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arXiv:1610.08280 · International Journal of Quantum Information

Restoring genuine tripartite entanglement under local amplitude damping

Mazhar Ali

Published Oct 1, 2016• 2 citations
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Abstract

We investigate the possibility to restore genuine tripartite entanglement under local amplitude damping. We show that it is possible to protect genuine entanglement using CNOT and Hadamard gates. We analyze several ordering of such recovery operations. We find that for recovery operations applied after exposing qubits to decoherence, there is no enhancement in lifetime of genuine entanglement. Actual retrieval of entanglement is only possible when reversal scheme is applied before and after the decoherence process. We find that retrieval of entanglement for mixture of [Formula: see text] state with white noise is more evident than the respective mixture of [Formula: see text] state. We also find the retrieval of entanglement for similar mixture of [Formula: see text] state as well.

DOI
10.1142/s0219749916500398

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We investigate the possibility to restore genuine tripartite entanglement under local amplitude damping. We show that it is possible to protect genuine entanglement using CNOT and Hadamard gates. We analyze several ordering of such recovery operations. We find that for recovery operations applied after exposing qubits to decoherence, there is no enhancement in lifetime of genuine entanglement. Actual retrieval of entanglement is only possible when reversal scheme is applied before and after the decoherence process. We find that retrieval of entanglement for mixture of [Formula: see text] state with white noise is more evident than the respective mixture of [Formula: see text] state. We also find the retrieval of entanglement for similar mixture of [Formula: see text] state as well.
Abstract Due to interaction with the environment, a quantum state is subjected to decoherence which becomes one of the major problems in many quantum systems. Amplitude damping is one of the most important decoherence processes. Here, we show that general two-qubit mixed states undergoing 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. We also propose a robust recovery scheme to protect the quantum states when the decay parameters or the input quantum states are not completely known.
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.
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.
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.
We propose a scheme to enhance entanglement from amplitude damping or correlated amplitude damping decoherence. We show that entanglement sudden death time can be prolonged by the initial single-qubit operation combined with local filtering operation. For the amplitude damping channel case, we give the optimal single-qubit operation for arbitrary pure state [Formula: see text]. For the correlated amplitude damping channel case, we find that single-qubit operation on the initial state can not only enhance the final entanglement but also avoid entanglement sudden death. Compared to the previous schemes, the optimal operations and local filtering operations used in our scheme are independent with the decay parameters of the environment.
We study genuine entanglement among three qubits undergoing a noisy process that includes dissipation, squeezing, and decoherence. We obtain a general solution and analyze the asymptotic quantum states. We find that most of these asymptotic states can be genuinely entangled depending upon the parameters of the channel, memory parameter, and the parameters of the initial states. We study Greenberger–Horne–Zeilinger (GHZ) states and W states, mixed with white noise, and determine the conditions for them to be genuinely entangled at infinity. We find that for these mixtures, it is possible to start with a bi-separable state (with a specific mixture of white noise) and end with genuine entangled states. However, the memory parameter μ must be very high. We find that in contrast to the two-qubit case, none of the three-qubit asymptotic states for n → ∞ are genuinely entangled.