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arXiv:2301.07490

Effects of weak measurements on sudden change of quantum discord

Bai, Mei, Xiang-Yu Qin, Xue‐Qun Yan

Published Jan 18, 2023• 1 citation
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Abstract

We study the peculiar dynamics of two qubits quantum discord with a sudden change in behavior. It is widely agreed in the literature nowadays that environment induce sudden change behavior of quantum discord. We explore the sudden change phenomenon under the action of local-independent environments, considering the discord of two-qubit which is obtained by means of the weak measurements on one of the two-qubit. It is shown that the sudden change phenomenon does not appear under weak measurements. We find that the quantum discord with weak measurements decays in a monotonic fashion, and show that quantum discord might exhibit a sudden change only for the strong (projective) measurement. We believe that environment is not the main role of the sudden change, but the quantum correlation itself is.

DOI
10.48550/arxiv.2301.07490

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We study the peculiar dynamics of two qubits quantum discord with a sudden change in behavior. It is widely agreed in the literature nowadays that environment induce sudden change behavior of quantum discord. We explore the sudden change phenomenon under the action of local-independent environments, considering the discord of two-qubit which is obtained by means of the weak measurements on one of the two-qubit. It is shown that the sudden change phenomenon does not appear under weak measurements. We find that the quantum discord with weak measurements decays in a monotonic fashion, and show that quantum discord might exhibit a sudden change only for the strong (projective) measurement. We believe that environment is not the main role of the sudden change, but the quantum correlation itself is.
It is known that quantum discord might experience a sudden transition in its dynamics when calculated for certain Bell-diagonal states (BDS) that are in interaction with their surroundings. We examine this phenomenon, known as the sudden change of quantum discord, considering the case of two qubits independently interacting with dephasing reservoirs. We first demonstrate that, for a class of initial states which can be chosen arbitrarily close to BDS, the transition is in fact not sudden, although it might numerically appear so if not studied carefully. Then, we provide an extension of this discussion covering the X\mathsf{X}X-shaped density matrices. Our findings suggest that the transition of quantum discord might be sudden only for an highly idealized zero-measure subset of states within the set of all possible initial conditions of two qubits.
Abstract The dynamics of quantum discord for two qubits independently interacting with dephasing reservoirs have been studied recently. The authors [Phys. Rev. A 88 (2013) 034304] found that for some Bell-diagonal states (BDS) which interact with their environments the calculation of quantum discord could experience a sudden transition in its dynamics, this phenomenon is known as the sudden change. Here in the present paper, we analyze the dynamics of normal quantum discord and super quantum discord for tripartite Bell-diagonal states independently interacting with dephasing reservoirs. Then, we find that basis change does not necessary mean sudden change of quantum correlations.
The dynamics of classical correlation and quantum correlation of two qubits in an independent and common dissipative cavity are studied. We show that for an independent case, the quantum correlation keeps constant and the correlation relation decays before the critical time point Ωt¯. On the other hand t>Ωt¯, for the classical correlation does not change and the quantum correlation is lost. These situations demonstrate that the phenomenon of sudden transition between classical and quantum decoherence appears during the time evolution. For the common case, the quantum correlation dynamics is quite different. It is displayed that for some initial states, the quantum correlation can increase up to the critical point of time, after which it decreases, which means that the quantum correlation presents a sudden change of behavior in their decay rates. But for other initial states, the quantum correlation can keep increasing up to some-steady state value. Furthermore, we also investigate the nonzero quantum correlation between two qubits induced by the dissipation of the cavity.
Super-quantum discord (SQD) with weak measurement is regarded as a kind of quantum correlation in quantum information processing. We compare and analyze the dynamical evolutions of SQD, quantum discord (QD), and quantum entanglement (QE) between two qubits in the correlated dephasing environmental model. The results indicate that (i) owing to the much smaller influence of weak measurement on the coherence of the system than that of von Neumann projection measurement, SQD with weak measurement is larger than QD, and (ii) dynamical evolution of QD or QE monotonically goes to zero with time, while SQD monotonically tends to a stable value and a freezing phenomenon occurs. The stable value after freezing mainly depends on the measurement strength and the purity of the initial quantum state.
\n\nIn this study, we investigate the dynamics of classical and quantum correlations for a two-qubit system in an XY spin-chain environment. Moreover, we focus on two coupling cases. We find that the quantum discord (QD) decay rates for the two cases differ in sudden change behavior and strongly depend on environmental parameters. An interesting scaling behavior for the QD is given under the weak-coupling condition. In the strong-coupling condition, the classical correlation (CC) and the QD oscillate quickly with time, but present regular distributions under a specific time interval. Moreover, the sudden change for the QD is presented by choosing the proper initial time and time interval. Finally, we find that the decay parts of the envelopes for the CC and QD satisfy a Gauss-related feature.\n
We address the effect of classical noise on the dynamics of quantum correlations, entanglement and quantum discord (QD), of two non-interacting qubits initially prepared in a Bell state. The effect of noise is modeled by randomizing the single-qubit transition amplitudes. We address both static and dynamic environmental noise corresponding to interaction with separate and common baths in either Markovian and non-Markovian regimes. In the Markov regime, a monotone decay of the quantum correlations is found, whereas for non-Markovian noise sudden death and revival phenomena may occur, depending on the characteristics of the noise. Entanglement and QD show the same qualitative behavior for all kind of noises considered. On the other hand, we find that separate and common environments may play opposite roles in preserving quantum correlations, depending on the noise regime considered.