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Physical Review A

Robustness and symmetry of deterministic quantum entanglement swapping

Hao Ming Zhao, Chuan-Jia Shan

Published Sep 19, 2024• 2 citations
Publisher

Abstract

In this paper, we present two quantum entanglement swapping schemes, a single-channel scheme and a dual-channel scheme, based on fiber channel transmission. We theoretically calculated the Einstein-Podolsky-Rosen- (EPR-) type variance and symmetry parameter factors of deterministic quantum entanglement swapping in these two schemes. By comparing the quantum entanglement swapping of the single- and dual-channel schemes, we show that the transmission distance of the dual-channel scheme is much longer than that of the single-channel scheme. Interestingly, the quantum correlation strength and symmetry of the two remote modes after deterministic quantum entanglement swapping are significantly improved when the optimal classical gain and loss efficiency of the loss channel are chosen. Moreover, the entanglement swapping will be robust and not suffer from sudden death when the entangled optical modes are transmitted in the lossy fiber channel. We also show that nonzero entanglement enables deterministic quantum entanglement swapping under both schemes when the EPR entanglement is a pure state. The two optimized schemes provide feasible technical references for long-distance metropolitan quantum communication.

DOI
10.1103/physreva.110.032618

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In this paper, we present two quantum entanglement swapping schemes, a single-channel scheme and a dual-channel scheme, based on fiber channel transmission. We theoretically calculated the Einstein-Podolsky-Rosen- (EPR-) type variance and symmetry parameter factors of deterministic quantum entanglement swapping in these two schemes. By comparing the quantum entanglement swapping of the single- and dual-channel schemes, we show that the transmission distance of the dual-channel scheme is much longer than that of the single-channel scheme. Interestingly, the quantum correlation strength and symmetry of the two remote modes after deterministic quantum entanglement swapping are significantly improved when the optimal classical gain and loss efficiency of the loss channel are chosen. Moreover, the entanglement swapping will be robust and not suffer from sudden death when the entangled optical modes are transmitted in the lossy fiber channel. We also show that nonzero entanglement enables deterministic quantum entanglement swapping under both schemes when the EPR entanglement is a pure state. The two optimized schemes provide feasible technical references for long-distance metropolitan quantum communication.
Einstein-Podolsky-Rosen (EPR) steering is a quantum mechanical phenomenon that allows one party to steer the state of a distant party by exploiting their shared entanglement. It has potential applications in secure quantum communication. In this paper, we present two swapping schemes of Gaussian EPR steering, single-channel and dual-channel schemes, by the technique of entanglement swapping. Two space-separated independent EPR steering states without a direct interaction present EPR steering after deterministic swapping. By comparing the EPR steering of the single-channel and dual-channel schemes, we show that the transmission distance of the single-channel scheme is much longer than that of the symmetric dual-channel scheme. Different from entanglement swapping, one-way EPR steering is presented after swapping over lossy channels. The most interesting thing is that the change of the EPR steering direction is observed in the dual-channel scheme. We also show that excess noise in a quantum channel will shorten the transmission distance of the swapping, even leading to the sudden death of EPR steering. The presented schemes provide a technical reference for remote quantum communications with EPR steering.
Einstein-Podolsky-Rosen (EPR)-entangled state light field at a telecommunication wavelength of 1.5 μm is an important quantum source for realizing the continuous variable quantum information processing and some quantum protocols over optical fiber channel. When the EPR-entangled state light field is distributed over the optical fiber channel, the disentanglement is always present because the the EPR entangled state interacts with the fiber channel. It affects the performance of quantum information processing. In this paper, we theoretically calculate the positive partial transposition (PPT) of the entangled state distributed over the optical fiber channel in the single-channel and dual-channel distribution scheme, respectively. Three types of initial entangled light field are considered and analyzed, they being an initial EPR entangled state, an EPR entangled state with asymmetric quadratures, and an EPR entangled state with asymmetric modes. Furthermore, the influence of the extra noise in the optical fiber on the transmission distance of EPR entangled state over the optical fiber channel is investigated. In the single-channel scheme or dual-channel scheme, the extra noise in the optical fiber channel leads the entangled state light field to be disentangled, and the transmission distance of EPR entangled state over the optical fiber channel to decrease rapidly with the increase of the extra noise. For maintaining the robustness of EPR entangled states in lossy optical fiber channels, the dual-channel scheme has more stringent requirements for the correlation quadrature symmetry and purity of the initial entangled state than the single-channel scheme. In the single fiber noise channel scheme, the maximum transmission distance and the robustness of the EPR entangled states with asymmetric modes are not sensitive to the asymmetry between modes. The change of asymmetry between modes does not lead to being disentangled. The maximum transmission distance does not change either. However, the decrease of asymmetry between modes results in the disentanglement in the double fiber noise channels’ scheme. The maximum transmission distance is reduced and the sudden death occurs to the entanglement. The present results will lay a foundation for continuous variables quantum information processing based on optical fiber, such as realizing continuous variables quantum communication over optical fiber and constructing metropolitan quantum network over optical fiber.
A real time deterministic quantum teleportation over a single fiber channel was implemented experimentally by exploiting the generated EPR entanglement at 1550 nm. A 1342 nm laser beam was used to transfer the classical information in real time and also acted as a synchronous beam to realize the synchronization of the quantum and classical information. The dependence of the fidelity on the transmission distance of the fiber channel was studied experimentally with optimizing the transmission efficiency of the lossy channel that was established to manipulate the beam of the EPR entanglement in Alice's site. The maximum transmission distance of the deterministic quantum teleportation was 10 km with the fidelity of 0.51 ± 0.01, which is higher than the classical teleportation limit of 1/2. The work provides a feasible scheme to establish metropolitan quantum networks over fiber channels based on deterministic quantum teleportation.
We present a quantum secure direct communication scheme achieved by swapping quantum entanglement. In this scheme a set of ordered Einstein-Podolsky-Rosen (EPR) pairs is used as a quantum information channel for sending secret messages directly. After insuring the safety of the quantum channel, the sender Alice encodes the secret messages directly by applying a series local operations on her particles sequence according to their stipulation. Using three EPR pairs, three bits of secret classical information can be faithfully transmitted from Alice to remote Bob without revealing any information to a potential eavesdropper. By both Alice and Bob's GHZ state measurement results, Bob is able to read out the encoded secret messages directly. The protocol is completely secure if perfect quantum channel is used, because there is not a transmission of the qubits carrying the secret message between Alice and Bob in the public channel.
We present a quantum secure direct communication scheme achieved by swapping quantum entanglement. In this scheme a set of ordered Einstein-Podolsky-Rosen (EPR) pairs is used as a quantum information channel for sending secret messages directly. After insuring the safety of the quantum channel, the sender Alice encodes the secret messages directly by applying a series local operations on her particle sequences according to their stipulation. Using three EPR pairs, three bits of secret classical information can be faithfully transmitted from Alice to remote Bob without revealing any information to a potential eavesdropper. By both Alice and Bob's GHZ state measurement results, Bob is able to read out the encoded secret messages directly. The protocol is completely secure if perfect quantum channel is used, because there is not a transmission of the qubits carrying the secret message between Alice and Bob in the public channel.
A novel deterministic secure quantum communication (DSQC) scheme is presented based on Einstein-Podolsky-Rosen (EPR) pairs and single photons in this study. In this scheme, the secret message can be encoded directly on the first particles of the prepared Bell states by simple unitary operations and decoded by performing the Bell-basis measurement after the additional classic information is exchanged. In addition, the strategy with two-step transmission of quantum data blocks and the technique of decoy-particle checking both are exploited to guarantee the security of the communication. Compared with some previous DSQC schemes, this scheme not only has a higher resource capacity, intrinsic efficiency and total efficiency, but also is more realizable in practical applications. Security analysis shows that the proposed scheme is unconditionally secure against various attacks over an ideal quantum channel and still conditionally robust over a noisy and lossy quantum channel.