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Chinese Physics B

Controlling the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environments*

Rong‐Yu Wu, Mao-Fa Fang

Published Oct 28, 2020• 1 citation
Publisher

Abstract

The uncertainty principle is a crucial aspect of quantum mechanics. It has been shown that the uncertainty principle can be tightened by quantum discord and classical correlation in the presence of quantum memory. We investigate the control of the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environment. Our results show that the entropic uncertainty of an observed system can be reduced and the quantum discord between the observed system and the quantum memory system can be enhanced in the steady state of the system by adding an dissipative ancilla. Particularly, via preparing the state of the system to the highest excited state with hight fidelity, the entropic uncertainty can be reduced markedly and the quantum discord can be enhanced obviously. We explain these results using the definition of state fidelity. Furthermore, we present an effective strategy to further reduce the the entropic uncertainty and to enhance the the quantum discord via quantum-jump-based feedback control. Therefore, our results may be of importance in the context of quantum information technologies.

DOI
10.1088/1674-1056/abc54d

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The uncertainty principle is a crucial aspect of quantum mechanics. It has been shown that the uncertainty principle can be tightened by quantum discord and classical correlation in the presence of quantum memory. We investigate the control of the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environment. Our results show that the entropic uncertainty of an observed system can be reduced and the quantum discord between the observed system and the quantum memory system can be enhanced in the steady state of the system by adding an dissipative ancilla. Particularly, via preparing the state of the system to the highest excited state with hight fidelity, the entropic uncertainty can be reduced markedly and the quantum discord can be enhanced obviously. We explain these results using the definition of state fidelity. Furthermore, we present an effective strategy to further reduce the the entropic uncertainty and to enhance the the quantum discord via quantum-jump-based feedback control. Therefore, our results may be of importance in the context of quantum information technologies.
Abstract The one-qubit teleportation protocol is one of the most well-known topics of quantum information theory. Indeed, the goal of this quantum protocol is to teleport an arbitrary quantum state. Herein, we investigate the entropic uncertainty relation in the presence of quantum memory (EUR-QM), quantum discord (QD), and fidelity of teleportation under dephasing, dissipative, and noisy environments. We relate the EUR-QM to QD and quantum teleportation and show analytically that there is a fully anti-correlated relation between QD and entropic uncertainty in a dephasing environment. In the process of our analysis, we also find an explicit relationship between the average fidelity of teleportation and the entropic uncertainty of the channel state. Significantly, the results report that the fidelity of teleportation and QD of the channel state are more stable and most efficiently under the influence of a dephasing environment than those under the influence of a dissipative or noisy environment. It turns out that under a dephasing environment, these results can be vital in practical goals where the maximum fidelity of teleportation and minimum uncertainty are required such as in quantum teleportation protocols and quantum computation.
The uncertainty of measurement on a quantum system can be reduced in presence of quantum memory [M. Berta et. al. Nature Phys. {\bf 6}, 659 (2010)]. By measurement on quantum memory, some information (non-classical information) is inaccessible, hence, it limits the lower bound of entropic uncertainty relation. In the present work, we improve the lower bound of entropic uncertainty relation in presence of quantum memory by considering inaccessibility of non classical correlation at Bob side and also compare the lower bound given by M. Berta et. al. and our prescription for two different kind of shared bipartite state.
Abstract We address the dynamics of the lower bound of geometric quantum discord and quantum-memory-assisted entropic uncertainty in a two-qutrit system when exposed to classical channels characterized by power-law (PL) and random telegraph (RT) noises. The system-channel coupling strategy is examined in two contexts: common qutrit-environment (CQE) and different qutrit-environment (DQE) configurations. We show that the geometric quantum discord functions remain anti-correlated with entropic uncertainty and decline as uncertainty appears in the system. The rate of entropic uncertainty appearance seems more prevalent than the decline rate of quantum discord function, suggesting that uncertainty causes the quantum correlations to fade in quantum systems. We find that non-local correlations estimated by the lower bound of geometric quantum discord are not destroyed even at the maximum entropic disorder and entropic uncertainty. In addition, the efficacy of entropic uncertainty and the lower bound is strongly influenced by the state’s purity factor, with the former being more robust at higher purity values and the latter at lower purity values. All the parameters impact entropic uncertainty, however, the mixedness of the state is noticed to greatly alter the generation of quantum memory. Besides, PL noise caused Markovian behavioral dynamics, and the RT noise allowed non-Markovian dynamics, while the latter remains more resourceful for the quantum correlations preservation and entropic uncertainty suppression. We also demonstrate how to model longer quantum correlations and provide optimal parameter settings for suppressing the dephasing and entropic uncertainty effects.
Abstract One of the fundamental arguments in quantum information theory is the uncertainty principle. According to this principle, two incompatible observables cannot be measured with high precision at the same time. In this work, we will use the entropic uncertainty relation in the presence of quantum memory. Considering a dissipative environment, the effects of the detuning between the transition frequency of a quantum memory and the center frequency of a cavity on entropic uncertainty bound and the quantum correlation between quantum memory and measured particle will be studied. It is shown that by increasing the detuning, quantum correlation is maintained. As a result, due to the inverse relationship between the uncertainty bound and quantum correlations, the measurement results are guessed more accurately.
One of the fundamental arguments in quantum information theory is the uncertainty principle. In accordance with this principle, two incompatible observables cannot be measured with high precision at the same time. In this work, we will use the entropic uncertainty relation in the presence of quantum memory. Considering a dissipative environment, the effects of the detuning between the transition frequency of a quantum memory and the center frequency of a cavity on entrpic uncertainty bound and quantum correlation between quantum memory and measured particle will be studied. It is shown that by increasing the detuning, quantum correlation is maintained. As a result, due to the inverse relationship between the uncertainty bound and quantum correlation, the measurement results is guessed more accurately.
Based on the time-convolutionless master-equation approach, the entropic uncertainty in the presence of quantum memory is investigated for a two-atom system in two dissipative cavities. We find that the entropic uncertainty can be controlled by the non-Markovian effect and the atom-cavity coupling. The results show that increasing the atom-cavity coupling can enlarge the oscillating frequencies of the entropic uncertainty and can decrease the minimal value of the entropic uncertainty. Enhancing the non-Markovian effect can reduce the minimal value of the entropic uncertainty. In particular, if the atom-cavity coupling or the non-Markovian effect is very strong, the entropic uncertainty will be very close to zero at certain time points, thus Bob can minimize his uncertainty about Alice's measurement outcomes.