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Laser Physics Letters

Quantum-memory-assisted entropic uncertainty, teleportation, and quantum discord under decohering environments

Mohammad Reza Pourkarimi, Saeed Haddadi

Published Jan 24, 2020• 47 citations
Publisher

Abstract

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.

DOI
10.1088/1612-202x/ab6a15

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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 We investigate thermal quantum correlations and the entropic uncertainty relation in the presence of quantum memory under two kinds of two-qubit spin squeezing models, namely the one-axis twisting model and two-axis countertwisting model. We provide the analytical expressions of quantum correlations and the entropic uncertainty relation in the ground state for these two models and we find a simple relationship between quantum discord and entropic uncertainty. It is found that there is a fully anti-correlated relationship between quantum correlations and entropic uncertainty. Also, the maximal quantum correlation and minimal uncertainty can be achieved when the spin squeezing parameters are large enough. Accordingly, these results may be significant in practical goals in which the maximum quantum correlation and minimum uncertainty are required such as in quantum key distribution and quantum computing.
By using the quantum-memory-assisted entropic uncertainty relation (EUR), we derive a computable tight upper bound for quantum discord, which applies to an arbitrary bipartite state. Detailed examples show that this upper bound is tighter than other known bounds in a wide regime. Furthermore, we show that for any tripartite pure state, the quantum-memory-assisted EUR imposes a constraint on the shareability of quantum correlations among the constituent parties. This conclusion amends the well-accepted result that quantum discord is not monogamous.
The entropic uncertainty relation imposes a limit on the accuracy of measurement outcomes of two conjugate observables, which can be reduced in the presence of quantum memory. We theoretically study the dynamical behaviors of the quantum-memory-assisted entropic uncertainty relation for a bipartite system under local nonequilibrium dephasing environments and a common nonequilibrium dephasing environment. Particularly, we study the influence of the competition between nonequilibrium and non-Markovianity in controlling the entropic uncertainty bound (EUB) in weak- and strong-coupling regimes. We find that the nonequilibrium nature renders a promising protocol to efficiently harness the EUB in both regimes without requiring any operations on the main system. Further, we reveal that the EUB can be significantly reduced in a common bath case compared to the case of local baths. Moreover, we elucidate the primary factor responsible for governing the dynamical behaviors of EUB by examining the interplay between quantum discord and the minimal missing information about the particle to be measured. In addition, we investigate the state preparation and measurement choice (SPMC) condition in both environmental setups with weak- and strong-coupling regimes. Remarkably, we show that the SPMC condition does not hold in the common environment scenario.