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Communications in Theoretical Physics

Quantum Correlations Evolution Asymmetry in Quantum Channels*

Meng Li, Yun‐Feng Huang, Guang‐Can Guo

Published Mar 1, 2017• 1 citation
Publisher

Abstract

Abstract It was demonstrated that the entanglement evolution of a specially designed quantum state in the bistochastic channel is asymmetric. In this work, we generalize the study of the quantum correlations, including entanglement and quantum discord, evolution asymmetry to various quantum channels. We found that the asymmetry of entanglement and quantum discord only occurs in some special quantum channels, and the behavior of the entanglement evolution may be quite different from the behavior of the quantum discord evolution. To quantum entanglement, in some channels it decreases monotonously with the increase of the quantum channel intensity. In some other channels, when we increase the intensity of the quantum channel, it decreases at first, then keeps zero for some time, and then rises up. To quantum discord, the evolution becomes more complex and you may find that it evolutes unsmoothly at some points. These results illustrate the strong dependence of the quantum correlations evolution on the property of the quantum channels.

DOI
10.1088/0253-6102/67/3/267

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Abstract It was demonstrated that the entanglement evolution of a specially designed quantum state in the bistochastic channel is asymmetric. In this work, we generalize the study of the quantum correlations, including entanglement and quantum discord, evolution asymmetry to various quantum channels. We found that the asymmetry of entanglement and quantum discord only occurs in some special quantum channels, and the behavior of the entanglement evolution may be quite different from the behavior of the quantum discord evolution. To quantum entanglement, in some channels it decreases monotonously with the increase of the quantum channel intensity. In some other channels, when we increase the intensity of the quantum channel, it decreases at first, then keeps zero for some time, and then rises up. To quantum discord, the evolution becomes more complex and you may find that it evolutes unsmoothly at some points. These results illustrate the strong dependence of the quantum correlations evolution on the property of the quantum channels.
The evolution of pairwise quantum correlations of Bell cat-states under amplitude damping is examined using the concept of quantum discord which goes beyond entanglement. A closed expression of the quantum discord is explicitly derived. We used of the Koashi-Winter relation. A relation which facilitates the optimization process of the conditional entropy. We also discuss the temporal evolution of bipartite quantum correlations under a dephasing channel and compare the behaviors of quantum discord and entanglement whose properties are characterized through the concurrence.
The evolution of pairwise quantum correlations of Bell cat states under amplitude damping is examined using the concept of quantum discord which goes beyond entanglement. A closed expression of the quantum discord is explicitly derived. We used the Koashi–Winter relation, a relation which facilitates the optimization process of the conditional entropy. We also discuss the temporal evolution of bipartite quantum correlations under a dephasing channel and compare the behaviors of quantum discord and entanglement whose properties are characterized through the concurrence.
Dynamics of an open two-qubit system is investigated in the post-Markovian regime, where the environments have a short-term memory. Each qubit is coupled to separate environment which is held in its own temperature. The inter-qubit interaction is modeled by XY-Heisenberg model in the presence of spin-orbit interaction and inhomogeneous magnetic field. The dynamical behavior of entanglement and discord has been considered. The results show that, quantum discord is more robust than quantum entanglement, during the evolution. Also the asymmetric feature of quantum discord can be monitored by introducing the asymmetries due to inhomogeneity of magnetic field and temperature difference between the reservoirs. By employing proper parameters of the model, it is possible to maintain non-vanishing quantum correlation at high degree of temperature. The results can provide a useful recipe for studying of dynamical behavior of two-qubit systems such as trapped spin-electrons in coupled quantum dots.
We investigate evolution of quantum correlations in ensembles of two-qubit nuclear spin systems via nuclear magnetic resonance techniques. We use discord as a measure of quantum correlations and the Werner state as an explicit example. We, first, introduce different ways of measuring discord and geometric discord in two-qubit systems and then describe the following experimental studies: (a) We quantitatively measure discord for Werner-like states prepared using an entangling pulse sequence. An initial thermal state with zero discord is gradually and periodically transformed into a mixed state with maximum discord. The experimental and simulated behavior of rise and fall of discord agree fairly well. (b) We examine the efficiency of dynamical decoupling sequences in preserving quantum correlations. In our experimental setup, the dynamical decoupling sequences preserved the traceless parts of the density matrices at high fidelity. But they could not maintain the purity of the quantum states and so were unable to keep the discord from decaying. (c) We observe the evolution of discord for a singlet-triplet mixed state during a radio-frequency spin-lock. A simple relaxation model describes the evolution of discord, and the accompanying evolution of fidelity of the long-lived singlet state, reasonably well.
It is known from the analysis of the density matrix for bipartite systems that the quantum discord (as a measure of quantum correlations) depends on the particular subsystem chosen for the projective measurements. We study asymmetry of the discord in a simple physical model of two spin-1/2 particles with the dipole-dipole interaction governed by the XY Hamiltonian in the inhomogeneous magnetic field. The dependence of the above discord asymmetry on the Larmor frequencies at both T = 0 (the ground state) and T > 0 has been investigated. It is demonstrated, in particular, that the asymmetry is negligible for high temperatures but it may become significant with a decrease in the temperature.
We investigate the dynamical evolution of quantum discord, entanglement and purity in an open quantum system of two coupled asymmetric harmonic oscillators interacting with a thermal environment. Using the Kossakowski-Lindblad master equation we analyze the time evolution starting with a squeezed vacuum state. In contrast to our previous study on entanglement evolution in asymmetric oscillators, the present work introduces XY-type position-position coupling together with a systematic joint analysis of quantum discord and purity alongside entanglement. We examine the combined effects of the squeezing parameter, asymmetry parameter, coupling constant, dissipation rate and temperature. We find that quantum discord and entanglement exhibit, in general, a non-monotonic decrease over time. Increasing temperature consistently accelerates the degradation of both quantum correlations and purity, whereas increasing dissipation accelerates the degradation of quantum correlations but leads to higher steady-state purity. Increasing the squeezing parameter provides a protective effect by enhancing initial correlations and prolonging entanglement survival time, while increasing the coupling constant leads to higher quantum correlations. The asymmetry parameter exhibits only a weak influence on the correlation evolution. Our analysis reveals that quantum discord demonstrates stronger resilience than entanglement, which can present more complex behaviour including entanglement sudden death and possible temporary revivals and re-suppressions. These findings provide valuable insights for developing robust quantum information protocols and strategies for preserving quantum correlations in realistic open quantum systems, with potential extensions to non-Markovian regimes and multi-mode architectures.