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arXiv:1004.0497 · Journal of Physics A Mathematical and Theoretical

Quantum information reclaiming after amplitude damping

Laleh Memarzadeh, Carlo Cafaro, Stefano Mancini

Published Jan 4, 2011• 14 citations
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Abstract

We design an effective method to investigate the quantum information reclaim from the environment after amplitude damping has occurred. In particular, we address the question of optimal measurement on the environment to perform the best possible correction on two- and three-dimensional quantum systems. While for qubits we show that the entanglement fidelity is the same for all possible measurements, for qutirits we find that different measurements give rise to different values of the entanglement fidelity. By searching over all possible measurements on the environment we uncover the optimal one leading to the maximum entanglement fidelity.

DOI
10.1088/1751-8113/44/4/045304

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We design an effective method to investigate the quantum information reclaim from the environment after amplitude damping has occurred. In particular, we address the question of optimal measurement on the environment to perform the best possible correction on two- and three-dimensional quantum systems. While for qubits we show that the entanglement fidelity is the same for all possible measurements, for qutirits we find that different measurements give rise to different values of the entanglement fidelity. By searching over all possible measurements on the environment we uncover the optimal one leading to the maximum entanglement fidelity.
We investigate the quantum information reclaim from the environment after amplitude damping has occurred. In particular we address the question of optimal measurement on the environment to perform the best possible correction on two and three dimensional quantum systems. Depending on the dimension we show that the entanglement fidelity (the measure quantifying the correction performance) is or is not the same for all possible measurements and uncover the optimal measurement leading to the maximum entanglement fidelity.
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.
Entanglement is the key to teleport an unknown quantum state with fidelity higher than classical limit. For decohering open quantum systems, entanglement decreases with the strength of interaction between quantum systems and the environment. As a result, teleportation fidelity decreases. The technique of weak measurement and its reversal help to protect entanglement in the presence of amplitude-damping decoherence. In this work, we have shown that the optimal protection of entanglement measured by concurrence does not always optimize teleportation fidelity in the presence of decoherence modeled by the amplitude damping decoherence. More specifically, when one of the systems interacts with the environment, optimization of entanglement and teleportation fidelity requires different strengths of reverse weak measurement. Here, the success probability of optimal protection of entanglement is higher than the success probability of optimal protection of teleportation fidelity. Interestingly, when both systems interact with the environment, optimization of entanglement implies optimization of teleportation fidelity. Therefore, the resources of quantum teleportation along with entanglement need to be explored.
Quantum entanglement is a critical resource for quantum information and quantum computation. However, entanglement of a quantum system is subjected to change due to the interaction with the environment. One typical result of the interaction is the amplitude damping that usually results in the reduction of the entanglement. Here we propose a protocol to protect quantum entanglement from the amplitude damping by applying Hadamard and CNOT gates. As opposed to some recently studied methods, the scheme presented here does not require weak measurement in the reversal process, leading to a faster recovery of entanglement. We propose a possible experimental implementation based on linear optical system.
Quantum entanglement is a critical resource for quantum information and quantum computation. However, entanglement of a quantum system is subjected to change due to the interaction with the environment. One typical result of the interaction is the amplitude damping that usually results in the reduction of the entanglement. Here we propose a protocol to protect quantum entanglement from the amplitude damping by applying Hadamard and CNOT gates. As opposed to some recently studied methods, the scheme presented here does not require weak measurement in the reversal process, leading to a faster recovery of entanglement. We propose a possible experimental implementation based on linear optical system.
Noise poses a fundamental challenge to quantum information processing, with amplitude-damping (AD) noise being particularly detrimental. Preserving high-fidelity quantum systems therefore relies critically on effective error correction and purification methods. In this work, we introduce a novel approach for mitigating AD noise that can be applied to both state and channel purification. Our method achieves a substantial enhancement in the fidelity of affected states or channels while maintaining a low resource overhead, requiring only one or two ancilla qubits in combination with two Clifford gates, and exhibits a relatively high success probability. This approach provides a practical and scalable framework for addressing AD noise in realistic quantum systems.