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Chinese Optics Letters

Improvement on controlled-controlled-NOT operation-based entanglement purification protocol

Yuanyuan Xu, Xun-Li Feng, Zhi‐Ming Zhang

Published Jan 1, 2012• 4 citations
Publisher

Abstract

We show that controlled-controlled-NOT (CCN) operation-based entanglement purification protocol can be further improved.CCN protocol requires Bell state measurements after performing the CCN operations.In the original CCN protocol, the measured states are assumed to be destroyed.However, if controlled-NOT gates are used to perform such Bell state measurements, in some unsuccessful situations of the CCN protocol, one can further purify the two mixed entangled states which are to be measured.In this way, the total efficiency of the CCN protocol is further increased.

DOI
10.3788/col201210.042701

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We show that controlled-controlled-NOT (CCN) operation-based entanglement purification protocol can be further improved.CCN protocol requires Bell state measurements after performing the CCN operations.In the original CCN protocol, the measured states are assumed to be destroyed.However, if controlled-NOT gates are used to perform such Bell state measurements, in some unsuccessful situations of the CCN protocol, one can further purify the two mixed entangled states which are to be measured.In this way, the total efficiency of the CCN protocol is further increased.
We show that controlled-controlled-NOT(CCN)operation-based entanglement purification protocol can be further improved.CCN protocol requires Bell state measurements after performing the CCN operations.In the original CCN protocol,the measured states are assumed to be destroyed.However,if controlled-NOT gates are used to perform such Bell state measurements,in some unsuccessful situations of the CCN protocol,one can further purify the two mixed entangled states which are to be measured.In this way,the total efficiency of the CCN protocol is further increased.
Abstract Entanglement between distant quantum systems is a critical resource for implementing quantum communication. This property is affected by external agents and can be restored by employing efficient entanglement purification protocols. In this work, we propose an entanglement purification protocol based on two entangling two-qubit operations that replace the usual controlled-NOT (CNOT) gate. These operations arise from a generalised quantum measurement and can be understood as measurement operators in a positive operator-valued measure. Furthermore, two variants of the core protocol are introduced and their performances are studied in terms of the overall success probability of reaching a Bell state and the number of purifiable states. Based on rank-two states, we can obtain analytical expressions for the success probability that we extend and refine using numerical calculations to the case of maximally entangled states. We also consider more general rank-three states to show that our procedure is in general more convenient compared to purification protocols based on Bell diagonal states. Finally, we test the protocols using initial random states. In all cases, we find a better performance and a larger amount of purifiable states using our schemes compared to the CNOT-based protocol.
We present an entanglement purification protocol for photonic mixed entangled states based on the two-mode polarization nondemolition parity detectors. Without the use of the controlled-NOT (CNOT) operations, the efficiency of our protocol can nearly approach that of the CNOT protocol. The total successful probability of our protocol can be nearly enhanced to the quantity twice as large as that of the linear-optics-based protocol. Besides, our protocol adopts common photon detectors rather than the sophisticated single-photon detectors required in the linear-optics-based protocol.
We present an efficient entanglement purification protocol (EPP) with controlled-not (CNOT) gates and linear optics. With the CNOT gates, our EPP can reach a higher fidelity than the conventional one. Moreover, it does not require the fidelity of the initial mixed state to satisfy F > 1/2. If the initial state is not entangled, it still can be purified. With the linear optics, this protocol can get pure maximally entangled pairs with some probabilities. Meanwhile, it can be used to purify the entanglement between the atomic ensembles in distant locations. This protocol may be useful in long-distance quantum communication.
We describe an entanglement purification protocol for a polarization Bell state. Different from the previous protocols, it does not require the controlled-not gate, and only uses linear optical elements to complete the task. This protocol requires multi-copy degraded mixed states, which can make this protocol obtain a high fidelity in one purification step. It can also be extended to purify the multi-photon Greenberger–Horne–Zeilinger (GHZ) state. This protocol may be useful in future long-distance communication.
The entangled coherent states (ECSs) have been widely used to realize quantum information processing tasks. However, the ECSs may suffer from photon loss and decoherence due to the inherent noise in quantum channel, which may degrade the fidelity of ECSs. To overcome these obstacles, we present a measurement-based entanglement purification protocol (MBEPP) for ECSs to distill some high-quality ECSs from a large number of low-quality copies. We first show the principle of this MBEPP without considering the photon loss. After that, we prove that this MBEPP is feasible to correct the error resulted from the photon loss. Additionally, this MBEPP only requires to operate the Bell state measurement without performing local two-qubit gates on the noisy pairs and the purified high-quality ECSs can be preserved for other applications. This MBEPP may have application potential in the implementation of long-distance quantum communication.