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arXiv:1802.03540 · Physical Review A

Hierarchy of the nonlocal advantage of quantum coherence and Bell nonlocality

Ming‐Liang Hu, Xiaomin Wang, Heng Fan

Published Sep 17, 2018• 88 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.98.032317

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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.
Nonlocal advantage of quantum coherence (NAQC) based on coherence complementarity relations is generally viewed as a stronger nonclassical correlation than Bell nonlocality. An arbitrary two-qubit state with NAQC must be an entangled state, which demonstrates that the criterion of NAQC can also be regarded as an entanglement witness. In this paper, we experimentally investigate the NAQC for Bell-diagonal states with high fidelity in an optics-based platform. We perform local measurements on a subsystem in three mutually unbiased bases and reconstruct the density matrices of the measured states by a quantum state tomography process. By analyzing characteristics of the l1{l}_{1}l1​ norm, relative entropy, and skew information of coherence with parameters of quantum states, NAQC for the quantum states is accurately captured, and it shows that our experimental results are well compatible with the theoretical predictions. Our results have shown that NAQC could be a new kind of entanglement witness and a useful physical resource for quantum information processing.
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.
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.
Abstract The non-local advantage of quantum coherence (NAQC) is regarded as a quantum correlation, which can be reflected by the violation of a set of inequalities based on various coherence measures. In this work, we explore the NAQC and Bell nonlocality (BN) in a two-qubit Heisenberg XYZ model. The results show that one can capture the BN in the case of both anti-ferromagnetism and ferromagnetism. By contrast, the NAQC cannot be achieved in the ferromagnetism case if the magnetic field is strong. Increases of inhomogeneity and temperature give rise to reductions of the NAQC and BN, and the achievement of the NAQC at high inhomogeneity or temperatures becomes very difficult. Also, the NAQC and BN strengthen with an increase of the mean coupling coefficient. A strong mean coupling coefficient leads to the freezing of the NAQC and BN when the inhomogeneity is low. The enhancement of the magnetic field can result in the fact that the NAQC and BN experience four processes, including reduction, sudden death, revival, and reduction. Additionally, the BN is easier to capture than the NAQC. Furthermore, we focus our attention on controlling the NAQC and BN via a local filtering operation. The results demonstrate that the operation can effectively strengthen the NAQC and BN, and can also help us to control the NAQC and BN in the Heisenberg XYZ chain.
Quantum imaginarity is a distinct resource in quantum information theory, yet its nonlocal properties have not been fully explored. Here, we report an experimental study of the nonlocal advantage of quantum imaginarity (NAQI), in which local measurements on one subsystem can steer the average imaginarity of the conditional states of the other subsystem beyond the corresponding classical bound. The l1l_1l1​-norm of imaginarity inequality is adopted as an experimentally accessible witness. A hybrid optimization algorithm that combines a genetic algorithm with sequential quadratic programming is developed to avoid local optima and accelerate the search for optimal measurement settings. Using polarization-encoded photonic qubits, we prepare two classes of two-qubit Bell-diagonal states and experimentally characterize the imaginarity of the conditional states following local measurements. Clear violations of the l1l_1l1​-norm of imaginarity inequality are observed, providing an experimental certification of NAQI. We further investigate the relationship among NAQI, the nonlocal advantage of quantum coherence (NAQC), and Bell nonlocality based on their respective inequality criteria. For the two-qubit Werner states considered in this work, the regions of states that violate the respective criteria satisfy DNAQC⊂DNAQI⊂DBN\mathcal{D}_{\rm NAQC}\subset\mathcal{D}_{\rm NAQI}\subset\mathcal{D}_{\rm BN}DNAQC​⊂DNAQI​⊂DBN​. Our work provides an experimental realization of NAQI and a comparison of different forms of quantum nonclassicality in a photonic platform.
Coherences in mutually unbiased bases of states of an isolated quantum system follow a complementarity relation. The nonlocal advantage of quantum coherence (NAQC), defined in a bipartite scenario, is a situation in which the average quantum coherences of the ensembles of one subsystem, effected by a measurement performed on the other subsystem, violate the complementarity relation. We analyze two criteria to detect NAQC for bipartite quantum states. We construct a more generalized version of the criterion to detect NAQC that is better than the standard criterion as it can capture more states exhibiting NAQC. We prove the local unitary invariance of these NAQC criteria. Further on, we focus on investigating the monogamy properties of NAQC in the tripartite scenario. We check for monogamy of NAQC from two perspectives, differentiated by whether or not the nodal observer in the monogamy relation performs the measurement for the nonlocal advantage. We find in particular that in the case where the nodal observer does not perform the measurement, a strong monogamy relation---an exclusion principle---is exhibited by NAQC.