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arXiv:1805.01859 · Physical Review A

Resilience of realism-based nonlocality to local disturbance

V. S. Gomes, R. M. Angelo

Published Jan 9, 2019• 22 citations
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Abstract

Employing a procedure called monitoring---via a completely positive trace preserving map that is able to interpolate between weak and projective measurements---we investigate the resilience of the recently proposed realism-based nonlocality to local and bilocal weak measurements. This analysis indicates realism-based nonlocality as the most ubiquitous and persistent form of quantumness within a wide class of quantum-correlation quantifiers. In particular, we show that the set of states possessing this type of quantumness forms a strict superset of symmetrically discordant states and, therefore, of discordant, entangled, steerable, and Bell-nonlocal states. Moreover, we find that, under monitoring, realism-based nonlocality is not susceptible to sudden death.

DOI
10.1103/physreva.99.012109

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Employing a procedure called monitoring---via a completely positive trace preserving map that is able to interpolate between weak and projective measurements---we investigate the resilience of the recently proposed realism-based nonlocality to local and bilocal weak measurements. This analysis indicates realism-based nonlocality as the most ubiquitous and persistent form of quantumness within a wide class of quantum-correlation quantifiers. In particular, we show that the set of states possessing this type of quantumness forms a strict superset of symmetrically discordant states and, therefore, of discordant, entangled, steerable, and Bell-nonlocal states. Moreover, we find that, under monitoring, realism-based nonlocality is not susceptible to sudden death.
From an operational criterion of physical reality, a quantifier of realism-based nonlocality was recently introduced for two-part quantum states. This measure has been shown to capture aspects that are rather different from Bell nonlocality. Here we take a step further and introduce a tripartite realism-based nonlocality quantifier. We show that this measure reduces to genuine tripartite entanglement for a certain class of pure tripartite states and manifests itself in correlated mixed states even in the absence of quantum correlations. A case study for noisy Greenberger-Horne-Zeilinger (GHZ) and WWW states points out the existence of scenarios where the realism-based nonlocality is monogamous.
Based on a recently proposed model of physical reality and an underlying criterion of nonlocality for contexts [A. L. O. Bilobran and R. M. Angelo, Europhys. Lett. 112, 40005 (2015)], we introduce a quantifier of realism-based nonlocality for bipartite quantum states, a concept that is profoundly different from Bell nonlocality. We prove that this measure reduces to entanglement for pure states, thus being free of anomalies in arbitrary dimensions, and identify the class of states with null realism-based nonlocality. Then we show that such a notion of nonlocality can be positioned in a low level within the hierarchy of quantumness quantifiers, meaning that it can occur even for separable states. These results open a different perspective for nonlocality studies.
From the premise that an observable is real after it is measured, we envisage a tomography-based protocol that allows us to propose a quantifier for the degree of indefiniteness of an observable given a quantum state. Then, we find that the reality of an observable can be inferred locally only if this observable is not quantumly correlated with an informer. In other words, quantum discord precludes Einstein's notion of separable realities. Also, by monitoring changes in the reality of a local observable upon measurements on a remote system, we are led to define a measure of nonlocality. Proved upper bounded by discordlike correlations and requiring indefiniteness as a basic ingredient, our measure signals nonlocality even for separable states, thus revealing nonlocal aspects that are not captured by Bell inequality violations.
Different nonlocal quantum correlations of entanglement, steering and Bell nonlocality are defined with the help of local hidden state and local hidden variable models. Considering their unique roles in quantum information processing, it is of importance to understand the individual nonlocal quantum correlation as well as their relationship. Here, we investigate the effects of amplitude damping decoherence on different nonlocal quantum correlations. In particular, we have theoretically and experimentally shown that the entanglement sudden death phenomenon is distinct from those of steering and Bell nonlocality. In our scenario, we found that all the initial states present sudden death of steering and Bell nonlocality, while only some of the states show entanglement sudden death. These results suggest that the environmental effect can be different for different nonlocal quantum correlations and, thus, it provides distinct operational interpretations of different quantum correlations.
We investigate quantum correlations in a hybrid qubit-qutrit system subject to both axial and planar single-ion anisotropies, dipolar spin-spin interactions, and Dzyaloshinskii-Moriya (DM) coupling. Using Negativity, Measurement-Induced Non-locality (MIN), Uncertainty-Induced Nonlocality (UIN), and Bell nonlocality (as quantified by the CHSH inequality) as measures, we analyze the interplay between anisotropy parameters, magnetic fields, and temperature on the survival of quantum correlations. Our results demonstrate that Bell nonlocality and entanglement (Negativity) are highly sensitive to temperature and anisotropy, exhibiting sudden death under thermal noise, whereas MIN and UIN are significantly more robust. In particular, these discord-like and information-theoretic measures provide the largest baseline and persist even in parameter regions where entanglement vanishes, highlighting their suitability as a quantumness witness in realistic conditions. Notably, our Bell nonlocality study is tailored to the asymmetric qubit-qutrit setting by exploiting a recently developed qubit-qudit CHSH maximization framework. However, Bell nonlocality is confirmed to be the most fragile, surviving only in narrow parameter windows at low temperature. A key finding of this work is that we observe the fragility hierarchy: Bell nonlocality ⊆\subseteq⊆ Negativity ⊆\subseteq⊆ UIN(MIN) in the qubit-qutrit setting. These results provide deeper insight into the relative robustness of distinct quantum resources in anisotropic qubit-qutrit models, suggesting that quantum discord-like measures, such as MIN and UIN, may serve as more practical resources than entanglement for quantum information tasks in thermally active spin systems.