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arXiv:1905.06814 · Physical Review A

Experimental investigation of the nonlocal advantage of quantum coherence

Zhiyong Ding, Huan Yang, Hao Yuan, Dong Wang, Jie Yang, Ye Liu

Published Aug 8, 2019• 45 citations
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Abstract

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 ${l}_{1}$ 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.

DOI
10.1103/physreva.100.022308

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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.
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.
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.
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) or steerability of local quantum coherence is a strong nonlocal resource based on coherence complementarity relations. In this work, we provide an upper bound on the number of observers who can independently steer the coherence of the observer in the other wing in a scenario where half of an entangled pair of spin-12\frac{1}{2}21​ particles is shared between a single observer (Bob) in one wing and several observers (Alices) on the other, who can act sequentially and independently of each other. We consider one-parameter dichotomic POVMs for the Alices and mutually unbiased basis in which Bob measures coherence in the case of the maximally entangled bipartite qubit state. We show that not more than two Alices can exhibit NAQC when the l1{l}_{1}l1​ norm of coherence measure is probed, whereas for two other measures of coherence, only one Alice can reveal NAQC within the same framework.
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.