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Quantum Information and Computation

Environment-assisted entanglement purification

Liang Qiu, Zhi Liu, Xin Wang

Published Sep 1, 2016• 2 citations
Publisher

Abstract

Two qubits in a pure entangled state passing through and interacting with amplitude damping noises will cause the decay of entanglement. Entanglement swapping combined with environment measurement is proposed to purify entanglement of the two-qubit state. Some initial states can be purified into the maximally entangled ones by just using the protocol for one time, in contrast to iteratively using the protocol given in Phys. Rev. A 89, 014303 (2014).

DOI
10.26421/qic16.11-12-4

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Two qubits in a pure entangled state passing through and interacting with amplitude damping noises will cause the decay of entanglement. Entanglement swapping combined with environment measurement is proposed to purify entanglement of the two-qubit state. Some initial states can be purified into the maximally entangled ones by just using the protocol for one time, in contrast to iteratively using the protocol given in Phys. Rev. A 89, 014303 (2014).
Abstract Based on the quantum technique of environment-assisted measurement and quantum measurement reversal, we systematically investigate the restoration of quantum entanglement for distributing a two-qubit pure state via three typical kinds of noisy quantum channels-amplitude damping, phase damping and depolarizing quantum channels. Special attention is paid to the unsymmetrical two-qubit arbitrarily entangled states transmission. The analytical or numerical simulations results show that for arbitrarily one-qubit entangled state or two-qubit states transmission, the output distant entanglement could be drastically restored to the initial value in all these three cases.
We study the time evolution of two two-state systems (two qubits) initially in the pure entangled states or the maximally entangled mixed states interacting with the individual environmental noise. It is shown that due to environment noise, all quantum entangled states are very fragile and become a classical mixed state in a short-time limit. But the environment can affect entanglement in very different ways. The type of decoherence process for certain entangled states belongs to amplitude damping, while the others belong to dephasing decoherence.
We find the necessary and sufficient condition under which two two-qubit mixed states can be purified into a pure maximally entangled state by local operations and classical communication. The optimal protocol for such transformation is obtained. This result leads to a necessary and sufficient condition for the exact purification of nnn copies of a two-qubit state.
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 find the necessary and sufficient condition under which two two-qubit mixed states can be purified into a pure maximally entangled state by local operations and classical communication. The optimal protocol for such transformation is obtained. This result leads to a necessary and sufficient condition for the exact purification of nnn copies of a two-qubit state.