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International Journal of Modern Physics B

Dynamics of quantum correlations for three-qubit states in a noisy environment

Tian-Wen Liu, Zhiyuan He, Xi-Wen Hou

Published May 31, 2019• 2 citations
Publisher

Abstract

Girolami and coworkers have proposed measures of quantum correlations and weaving [Girolami et al., Phys. Rev. Lett. 119, 140505 (2017)]. This work derives the analytic time-evolution of such measures and weaving for two kinds of initial states in three qubits under an amplitude-damping and a dephasing noisy environment. It is shown that the 2-partite correlation is forever frozen, which is dependent on an initial state and the property of noise.

DOI
10.1142/s0217979219501455

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Girolami and coworkers have proposed measures of quantum correlations and weaving [Girolami et al., Phys. Rev. Lett. 119, 140505 (2017)]. This work derives the analytic time-evolution of such measures and weaving for two kinds of initial states in three qubits under an amplitude-damping and a dephasing noisy environment. It is shown that the 2-partite correlation is forever frozen, which is dependent on an initial state and the property of noise.
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.
We study the time evolution of two two-state systems (two qubits) initially in the pure entangled states or the maximally entangled mixed states interacting with the individual environmental noise. It is shown that due to environment noise, all quantum entangled states are very fragile and become a classical mixed state in a short-time limit. But the environment can affect entanglement in very different ways. The type of decoherence process for certain entangled states belongs to amplitude damping, while the others belong to dephasing decoherence.
By applying a modified conjugate gradient method in the evaluation of three-qubit residual entanglement, the disentanglement of three-qubit states in an amplitude-damping and dephasing environment is investigated numerically. It is found that the decay of tripartite entanglement is faster than bipartite entanglement in the same qubits-noise system, which indicates that multipartite entanglement is more fragile than bipartite entanglement in resisting quantum noises. Similar to the case of a two-qubit system, three-qubit entanglement subject to an open environment may also disappear abruptly (sudden death) or decrease asymptotically, which is dependent on the conditions of the initially entangled quantum state and the properties of quantum noise.
Abstract It is known that the inevitable interaction of the entangled qubits with their environments may result in the degradation of quantum correlation. We study the decoherence of two remote qubits under general local single- and two-sided amplitude-damping channel (ADC). By using concurrence, quantum discord and Clauser–Horne–Shimony–Holt (CHSH) inequality, we find that the relation between the residual quantum correlations and the initial ones are different. Recently, Wang et al. [Int. J. Theor. Phys. 54 (2015) 5] showed that there exist a set of partially entangled states that are more robust than maximally entangled states in terms of the residual quantum correlation measured by concurrence, fully entangled fraction and quantum discord, respectively. Here we find that both in single- and two-sided ADC, only the evolution of CHSH inequality with the initial parameter is proportional to that of the initial nonlocality. That means the initial state with maximally nonlocality will retain its role in the evolution. It implies that the evolution of nonlocality may reveal the characteristics of quantum state better. Furthermore, we discuss the evolutions of the three different quantum measurements with the initial parameter under generalized amplitude damping channel (GADC) and find that they are all proportional to that of the initial state.
In the present paper, the joint effects of two kinds of classical environmental noises, without direct interaction among each other, on the dynamics of quantum correlations (QCs) of a three-qubit system coupled in independent environments is investigated. More precisely, we join the random telegraph noise (RTN) and the static noise (SN) and focus on the dynamics of entanglement and quantum discord (QD) when the qubits are initially prepared in the GHZ- and W-type states. The overall noise affecting the qubits is obtained by combining the RTN and SN in two different setups. The results show that the disorder of the environmental noise as well as its memory qualities and the purity of the initial state considered play a crucial role in the time evolution of the system in such a way that the dynamics of QCs can be controlled by varying them. In fact, we show that, depending on the initial state and noise regime considered, the rate of collapse of QCs may either decrease or increase with the increase of the degree of disorder of the SN, the switching rate of the RTN and the purity of the initial state.
We investigate the dynamics of quantum and classical correlations in a system of two qubits under local colored-noise dephasing channels. The time evolution of a single qubit interacting with its own environment is described by a memory kernel non-Markovian master equation. The memory effects of the non-Markovian reservoirs introduce new features in the dynamics of quantum and classical correlations compared to the white noise Markovian case. Depending on the geometry of the initial state, the system can exhibit frozen discord and multiple sudden transitions between classical and quantum decoherence [L. Mazzola, J. Piilo and S. Maniscalco, Phys. Rev. Lett. 104 (2010) 200401]. We provide a geometric interpretation of those phenomena in terms of the distance of the state under investigation to its closest classical state in the Hilbert space of the system.