Genuine Nonlocality Research Articles

The maximal violation of the Svetlichny inequality for “X” states and the extended GHZ states

For a quantum system, violation of a Svetlichny inequality indicates the existence of genuine nonlocality. Through the same mathematical analysis approach, we derive the analytical expressions of the maximal violation of the Svetlichny inequality for certain three-qubit pure states and mixed “X” states. These pure states represented in the five-parameter form belong to extended GHZ states. It is convenient to use the obtained expression to distinguish the genuine nonlocal states in these states. We also obtain the analytical expression of the maximal violation of Svetlichny inequality for a subclass of four-qubit “X” states. We show the application potentiality of these expressions by designing two schemes where quantum resources are converted from less qubits “X” states to more qubits “X” states.

Minimum detection efficiencies for loophole-free genuine nonlocality tests

Minimum detection efficiencies for loophole-free genuine nonlocality tests

Tripartite Svetlichny test with measurement dependence

The Bell test, as an important method for detecting nonlocality, is widely used in device-independent quantum information processing tasks. The security of these tasks is based on an assumption called measurement independence. Since this assumption is difficult to be guaranteed in practical Bell tests, it is meaningful to consider the effect of reduced measurement independence (i.e., measurement dependence) on Bell tests. Some research studies have shown that nonlocality can be detected even if measurement dependence exists. However, the relevant results are all based on bipartite Bell tests, and the results for multipartite Bell tests are still missing. In this paper, we explore this problem in the tripartite Svetlichny test. By considering flexible lower and upper bounds on the degree of measurement dependence, we obtain the relation among measurement dependence, guessing probability, and the maximal value of Svetlichny inequality. Our results reveal the case in which genuine nonlocality is nonexistent; at this point, the outcomes of the Bell test cannot be applied in device-independent quantum information processing tasks.

Distinguishability-based genuine nonlocality with genuine multipartite entanglement

Distinguishability-based genuine nonlocality with genuine multipartite entanglement

Sharing tripartite nonlocality sequentially by arbitrarily many independent observers

Bipartite entangled states whose violations of the Clauser-Horne-Shimony-Holt Bell inequality can be observed by a single Alice and arbitrarily many sequential Bobs exist [Brown and Colbeck, Phys. Rev. Lett. 125, 090401 (2020)]. Here we consider their analogs for tripartite systems: a tripartite entangled state is shared among Alice, Bob, and multiple Charlies. The first Charlie measures his qubit and then passes his qubit to the next Charlie, who measures again with other measurements, and so on. The goal is to maximize the number of Charlies that can observe some kind of nonlocality with the single Alice and Bob. It has been shown that at most two Charlies can share genuine nonlocality of the Greenberger-Horne-Zeilinger state via the violation of the Svetlichny inequality with Alice and Bob [S. Saha et al., Quantum Inf. Process. 18, 42 (2019); Zhang and Fei, Phys. Rev. A 103, 032216 (2021)]. In this work, we show that arbitrarily many Charlies can have standard nonlocality (via violations of the Mermin inequality) and some other kind of genuine nonlocality (which is known as genuinely nonsignal nonlocality) with a single Alice and single Bob.

Detection of the genuine non-locality of any three-qubit state

It is known that the violation of Svetlichny inequality by any three-qubit state described by the density operator ρABC witness the genuine non-locality of ρABC. But it is not an easy task as the problem of showing the genuine non-locality of any three-qubit state reduces to the problem of a complicated optimization problem. Thus, the detection of genuine non-locality of any three-qubit state may be considered a challenging task. Therefore, we have taken a different approach and derived the lower and upper bound of the expectation value of the Svetlichny operator with respect to any three-qubit state to study this problem. The expression of the obtained bounds depends on whether the reduced two-qubit entangled state is detected by the CHSH witness operator or not. It may be expressed in terms of the following quantities such as (i) the eigenvalues of the product of the given three-qubit state and the composite system of single qubit maximally mixed state and reduced two-qubit state and (ii) the non-locality of reduced two-qubit state. We then achieve the inequality whose violation may detect the genuine non-locality of any three-qubit state. A few examples are cited to support our obtained results. Lastly, we discuss its possible implementation in the laboratory.

Unextendible product operator basis

Quantum nonlocality is associated with the local indistinguishability of orthogonal states. Unextendible product basis (UPB), a widely used tool in quantum information, exhibits nonlocality, which is the powerful resource for quantum information processing. In this work, we extend the definitions of nonlocality and genuine nonlocality from states to operators. We also extend UPB to the notions of unextendible product operator basis, unextendible product unitary operator basis (UPUOB), and strongly UPUOB. We construct their examples and show the nonlocality of some strongly UPUOBs under local operations and classical communications. We study the phenomenon of these operators acting on quantum states. As an application, we distinguish the two-dimensional strongly UPUOB, which only consumes three ebits of entanglement. Our results imply that such UPUOBs exhibit nonlocality as UPBs, and the distinguishability of them requires entanglement resources.

Multiparty orthogonal product states with minimal genuine nonlocality

Nonlocality without entanglement and its subsequent generalizations offer deep information-theoretic insights and subsequently find several useful applications. The concept of a genuinely nonlocal set of product states emerges as a natural multipartite generalization of this phenomenon. The existence of such sets eventually raises the problem concerning their entanglement-assisted discrimination. Here, we construct examples of genuinely nonlocal product states for an arbitrary number of parties. The strength of genuine nonlocality of these sets can be considered minimal as their perfect discrimination is possible with entangled resources residing in Hilbert spaces having the smallest possible dimensions. Our constructions lead to fully separable measurements that are impossible to implement even if all but one party come together. Furthermore, they also provide the opportunity to compare different multipartite states that otherwise are incomparable under single copy local manipulation.

Local distinguishability based genuinely quantum nonlocality without entanglement

Recently, Halder et al (2019 Phys. Rev. Lett. 122 040403) proposed the concept of strong nonlocality without entanglement: an orthogonal set of fully product states in multipartite quantum systems that is locally irreducible for every bipartition of its subsystems. Due to the complexity of the problem, most results are limited to tripartite systems. Here we consider a weaker form of nonlocality which is called local distinguishability based genuine nonlocality. A set of orthogonal multipartite quantum states is said to be genuinely nonlocal if it is locally indistinguishable for every bipartition of the subsystems. In this work, we study how to construct sets of orthogonal product states which are genuinely nonlocal. Firstly, we present a set of product states with simple structure in bipartite systems that is locally indistinguishable. After that, based on a simple observation, we present a general method to construct genuinely nonlocal sets of multipartite product states by using those sets that are genuinely nonlocal but with less parties. As a consequence, we obtain that genuinely nonlocal sets of fully product states exist in any L parties systems provided L ⩾ 3 and d i ⩾ 3 for all i.

Sharing quantum nonlocality and genuine nonlocality with independent observables

Recently the authors in [Phys. Rev. Lett. 125, 090401 (2020)] considered the following scenario: Alice and Bob each have half of a pair of entangled qubit state. Bob measures his half and then passes his part to a second Bob who measures again and so on. The goal is to maximize the number of Bobs that can have an expected violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality with the single Alice. By taking the maximally entangled pure two-qubit state as an example, it has been constructively proved that arbitrarily many independent Bobs can share the nonlocality with the single Alice. Here we demonstrate that arbitrarily many independent observers can share the nonlocality of a single arbitrary dimensional bipartite entangled but not necessary two-qubit entangled state. Further, taking the generalized GHZ states as an example, we show that at most two Charlies can share the genuine nonlocality of a single generalized GHZ state with an Alice and a Bob.

Tight upper bound on the quantum value of Svetlichny operators under local filtering and hidden genuine nonlocality

Nonlocal quantum correlations among the quantum subsystems play essential roles in quantum science. The violation of the Svetlichny inequality provides sufficient conditions of genuine tripartite nonlocality. We provide tight upper bounds on the maximal quantum value of the Svetlichny operators under local filtering operations, and present a qualitative analytical analysis on the hidden genuine nonlocality for three-qubit systems. We investigate in detail two classes of three-qubit states whose hidden genuine nonlocalities can be revealed by local filtering.

Violation of Svetlichny inequality in Triple Jaynes-Cummings Models

We study the genuine tripartite nonlocality of some qubit states in a triple JCM. In this model, each atom state (A, B or C) was initially prepared with an independent cavity (a, b or c). By using two kinds of GHZ-like states as the atomic initial states, we investigate the genuine tripartite nonlocality as the time evolutions for the non-interaction three-qubit subsystems. We also study the genuine tripartite nonlocality of the subsystems by using the Svetlichny inequality. For the subsystems of three atoms ABC and three cavity modes abc, we show that they are genuinely nonlocal at certain period intervals of time. The states of all the other inequivalent subsystems satisfy the Svetlichny inequality for two types of GHZ-like states.

Bell inequalities tailored to the Greenberger–Horne–Zeilinger states of arbitrary local dimension

In device-independent quantum information processing Bell inequalities are not only used as detectors of nonlocality, but also as certificates of relevant quantum properties. In order for these certificates to work, one very often needs Bell inequalities that are maximally violated by specific quantum states. Recently, in Salavrakos et al (2017 Phys. Rev. Lett. 119 040402) a general class of Bell inequalities, with arbitrary numbers of measurements and outcomes, has been designed, which are maximally violated by the maximally entangled states of two quantum systems of arbitrary dimension. In this work, we generalize these results to the multipartite scenario and obtain a general class of Bell inequalities maximally violated by the Greenberger–Horne–Zeilinger states of any number of parties and any local dimension. We then derive analytically their maximal quantum and nonsignaling values. We also obtain analytically the bound for detecting genuine nonlocality and compute the fully local bound for a few exemplary cases. Moreover, we consider the question of adapting this class of inequalities to partially entangled Greenberger–Horne–Zeilinger-like states for some special cases of low dimension and small number of parties. Through numerical methods, we find classes of inequalities maximally violated by these partially entangled states.

Bell correlation depth in many-body systems

While the interest in multipartite nonlocality has grown in recent years, its existence in large quantum systems is difficult to confirm experimentally. This is mostly due to the inadequacy of standard multipartite Bell inequalities to many-body systems: such inequalities usually rely on expectation values involving many parties and require an individual addressing of each party. In a recent work [J. Tura et al. Science 344, 6189 (2014)] some of us proposed simpler Bell inequalities overcoming such difficulties, opening the way for the detection of Bell correlations with trusted collective measurements through Bell correlation witnesses [R. Schmied et al. Science 352, 441 (2016)], hence demonstrating the presence of Bell correlations with assumptions on the statistics. Here, we address the question of assessing the number of particles sharing genuinely nonlocal correlations in a multipartite system. This endeavour is a priori challenging, as known Bell inequalities for genuine nonlocality suffer from the above shortcomings, plus a number of measurement settings scaling exponentially with the system size. We first show that most of these constraints drop once the witnesses corresponding to these inequalities are expressed: in systems where multipartite expectation values can be evaluated, these witnesses can reveal genuine nonlocality for an arbitrary number of particles with just two collective measurements. We then introduce a general framework focused on two-body Bell-like inequalities. We show that they also provide information about the number of particles that are genuinely nonlocal. Then, we characterize all such inequalities for a finite system size. We provide witnesses of Bell correlation depth $k\leq6$ for any number of parties, within experimental reach. A violation for depth $6$ is achieved with existing data from an ensemble of 480 atoms.

Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios

In the present work, we study tripartite quantum steering of quantum correlations arising from two local dichotomic measurements on each side in the two types of partially device-independent scenarios: $1$-sided device-independent scenario where one of the parties performs untrusted measurements while the other two parties perform trusted measurements and $2$-sided device-independent scenario where one of the parties performs trusted measurements while the other two parties perform untrusted measurements. We demonstrate that tripartite steering in the $2$-sided device-independent scenario is weaker than tripartite steering in the $1$-sided device-independent scenario by using two families of quantum correlations. That is these two families of quantum correlations in the $2$-sided device-independent framework detect tripartite entanglement through tripartite steering for a larger region than that in the $1$-sided device-independent framework. It is shown that tripartite steering in the $2$-sided device-independent scenario implies the presence of genuine tripartite entanglement of $2\times 2 \times 2$ quantum system, even if the correlation does not exhibit genuine nonlocality or genuine steering.

An approach for quantitatively analyzing the genuine tripartite nonlocality of general three-qubit states

Nonlocality is an important resource for quantum information processing. Genuine tripartite nonlocality, which is sufficiently confirmed by the violation of Svetlichny inequality, is a kind of more precious resource than the standard one. The genuine tripartite nonlocality is usually quantified by the amount of maximal violation of Svetlichny inequality. The problem of detecting and quantifying the genuine tripartite nonlocality of quantum states is of practical significance but still open for the case of general three-qubit quantum states. In this paper, we quantitatively investigate the genuine nonlocality of three-qubit states, which not only include pure states but also include mixed states. Firstly, we derive a simplified formula for the genuine nonlocality of a general three-qubit state, which is a function of the corresponding three correlation matrices. Secondly, we develop three properties of the genuine nonlocality which can help us to analyze the genuine nonlocality of complex states and understand the nature of quantum nonlocality. Further, we get analytical results of genuine nonlocality for two classes of three-qubit states which have special correlation matrices. In particular, the genuine nonlocality of generalized three-qubit GHZ states, which is derived by Ghose et al. (Phys. Rev. Lett. 102, 250404, 2009), and that of three-qubit GHZ-symmetric states, which is derived by Paul et al. (Phys. Rev. A 94, 032101, 2016), can be easily derived by applying the strategy and properties developed in this paper.

Improvement in device-independent witnessing of genuine tripartite entanglement by local marginals

We consider the problem of determining the presence of genuine multipartite entanglement through the violation of Mermin's Bell-type inequality (MI). Though the violation of MI cannot certify the presence of genuine nonlocality, but can certify genuine tripartite entanglement whenever the violation is strictly greater than $2\sqrt{2}$. Here we show that MI suffices as genuine entanglement witness even when its value is $2\sqrt{2}$ if at least two of the local marginal distributions are not completely random provided the local Hilbert space dimension of at least one of the sub-systems is two. Thus local marginals suffice as semi-device independent genuine entanglement witness. This is intriguing in a sense, as the local properties of a composite system can help to identify its global property. Furthermore, analyzing another quantity constructed from Mermin polynomials we show that genuine entanglement certification task for the correlations with MI violation equal to $2\sqrt{2}$ can actually be made fully device independent.

Freezing dynamics of genuine entanglement and loss of genuine nonlocality under collective dephasing

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 is lost in a finite time. We show the sensitivity of asymptotic states being genuinely entangled by mixing white noise.

Time-invariant entanglement and sudden death of nonlocality for multipartite systems under collective dephasing

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 point out that quantum states exhibiting time-invariant entanglement must live in both decoherence free subspace and in the subspaces orthogonal to it. The previous studies on this feature for two qubits can be recovered from our studies as a special case. We also study the nonlocality of quantum states under collective dephasing. We find that although genuine entanglement of quantum states may not change, however their nonlocality changes. We discuss the possibility of finite time end of genuine nonlocality.

Nonlocality of three-qubit Greenberger-Horne-Zeilinger–symmetric states

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 expressions of maximum violation value of most efficient Bell inequalities we obtain the conditions of standard nonlocality and genuine nonlocality of this class of states. Also relation between entanglement and nonlocality is discussed for this class of states. Interestingly, genuine entanglement of GHZ-symmetric states is necessary to reveal standard nonlocality. However, it is not sufficient to exploit the same.