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arXiv:1904.06838

Robustness of 2 x N x M entangled states against qubit loss

S. M. Zangi, Cong‐Feng Qiao

Published Apr 15, 2019• 0 citations
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Abstract

Entanglement in quantum systems is usually degraded by interaction with the environment. From time to time, some parties of a multipartite entangled system may become decoherent with other parties of the system due to the interference with the environment. In this situation, it is interesting to know how much information the residual system would keep on carrying. In this paper, as a starting point for any entangled system, we investigate the property of the 2 x N x M state with qubit being disentangled, which is characterized by the measurement of robustness.

DOI
10.48550/arxiv.1904.06838

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Entanglement in quantum systems is usually degraded by interaction with the environment. From time to time, some parties of a multipartite entangled system may become decoherent with other parties of the system due to the interference with the environment. In this situation, it is interesting to know how much information the residual system would keep on carrying. In this paper, as a starting point for any entangled system, we investigate the property of the 2 x N x M state with qubit being disentangled, which is characterized by the measurement of robustness.
Robustness of the Entangled States 2×N×M2 \times N \times M2×N×M Against Qubit Loss
A quantum system may suffer from local noises in experiment, and be disturbed partially or completely. In practice, sometimes the multipartite quantum system lose some parts due to local noises, and in this case it is interesting to know whether the residual system still carry information or not. Robust quantum states have the ability to carry on information after the loss of some partites. In this paper, we study 2×N×M2 \times N \times M2×N×M class of quantum states and identify all robust and fragile states with respect to loss of qubit. We also show the robustness of the 2×N×M2 \times N \times M2×N×M robust quantum system after the loss of qubit.
The robustness of multipartite entanglement of systems undergoing decoherence is of central importance to the area of quantum information. Its characterization depends, however, on the measure used to quantify entanglement and on how one partitions the system. Here we show that the unambiguous assessment of the robustness of multipartite entanglement is obtained by considering the loss of functionality in terms of two communication tasks, namely the splitting of information between many parties and the teleportation of states.
When some of the parties of a multipartite entangled pure state are lost, the question arises whether the residual mixed state is also entangled, in which case the initial entangled pure state is said to be robust against particle loss. In this paper, we investigate this entanglement robustness for NNN-qubit pure states. We identify exhaustively all entangled states that are fragile, i.e., not robust, with respect to the loss of any single qubit of the system. We also study the entanglement robustness properties of symmetric states and put these properties in the perspective of the classification of states with respect to stochastic local operations assisted with classic communication (SLOCC classification).
Abstract We investigate the entanglement robustness of N-qubit W superposition state against particle loss with quantum Fisher information. In the noninteracting environment, the quantum Fisher information of reduced W superposition state is found same as the W superposition state when the number of qubits larger than 5, which shows very strong entanglement robustness compared to Twin-Fock state and Greenberger-Horne-Zeilinger state. Meanwhile, the effect of re-particle-loss is also studied and it presents a rapid decay of quantum Fisher information with the increase of losing qubits, indicating the weak entanglement robustness. In the interacting environment, the results show that the reduced W superposition state performs better than it in noninteracting environment. Alternatively, with the increase of qubits (N > 5) the reduced W superposition state behaves much more robust than original state. To vividly approach the real noisy environment, the effects of different decoherence channels are also considered.
We investigate the entanglement robustness of an N-qubit W superposition state against particle loss with quantum Fisher information. In the noninteracting environment, the quantum Fisher information of reduced W superposition state is found same as it from W superposition state when the number of qubits is larger than 5, which shows very strong entanglement robustness compared to Twin-Fock state and Greenberger-Horne-Zeilinger state. Meanwhile, the re-particle-loss effect is also studied and it presents a rapid decay of quantum Fisher information with the increase of the number of losing qubits, indicating the weak entanglement robustness. In the Ising-type interacting environment, the results show that reduced W superposition state performs better than it in noninteracting environment. With the increasing qubits (N>5) the reduced W superposition state behaves much more robust than original W state. To simulate a real noisy environment, the effects of different decoherence channels are also considered.
The destruction of entanglement of open quantum systems by decoherence is investigated in the asymptotic long-time limit. For this purpose a general and analytically solvable decoherence model is presented which does not involve any weak-coupling or Markovian assumption. It is shown that two fundamentally different classes of entangled states can be distinguished and that they can be influenced significantly by two important environmental properties, namely, its initially prepared state and its size. Quantum states of the first class are fragile against decoherence so that they can be disentangled asymptotically even if coherences between pointer states are still present. Quantum states of the second type are robust against decoherence. Asymptotically they can be disentangled only if also decoherence is perfect. A simple criterion for identifying these two classes on the basis of two-qubit entanglement is presented.