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Laser Physics Letters

Distribution and monogamy of quantum coherence for open three-qubit systems under local noisy channels

Ming-Jie Liao, Hao‐Sheng Zeng

Published Mar 11, 2021• 1 citation
Publisher

Abstract

Abstract We study the distribution and monogamous relations of quantum coherence for three-qubit systems under the influence of local amplitude-damping, phase-damping and random unitary channels, respectively. We find that under the influence of the considered channels, the W state has both global and bipartite coherence, and its monogamy is always equal to zero. For the Greenberger–Horne–Zeilinger) state, however, there is only global coherence in the time evolution and the monogamy is always positive. We also present a partially entangled state, | Ψ ⟩ , which has global, bipartite, and monomeric coherences and negative monogamy during the whole time evolution.

DOI
10.1088/1612-202x/abe304

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Abstract We study the distribution and monogamous relations of quantum coherence for three-qubit systems under the influence of local amplitude-damping, phase-damping and random unitary channels, respectively. We find that under the influence of the considered channels, the W state has both global and bipartite coherence, and its monogamy is always equal to zero. For the Greenberger–Horne–Zeilinger) state, however, there is only global coherence in the time evolution and the monogamy is always positive. We also present a partially entangled state, | Ψ ⟩ , which has global, bipartite, and monomeric coherences and negative monogamy during the whole time evolution.
Exploring an analytical expression for the convex roof of the pure state squared concurrence for rank 2 mixed states the entanglement of a system of three particles under decoherence is studied, using the monogamy inequality for mixed states and the residual entanglement obtained from it. The monogamy inequality is investigated both for the concurrence and the negativity in the case of local independent phase damping channel acting on generalized Greenberger-Horne-Zeilinger states of three particles and the local independent amplitude damping channel acting on generalized $\ensuremath{\mid}\mathrm{W}⟩=\ensuremath{\mid}001⟩+\ensuremath{\mid}010⟩+\ensuremath{\mid}100⟩$ state of three particles. It is shown that the bipartite entanglement between one qubit and the rest has a qualitative similar behavior to the entanglement between individual qubits, and that the residual entanglement in terms of the negativity cannot be a good entanglement measure for mixed states, since it can increase under local decoherence.
We study the dynamics of quantum dissension for three qubit states in various dissipative channels such as amplitude damping, dephasing and depolarizing. Our study is solely based on Markovian environments where quantum channels are without memory and each qubit is coupled to its own environment. We start with mixed GHZ, mixed W, mixture of separable states, a mixed biseparable state, as the initial states and mostly observe that the decay of quantum dissension is asymptotic in contrast to sudden death of quantum entanglement in similar environments. This is a clear indication of the fact that quantum correlation in general is more robust against the effect of noise. However, for a given class of initial mixed states we find a temporary leap in quantum dissension for a certain interval of time. More precisely, we observe the revival of quantum correlation to happen for certain time period. This signifies that the measure of quantum correlation such as quantum discord, quantum dissension, defined from the information theoretic perspective is different from the correlation defined from the entanglement-separability paradigm and can increase under the effect of the local noise. We also study the effects of these channels on the monogamy score of each of these initial states. Interestingly, we find that for certain class of states and channels, there is change from negative values to positive values of the monogamy score with classical randomness as well as with time. This gives us an important insight in obtaining states which are freely sharable (polygamous state) from the states which are not freely sharable (monogamous). This is indeed a remarkable feature, as we can create monogamous states from polygamous states Monogamous states are considered to have more signatures of quantum ness and can be used for security purpose.
The limitation on the shareability of quantum entanglement over several parties, the so-called monogamy of entanglement, is an issue that has received considerable attention from the quantum information community over the last decade. A natural question of interest in this connection is whether monogamy of correlations is true for correlations other than entanglement. This issue is examined here by choosing quantum deficit, proposed by A. K. Rajagopal and R. W. Rendell [Phys. Rev. A 66, 022104 (2002)], an operational measure of correlations. In addition to establishing the polygamous nature of the class of three-qubit symmetric pure states characterized by two distinct Majorana spinors (to which the WWW states belong), those with three distinct Majorana spinors [to which Greenberger-Horne-Zeilinger (GHZ) states belong] are shown to either obey or violate monogamy relations. While the generalized WWW states can be monogamous or polygamous, the generalized GHZ states exhibit monogamy with respect to quantum deficit. The issue of using monogamy conditions based on quantum deficit to witness the states belonging to stochastic local operations and classical communication (SLOCC) inequivalent classes is discussed in light of these results.
We discuss entanglement evolution of a multiqubit system in which one of its qubits is subjected to a general noisy channel. For such a system, an evolution equation of entanglement for a lower bound for multiqubit concurrence is derived. Using this evolution equation, the entanglement dynamics of an initially mixed three-qubit state composed of a Greenberger-Horne-Zeilinger (GHZ) and a WWW state is analyzed if one of the qubits is affected by a phase, an amplitude, or a generalized amplitude damping channel.
This paper is to investigate the effects of quantum noises on entanglement localization by taking an example of reducing a three-qubit Greenberger-Horne-Zeilinger (GHZ) state to a two-qubit entangled state. We consider, respectively, two types of quantum decoherence, i.e., amplitude-damping and depolarizing decoherence, and explore the best von Neumann measurements on one of three qubits of the triple GHZ state for making the amount of entanglement of the collapsed bipartite state be as large as possible. The results indicate that different noises have different impacts on entanglement localization, and that the optimal strategy for reducing a three-qubit GHZ state to a two-qubit one via local measurements and classical communications in the amplitude-damping case is different from that in the noise-free case. We also show that the idea of entanglement localization could be utilized to improve the quality of bipartite entanglement distributing through amplitude-damping channels. These findings might shed a new light on entanglement manipulations and transformations.