrees of freedom. And for the reconstructed photon sequence... Its degrees of freedom The photon sequence that needs to be retained with Alice's end degrees of freedom They have the same structure and are entangled.

[0024] Example: Based on the scheme of the present invention, this embodiment has 10 relay nodes; in step 1, the entanglement of continuous variables on the X–P degree of freedom is a two-mode compressed state, and the entanglement correlation is characterized by the EPR-type correlation between amplitude and phase orthogonality quantities. In step 2, frequency domain filtering is performed on the photon sequence, followed by time domain gating of the frequency-domain filtered photon sequence. The filtering range of the frequency domain filtering constrains the photon sequence. The fidelity of short-time narrow-band T–E degrees of freedom is greater than 0.5; the time-domain gating restricts the selection range of photon sequences. The short-time narrow-band fidelity of the T–E degrees of freedom is greater than 0.5. Step 3, the all-optical entanglement swapping operation, involves the relay node using a high-efficiency amplifier to perform photon sequence... and photon sequence A dual-mode parametric amplification operation is applied, followed by optical correction of the photon sequence after the dual-mode parametric amplification operation via a 3dB optical coupler to obtain entangled photons; step 4 involves processing the entangled photon sequence... A periodically polarized lithium niobate waveguide is injected, triggering a non-degenerate spontaneous parametric downconversion process under pump light. Finally, after local Gaussian modulation, the continuous variable entanglement is reconstructed, resulting in an output photon sequence. A continuous variable hyperentangled structure that regains X–P and T–E degrees of freedom; Further analysis of the method described in the embodiments and the method in Reference 2, focusing on end-to-end generation rates, yields... Figure 2 The results shown in the figure illustrate the relationship between the end-to-end generation rate and the end-to-end distance under optimal deployment conditions, where the curves correspond to different relay distances (the distance between two repeaters). It is clear that the performance of the method in this invention (solid line) is superior to that of the method in Reference 2 (long dashed line), demonstrating the significant advantages of this scheme in terms of generation rate and cascading performance. For the direct transmission method without deployed repeaters (short dashed line), this scheme quickly surpasses the direct transmission case, which aligns with the consensus of medium-to-long-distance relay deployment and short-distance direct transmission, and also reflects the effectiveness of the relay scheme.

Claims

1. A continuous-variable quantum repeater method based on all-optical entanglement swapping, characterized in that, The method includes the following steps: Step 1: Alice at the transmitting end prepares a set of photon sequence pairs. The photon sequence pair exhibits continuous variable entanglement in both orthogonal amplitude-phase (X–P) and time-energy (T–E) degrees of freedom, where the photon sequence The photon sequence is retained at the Alice end. Send to the relay node adjacent to the sender Alice. ; This represents the j-th signal photon from the transmitting end, Alice. This represents the j-th idle photon sent to Bob at the receiving end, and k represents the total number of photons in the photon sequence. ; Step 2: Relay Node Received photon sequence contaminated by channel noise relay node Photon sequences were filtered using frequency domain and gated using time domain. The T–E degrees of freedom were purified and screened to obtain the purified photon sequence. ; Step 3: Relay Node Prepare a pair of photon sequence pairs The photon sequence pair and the photon sequence They have the same entangled structure in the X–P degrees of freedom; relay nodes The purified photon sequence and photon sequence Perform an all-optical entanglement swap operation to obtain the entangled photon sequence. ; Step 4: Relay Node Photon sequence Reconstruction yields the reconstructed photon sequence. The reconstruction is performed without destroying the photon sequence. Reconstructing photon sequences under the premise of existing X–P continuous variable entanglement structure T–E degree of freedom entanglement to generate photon sequences Reconstructed photon sequences with the same entanglement structure in both the X–P and T–E degrees of freedom ; Step 5: Relay Node Reconstructing the photon sequence Send it to the next relay node, repeating steps 2 through 4 until the receiver Bob receives the photon sequence transmitted via the quantum channel.

2. The continuous-variable quantum repeater method based on all-optical entanglement swapping as described in claim 1, characterized in that, In step 1, the entanglement of continuous variables on the X–P degrees of freedom is a two-mode compressed state, and the entanglement correlation is characterized by the EPR-type correlation between amplitude and phase orthogonality.

3. The continuous-variable quantum repeater method based on all-optical entanglement swapping as described in claim 1, characterized in that, The frequency domain filtering restricts the photon sequence. The short-time narrow-band fidelity of the T–E degrees of freedom is greater than 0.5; The time-domain gating restricts the photon sequence selection range. The fidelity of the short-time narrow-band T–E degree of freedom is greater than 0.

5.

4. The continuous-variable quantum repeater method based on all-optical entanglement swapping as described in claim 1, characterized in that, The frequency domain filtering in step 2 is for the photon sequence Apply a window function to the frequency variable ω , in, express frequency, Indicates the filtering range for frequency filtering; The time-domain gating is for photon sequences Applying a window function to the time variable t , in, Indicates the preparation of photon sequences The corresponding time, This indicates the filtering range for time-domain gating.

5. The continuous-variable quantum repeater method based on all-optical entanglement swapping as described in claim 1, characterized in that, Step 3, the all-optical entanglement swapping operation, includes the relay node using a high-efficiency amplifier to perform photon sequence... and photon sequence A dual-mode parametric amplification operation is applied, and then an optical correction operation is performed on the photon sequence after the dual-mode parametric amplification operation is applied through a linear optical coupler to obtain entangled and swapped photons.

6. The continuous-variable quantum repeater method based on all-optical entanglement swapping as described in claim 5, characterized in that, The linear optical coupler is a 3 dB optical coupler.

7. The continuous-variable quantum repeater method based on all-optical entanglement swapping as described in claim 1 is characterized in that, The reconstruction is performed using non-degenerate spontaneous parametric down-transformation.

8. The continuous-variable quantum repeater method based on all-optical entanglement swapping as described in claim 1, characterized in that, The reconstruction is performed using non-degenerate spontaneous parametric down-conversion and local Gaussian modulation.

9. The continuous-variable quantum repeater method based on all-optical entanglement swapping as described in claim 7 or 8, characterized in that, The non-degenerate spontaneous parametric downconversion process in step 4 is implemented in a periodically polarized lithium niobate waveguide or an equivalent nonlinear optical medium.

10. A quantum communication system, comprising a transmitter Alice, a receiver Bob, multiple relay nodes, and a quantum relay protocol, characterized in that, The quantum repeater protocol employs the repeater method described in claim 1.

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