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Robustness of the Entangled States $2 \times N \times M$ Against Qubit Loss

S. M. Zangia, Junli Li, Cong-Feng Qiaoa

Published Apr 15, 2019• 0 citations
OpenAlex

Abstract

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 $2 \times N \times M$ class of quantum states and identify all robust and fragile states with respect to loss of qubit. We also show the robustness of the $2 \times N \times M$ robust quantum system after the loss of qubit.

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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.
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).
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.
We investigate the relation between the entanglement and the robustness of a multipartite system to a depolarization noise. We find that the robustness of a two-qubit system in an arbitrary pure state depends completely on its entanglement. However, this is not always true in a three-qubit system. There is a residual effect on the robustness of a three-qubit system in an arbitrary superposition of a Greenberger-Horne-Zeilinger state and a WWW state. Its entanglement determines the trend of its robustness. However, there is a splitting on its robustness under the same entanglement. Its robustness not only has the same periodicity as its three-tangle but also alters with its three-tangle synchronously. There is also a splitting on the robustness of an nnn-qubit (n>3n>3n>3) system although it is more complicated.
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.
Bipartite entangled states between a qubit and macroscopically distinct states of a mesoscopic system, known as micro-macro entangled states, are emerging resources for quantum information processing. One main challenge in generating such states in the laboratory is their fragility to environmental noise. We analyze this fragility in detail for single-particle noise by identifying what factors play a role in the robustness and quantifying their effect. There is a trade-off between the macroscopicity of a micro-macro entangled state and the robustness of its bipartite entanglement to environmental noise. We identify symmetric micro-macro entangled states as the most robust states to single-particle noise. We show that the robustness of bipartite entanglement of such states to single-particle noise decreases as the second order of macroscopicity, which identifies a regime where the bipartite entangled state is both robust and macroscopic. Our result is a step towards retaining quantum characteristics on large scales and experimental realization of micro-macro entangled spin states and their use for connecting separated qubits. Moreover, it advances our understanding of quantum to classical transition.
In the context of quantum information, we investigate extensively some important classes of a general form of a two-qubit system under Lorentz transformation. It is shown Lorentz transformation causes a decay of entanglement and consequently information loses. On the other hand, it generates entangled states between systems prepared initially in a separable states. The partial entangled states are more robust under Lorentz transformation than maximally entangled states. Therefore the rate of information lose is larger for maximum entangled states compared with that for partially entangled states.