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arXiv:1305.4627 · Physical Review A

Restoration of a quantum state in a dephasing channel via environment-assisted error correction

Xinyu Zhao, Samuel R. Hedemann, Ting Yu

Published Aug 19, 2013• 43 citations
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Abstract

In this paper, we propose an environment-assisted error correction scheme to fully recover a multiple-qubit state subject to a phase damping noise. We establish the theoretical framework and the operational procedure to restore an unknown initial quantum state for an $N$-qubit model interacting with either individual baths or a common bath. We give an explicit construction of the random unitary (RU) Kraus decomposition for an $N$-qubit model interacting with a common bath. We also demonstrate how to use only one unitary reversal operation to restore an arbitrary state with phase damping noise. In principle, the initial state can always be recovered with a success probability of 1. Interestingly, we found that non-RU decomposition can also be used to restore some particular entangled states. This may open a new path to restore a quantum entangled state beyond the standard RU scheme.

DOI
10.1103/physreva.88.022321

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In this talk, I will present an explicit scheme to fully recover a multiple-qubit state subject to a phase damping noise. We establish the theoretical framework and the operational procedure to restore an unknown initial quantum state for an N-qubit model interacting with either individual baths or a common bath. We give an explicit construction of the random unitary (RU) Kraus decomposition for an N-qubit model interacting with a common bath. We also demonstrate how to use only one unitary reversal operation to restore an arbitrary state with phase damping noise. In principle, the initial state can always be recovered with a success probability of 1. Interestingly, we found that non-RU decomposition can also be used to restore some particular entangled states. This may open a new path to restore a quantum state beyond the standard RU scheme.
In this paper, a quantum state restoration scheme is proposed based on the environment-assisted error correction (EAEC) scheme. By introducing a weak measurement reversal (WMR) operation, we will show how to recover an initial state of a quantum open system without invoking random unitary decompositions which are known to be absent in many important physical systems. We illustrate our scheme and compare it with a scheme purely based on the WMR operation in the case of a dissipative channel. In the proposed scheme, the successful probability for recovering an unknown initial state can be significantly improved when the information obtained from an environment measurement is taken into account. Moreover, we show that the applicable range of our proposed scheme is wider than the EAEC scheme. Finally, the optimization of the successful probability for possible Kraus decompositions is discussed.
Abstract We examine the validity of the environment-assisted measurement (EAM) and quantum measurement reversal (QMR) operations in the restoration of distributed entanglement for two-qubit transmission under three typical kinds of noisy quantum channels, i.e. an amplitude damping channel, a phase damping channel and a depolarizing quantum channel. Given the parameters of the Bell-like initial qubits’ state and , we derive exact expressions for the optimal final quantum entanglement, showing explicitly that combining the EAM and QMR operations does indeed help in recovering the distributed entanglement from the various decoherence sources. Comparing with the results obtained using the weak measurement and QMR method, our results show notable superiorities in adaptation scope and success probability.
Several instructions need to be considered in order to transfer classical error correction techniques to the quantum regime. The quantum error correction field has been developed to face these issues. One of the common source of errors in quantum systems is environment decoherence. Due to interaction with the environment, the quantum states of a system entangle with the environment and are subject to decoherence. In this thesis, we mainly focused on the amplitude damping which is one of the most important models of decoherence processes. We showed that general two-qubit mixed states undergoing an amplitude damping, can be almost completely restored using a reversal procedure. This reversal procedure through CNOT and Hadamard gates could also protect the entanglement of two-qubit mixed states from general amplitude damping. Concurrence and fidelity are two measurements used in order to examine how our proposed scheme performs. Furthermore, to give generality to our scheme, we proposed a robust recovery scheme to protect the quantum states when the decay parameters or the input quantum states are not completely known.
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.