Nonlocality and quantum entanglement constitute two special aspects of the quantum correlations existing in quantum systems, which are of paramount importance in quantum-information theory. Traditionally, they have been regarded as identical (equivalent, in fact, for pure two qubit states, that is, {\it Gisin's Theorem}), yet they constitute different resources. Describing nonlocality by means of the violation of several Bell inequalities, we obtain by direct optimization those states of two qubits that maximally violate a Bell inequality, in terms of their degree of mixture as measured by either their participation ratio $R=1/Tr(ρ^2)$ or their maximum eigenvalue $λ_{max}$. This optimum value is obtained as well, which coincides with previous results. Comparison with entanglement is performed too. An example of an application is given in the XY model. In this novel approximation, we also concentrate on the nonlocality for linear combinations of pure states of two qubits, providing a closed form for their maximal nonlocality measure. The case of Bell diagonal mixed states of two qubits is also extensively studied. Special attention concerning the connection between nonlocality and entanglement for mixed states of two qubits is paid to the so called maximally entangled mixed states. Additional aspects for the case of two qubits are also described in detail. Since we deal with qubit systems, we will perform an analogous study for three qubits, employing similar tools. Relation between distillability and nonlocality is explored quantitatively for the whole space of states of three qubits. We finally extend our analysis to four qubit systems, where nonlocality for generalized Greenberger-Horne-Zeilinger states of arbitrary number of parties is computed.
Quantum nonlocality can be revealed "via local contextuality" in qudit-qudit entangled systems with $d > 2$, that is, through the violation of inequalities containing Alice-Bob correlations that admit a local description, and Alice-Alice correlations (between the results of sequences of measurements on Alice's subsystem) that admit a local (but contextual) description. A fundamental question to understand the respective roles of entanglement and local contextuality is whether nonlocality via local contextuality exists when the parties have only qubit-qubit entanglement. Here we respond affirma…
We discuss the relation between entanglement and nonlocality in the hidden nonlocality scenario. Hidden nonlocality signifies nonlocality that can be activated by applying local filters to a particular state that admits a local hidden-variable model in the Bell scenario. We present a fully-biseparable three-qubit bound entangled state with a local model for the most general (non-sequential) measurements. This proves for the first time that bound entangled states can admit a local model for general measurements. We furthermore show that the local model breaks down when suitable local filters ar…
We study the relations between quantum coherence and quantum nonlocality, genuine quantum entanglement and genuine quantum nonlocality. We show that the coherence of a qubit state can be converted to the nonlocality of two-qubit states via incoherent operations. The results are also generalized to qudit case. Furthermore, rigorous relations between the quantum coherence of a single-partite state and the genuine multipartite quantum entanglement, as well as the genuine three-qubit quantum nonlocality are established.
Incompatibility and nonlocality are not only of foundational interest but also act as important resources for quantum information theory. In the Clauser-Horne-Shimony-Holt (CHSH) scenario, the incompatibility of a pair of observables is known to be equivalent to Bell nonlocality. Here, we investigate these notions in the context of qubit channels. The Bell-CHSH inequality has a greater perspective--compared to any genuine tripartite nonlocality scenario--while determining the interplay between nonlocality breaking qubit channels and incompatibility breaking qubit channels. In the Bell-CHSH sce…
Nonlocality and entanglement are not only the fundamental characteristics of quantum mechanics but also important resources for quantum information and computation applications. Exploiting the quantitative relationship between the two different resources is of both theoretical and practical significance. The common choice for quantifying the nonlocality of a two-qubit state is the maximal violation of the Clauser-Horne-Shimony-Holt inequality. That for entanglement is entanglement of formation, which is a function of the concurrence. In this paper, we systematically investigate the quantitativ…
Entanglement and Bell nonlocality are used to describe quantum inseparabilities. Bell-nonlocal states form a strict subset of entangled states. A natural question arises concerning how much territory Bell nonlocality occupies entanglement for a general two-qubit entangled state. In this work, we investigate the relation between entanglement and Bell nonlocality by using lots of randomly generated two-qubit states, and give out a constraint inequality relation between the two quantum resources. For studying the upper or lower boundary of the inequality relation, we discover maximally (minimally…
We study the Bell nonlocality of high dimensional quantum systems based on quantum entanglement. A quantitative relationship between the maximal expectation value B of Bell operators and the quantum entanglement concurrence C is obtained for even dimension pure states, with the upper and lower bounds of B governed by C.
We study the entanglement and the Bell nonlocality of a coupled two-qubit system, in which each qubit is coupled with one individual environment. We study how the nonequilibrium environments (with different temperatures or chemical potentials) influence the entanglement and the Bell nonlocality. The nonequilibrium environments can have constructive effects on the entanglement and the Bell nonlocality. Nonequilibrium thermodynamic cost can sustain the thermal energy or particle current and enhance the entanglement and the Bell nonlocality. However, the nonequilibrium conditions (characterized b…
We investigate the dynamics of entanglement and nonlocality for multipartite quantum systems under collective dephasing. Using an exact and computable measure for genuine entanglement, we demonstrate the possibility of a non trivial phenomenon of time-invariant entanglement for multipartite quantum systems. We find that for four qubits, there exist quantum states, which are changing continously nevertheless their genuine entanglement remains constant. Based on our numerical results, we conjecture that there is no evidence of time-invariant entanglement for quantum states of three qubits. We po…
In this note, we study Cabello's nonlocality argument (CNA) for three-qubit systems configured in the generalized GHZ state. For this class of states, we show that CNA runs for almost all entangled ones, and that the maximum probability of success of CNA is 14% (approx.), which is attained for the maximally entangled GHZ state. This maximum probability is slightly higher than that achieved for the standard Hardy's nonlocality argument (HNA) for three qubits, namely 12.5%. Also, we show that the success probability of both HNA and CNA for three-qubit systems can reach a maximum of 50% in the fr…
Entanglement, quantum steering and nonlocality are distinct quantum correlations which are the resources behind various of quantum information and quantum computation applications. However, a central question of determining the precise quantitative relation among them is still unresolved. Here, we present a mapping criterion between Bell nonlocality and quantum steering in bipartite qudit-qubit system, as well as a mapping criterion between quantum steering and quantum entanglement in bipartite qubit-qudit system, starting from the fundamental concepts of quantum correlations. Precise quantita…
Strong quantum nonlocality was introduced recently as a stronger manifestation of nonlocality in multipartite systems through the notion of local irreducibility in all bipartitions. Known existence results for sets of strongly nonlocal orthogonal states are limited to product states. In this paper, based on the Rubik's cube, we give the first construction of such sets consisting of entangled states in $d\otimes d\otimes d$ for all $d\geq 3$. Consequently, we answer an open problem given by Halder \emph{et al.} [Phys. Rev. Lett. \textbf{122}, 040403 (2019)], that is, orthogonal entangled bases …
Quantum nonlocality without entanglement is a fantastic phenomenon in quantum theory. This kind of quantum nonlocality is based on the task of local discrimination of quantum states. Recently, Bandyopadhyay and Halder [Phys. Rev. A 104, L050201 (2021)] studied the problem: is there any set of orthogonal states which can be locally distinguishable, but under some orthogonality preserving local measurement, each outcome will lead to a locally indistinguishable set. We say that the set with such property has hidden nonlocality. Moreover, if such phenomenon can not arise from discarding subsystems…
We study the dynamics of genuine multipartite entanglement for quantum systems upto four qubits interacting with general collective dephasing process. Using a computable entanglement monotone for multipartite systems, we observe the feature of freezing dynamics of genuine entanglement for three and four qubits entangled states. We compare the dynamics with that of random states and find that most states exibit this feature. We then study the effects of collective dephasing on genuine nonlocality and find out that although quantum states remain genuinely entangled yet their genuine nonlocality …
Einstein-Podolsky-Rosen steering is a form of inseparability in quantum theory commonly acknowledged to be intermediate between entanglement and Bell nonlocality. However, this statement has so far only been proven for a restricted class of measurements, namely projective measurements. Here we prove that entanglement, one-way steering, two-way steering and nonlocality are genuinely different considering general measurements, i.e. single round positive-operator-valued-measures. Finally, we show that the use of sequences of measurements is relevant for steering tests, as they can be used to reve…
Analysis of Quantum Correlation in Successive Spin Measurements, Classical Communication of Spin $S$ Singlet States and Quantum Nonlocality of two Qubit Entangled States
We examine the possibilities of non-trivial phenomena of time-invariant entanglement and freezing dynamics of entanglement for qutrit-qutrit quantum systems. We find no evidence for time-invariant entanglement, however, we do observe that quantum states freeze their entanglement after decaying for some time. It is interesting that quantum states are changing whereas their entanglement remains constant. We find that the combined action of decoherence free subspaces and subspaces where quantum states decay, facilitate this phenomenon. This study is an extension of similar phenomena observed for …
Mixed states appear naturally in experiment over pure states. So for studying different notions of nonlocality and their relation with entanglement in realistic scenarios, one needs to consider mixed states. In a recent article [Phys. Rev. Lett. \textbf{108}, 020502 (2012)], a complete characterization of entanglement of an entire class of mixed three qubit states with the same symmetry as Greenberger-Horne-Zeilinger state known as GHZ-symmetric states, has been achieved. In this paper we investigate different notions of nonlocality of the same class of states. By finding the analytical expres…
Lower-bounding entanglement with nonlocality in a general Bell's scenario
University of Science and Technology of China（中国科学技术大学）；Hefei National Research Center for Physical Sciences at the Microscale（合肥微尺度物质科学国家研究中心）；School of Physical Sciences, University of Science and Technology of China（中国科学技术大学物理科学学院）；School of Physics and Optoelectronics Engineering, Anhui University（安徽大学物理与光电工程学院）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
Determining relationships between different types of quantum correlations in open composite quantum systems is important since it enables the exploitation of a type by knowing the amount of another type. We here review, by giving a formal demonstration, a closed formula of the Bell function, witnessing nonlocality, as a function of the concurrence, quantifying entanglement, valid for a system of two noninteracting qubits initially prepared in extended Werner-like states undergoing any local pure-dephasing evolution. This formula allows for finding nonlocality thresholds for the concurrence dep…
Strong nonlocality based on local distinguishability is a stronger form of quantum nonlocality recently introduced in multipartite quantum systems: an orthogonal set of multipartite quantum states is said to be of strong nonlocality if it is locally irreducible for every bipartition of the subsystems. Most of the known results are limited to sets with product states. Shi et al. presented the first result of strongly nonlocal entangled sets in [Phys. Rev. A 102, 042202 (2020)] and there they questioned the existence of strongly nonlocal set with genuine entanglement. In this work, we relate the…
While all bipartite pure entangled states are known to generate correlations violating a Bell inequality, and are therefore nonlocal, the quantitative relation between pure-state entanglement and nonlocality is poorly understood. In fact, some Bell inequalities are maximally violated by non-maximally entangled states and this phenomenon is also observed for other operational measures of nonlocality. In this work, we study a recently proposed measure of nonlocality defined as the probability that a pure state displays nonlocal correlations when subjected to random measurements. We first prove t…
