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Physical Review A

Electronic entanglement purification scheme enhanced by charge detections

Xun‐Li Feng, L. C. Kwek, C. H. Oh

Published Jun 14, 2005• 43 citations
Publisher

Abstract

We present an entanglement purification scheme for the mixed entangled states of electrons with the aid of charge detections. Our scheme adopts the electronic polarizing beam splitters rather than the controlled-NOT (CNOT) operations, but the total successful probability of our scheme can reach the quantity as large as that of the the CNOT-operation-based protocol and twice as large as that of linear-optics-based protocol for the purification of photonic entangled states. Thus our scheme can achieve a high successful prabability without the usage of CNOT operations.

DOI
10.1103/physreva.71.064301

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We present an entanglement purification scheme for the mixed entangled states of electrons with the aid of charge detections. Our scheme adopts the electronic polarizing beam splitters rather than the controlled-NOT (CNOT) operations, but the total successful probability of our scheme can reach the quantity as large as that of the the CNOT-operation-based protocol and twice as large as that of linear-optics-based protocol for the purification of photonic entangled states. Thus our scheme can achieve a high successful prabability without the usage of CNOT operations.
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We propose a scheme for purification of a general mixed entangled state. In this scheme, we start from a large number of general mixed entangled states and end up, after local operation and classical communication, with a smaller number of Bell diagonal states with higher entanglement. In particular, the scheme can purify one maximally entangled state from two entangled pairs prepared in a class of mixed entangled state. Furthermore we propose a linear optical implementation of the present scheme with polarization beam splitters and photon detectors.
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 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.