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Chinese Physics B

Nonlocal advantage of quantum coherence in a dephasing channel with memory*

Ming‐Liang Hu, Yuhan Zhang, Heng Fan

Published Dec 1, 2020• 54 citations
Publisher

Abstract

We investigate nonlocal advantage of quantum coherence (NAQC) in a correlated dephasing channel modeled by the multimode bosonic reservoir. We obtain analytically the dephasing and memory factors of this channel for the reservoir having a Lorentzian spectral density, and analyze how they affect the NAQC defined by the l 1 norm and relative entropy. It is shown that the memory effects of this channel on NAQC are state-dependent, and they suppress noticeably the rapid decay of NAQC for the family of input Bell-like states with one excitation. For the given transmission time of each qubit, we also obtain the regions of the dephasing and memory factors during which there is NAQC in the output states.

DOI
10.1088/1674-1056/abcf4a

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Abstract We investigate the nonlocal advantage of quantum coherence (NAQC) for two qubits coupled via the Heisenberg interaction and embedded in their respective thermal and dephasing reservoirs. Unlike the case of two uncoupled qubits, we showed that in the presence of the Heisenberg interaction, the decay rate of the NAQC can be reduced and the strength of the NAQC can be enhanced for certain initial states. Moreover, the Heisenberg interaction of two spins can induce generation of NAQC from the initial product states, and the generated NAQC approaches asymptotically to its maximum with the increasing anisotropy of the Heisenberg interaction.
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Quantum coherence and nonlocality capture the nature of quantumness from different aspects. For the two-qubit states with a diagonal correlation matrix, we prove strictly a hierarchy between the nonlocal advantage of quantum coherence (NAQC) and Bell nonlocality by showing geometrically that the NAQC created on one qubit by local measurement on another qubit captures quantum correlation which is stronger than Bell nonlocality. For general states, our numerical results present strong evidence that this hierarchy may still hold. So the NAQC states form a subset of the states that can exhibit Bell nonlocality. We further propose a measure of NAQC that can be used for a quantitative study of it in bipartite states.
Abstract Quantum correlations in a state can be quantified from different aspects. The nonlocal advantage of quantum coherence (NAQC) captures quantum correlation stronger than entanglement and Bell nonlocality. We investigate the NAQC-type quantum correlation in the Heisenberg XY model and showed that both the anisotropy of the interaction between two spins and the external transverse magnetic field can serve as efficient parameters for tuning the NAQC-type quantum correlation. In particular, for the relative low temperature case there is a finite parameter region in which the strength of the NAQC-type quantum correlation is of about its maximum 1. We also found there are quantum states for which the NAQC-type quantum correlations defined by the l 1 norm of coherence and the relative entropy of coherence have a different ordering.
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By local measurements on party AAA of a system AB\mathit{AB}AB and classical communication between its two parties, one can achieve a nonlocal advantage of quantum coherence (NAQC) on party BBB. For the l1{l}_{1}l1​ norm of coherence and the relative entropy of coherence, we generalized the framework of NAQC for two qubits and derived the criteria which capture NAQC in the ($d\ifmmode\times\else\texttimes\fi{}d$)-dimensional states when ddd is a power of a prime. We also presented a framework for formulating NAQC and showed through explicit examples its capacity for capturing the NAQC states. Moreover, we proved that any bipartite state with NAQC is quantum entangled; thus the obtained criteria can also be used as an entanglement witness.