We present a generic method to construct a product basis exhibiting Nonlocality Without Entanglement with $n$ parties each holding a system of dimension at least $n-1$. This basis is generated via a quantum circuit made of control-Discrete Fourier Transform gates acting on the computational basis. The simplicity of our quantum circuit allows for an intuitive understanding of this new type of nonlocality. We also show how this circuit can be used to construct Unextendible Product Bases and their associated Bound Entangled States. To our knowledge, this is the first method which, given a general Hilbert space $\bigotimes_{i=1}^n {\cal H}_{d_i}$ with $d_i\le n-1$, makes it possible to construct (i) a basis exhibiting Nonlocality Without Entanglement, (ii) an Unextendible Product Basis, and (iii) a Bound Entangled state.
Genuine multipartite entanglement has been found in some spin chain systems. However, genuine multipartite nonlocality, which is much rarer than genuine multipartite entanglement, has never been found in any spin chain system. Here we present genuine multipartite nonlocality in a spin chain system. After introducing the definition of genuine multipartite nonlocality and a multipartite Bell-type inequality, we construct a group of joint measurements for the inequality in a one-dimensional ferromagnetic $N$-qubit chain with nearest-neighbor XXZ interaction, and many violations to the inequality …
The relation between entanglement and nonlocality is discussed in the case of multipartite quantum systems. We show that, for any number of parties, there exist genuinely multipartite entangled states which admit a fully local hidden variable model, i.e. where all parties are separated. Hence, although these states are entangled in the strongest possible sense, they cannot lead to Bell inequality violation considering general non-sequential local measurements. Then, we show that the nonlocality of these states can nevertheless be activated using sequences of local measurements, thus revealing …
We propose a hierarchy of Bell-type inequalities for arbitrary $n$-partite systems that identify the different degrees of nonlocality ranging from standard to genuine multipartite nonlocality. After introducing the definition of nonsignaling $m$-locality, we show that the observed joint probabilities in any nonsignaling $m$-local realistic models should satisfy the $(m-1)$-th Bell-type inequality. When $m=2$ the corresponding inequality reduces to the one shown in [Phys. Rev. Lett. 112, 140404 (2014)] whose violation indicates genuine multipartite nonlocality, and when $m=n$ the corresponding …
Nonlocality swapping of bipartite binary correlated boxes can be realized by a \emph{coupler} ($χ$) in nonsignaling models. By studying the swapping process we find that the previous bipartite coupler can be applied to the swapping of two multipartite boxes, and then generate a multipartite box with more users than that of any of the boxes before swapping. Here quantum bound still appears in the scheme. The bipartite coupler also can be applied to a hybrid scheme of generating a multipartite extremal box from many PR boxes. As the analogue of multipartite entanglement swapping, we generalize t…
The Clauser-Horne-Shimony-Holt-type noncontextuality inequality and the Svetlichny inequality are derived from the Alicki-Van Ryn quantumness witness. Thus a connection between quantumness and quantum contextuality, and that between quantumness and genuine multipartite nonlocality, are established.
Quantum entanglement and nonlocality are inextricably linked. However, while entanglement is necessary for nonlocality, it is not always sufficient in the standard Bell scenario. We derive sufficient conditions for entanglement to give rise to genuine multipartite nonlocality in networks. We find that any network where the parties are connected by bipartite pure entangled states is genuine multipartite nonlocal, independently of the amount of entanglement in the shared states and of the topology of the network. As an application of this result, we also show that all pure genuine multipartite e…
While Bell nonlocality of a bipartite system is counter-intuitive, multipartite nonlocality in our many-body world turns out to be even more so. Recent theoretical study reveals in a theory-agnostic manner that genuine multipartite nonlocal correlations cannot be explained by any causal theory involving fewer-partite nonclassical resources and global shared randomness. Here we provide a Bell-type inequality as a test for genuine multipartite nonlocality in network by exploiting a matrix representation of the causal structure of a multipartite system. We further present experimental demonstrati…
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.
Wiseman and co-workers (Phys. Rev. Lett. 98, 140402, 2007) proposed a distinction between the nonlocality classes of Bell's nonlocality, steering and entanglement based on whether or not an overseer trusts each party in a bipartite scenario where they are asked to demonstrate entanglement. Here we extend that concept to the multipartite case and derive inequalities that progressively test for those classes of nonlocality, with different thresholds for each level. This framework includes the three classes of nonlocality above in special cases and introduces a family of others.
We introduce a multipartite extension of an information-theoretic distance first introduced in [Nature 341, 119 (1989)]. We use this new distance to derive entropic tests of multipartite nonlocality for three and for an arbitrary even number of qubits as well as a test of state-independent contextuality. In addition, we re-derive the tripartite Mermin inequality and a state-independent non-contextuality inequality by Cabello [Phys. Rev. Lett. 101, 210401 (2008)]. This suggests that the information-theoretic distance approach to multipartite nonlocality and state-independent contextuality can p…
As with entanglement, different forms of Bell nonlocality arise in the multipartite scenario. These can be defined in terms of relaxations of the causal assumptions in local hidden-variable theories. However, a characterisation of all the forms of multipartite nonlocality has until now been out of reach, mainly due to the complexity of generic multipartite causal models. Here, we employ the formalism of Bayesian networks to reveal connections among different causal structures that make a both practical and physically meaningful classification possible. Our framework holds for arbitrarily many …
The behaviour under particle loss of entanglement and nonlocality is investigated in multipartite quantum systems. In particular, we define a notion of persistency of nonlocality, which leads to device-independent tests of persistent entanglement. We investigate the persistency of various classes of multipartite quantum states, exhibiting a variety of different behaviours. A particular attention is devoted to states featuring maximal persistency. Finally we discuss a link between the symmetry of a state and its persistency, illustrating the fact that too much symmetry reduces the strength of c…
In this letter we propose a set of conditions on the joint probabilities as a test of genuine multipartite nonlocality without inequality. Our test is failed by all non-signaling local models in which even nonlocal correlations among some observables (not all) are allowed as long as these correlations respect the non-signaling principle. A pass of our test by a state therefore indicates that this state cannot be simulated by any non-signaling local models, i.e., the state exhibits genuine multipartite nonlocality. It turns out that all entangled symmetric n-qubit ($n \geq 3$) states pass our t…
Testing Genuine Multipartite Nonlocality via an Inflated Network with Multi-copy Entangled States
International Quantum Academy（国际量子科学院）；Southern University of Science and Technology（南方科技大学）；School of Information Science and Technology, Southwest Jiaotong University（西南交通大学信息科学与技术学院）；Hefei National Laboratory（合肥国家实验室）；School of Physics, Nankai University（南开大学物理学院）；School of Mathematical Sciences, Capital Normal University（首都师范大学数学科学学院）；Max-Planck-Institute for Mathematics in the Sciences（马克斯·普朗克科学研究所）
The Clauser-Horne-Shimony-Holt inequality was originally proposed as a Bell inequality to detect nonlocality in bipartite systems. However, it can also be used to certify the nonlocality of multipartite quantum states. We apply this to study the nonlocality of multipartite Greenberger-Horne-Zeilinger, W and graph states under local decoherence processes. We derive lower bounds on the critical local-noise strength tolerated by GHZ states before becoming local. In addition, for the whole noisy dynamics, we derive lower bounds on the corresponding nonlocal content for the three classes of states.…
Distinct from Bell's approach, Wigner had derived a form of local realist (LR) inequality which is quantum mechanically violated for a bipartite maximally entangled state. Subsequently, this approach was generalized to obtain a multipartite LR inequality. However, the violation of such generalised Wigner's inequality does not guarantee nonlocality between all possible different bipartitions of the multipartite system. In the present work, this limitation has been overcome by formulating a further generalisation of Wigner's approach through the derivation of a set of LR inequalities with respec…
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…
Local measurements on bipartite maximally entangled states can yield correlations that are maximally nonlocal, monogamous, and associated to fully random outcomes. This makes these states ideal for bipartite cryptographic tasks. Genuine-multipartite nonlocality constitutes a stronger notion of nonlocality that appears in the multipartite case. Maximal genuine-multipartite nonlocality, monogamy and full random outcomes are thus highly desired properties for multipartite correlations in intrinsically genuine-multipartite cryptographic scenarios. We prove that local measurements on Greenberger-Ho…
In this paper, we investigate the dynamics behaviors of genuine multipartite Einstein-Podolsky-Rosen steering (GMS) and genuine multipartite nonlocality (GMN), and explore how to recover the lost GMS and GMN under a mixed decoherence system. Explicitly, the decoherence system can be modeled by that a tripartite Werner-type state suffers from the non-Markovian regimes and one subsystem of the tripartite is under a non-inertial frame. The conditions for steerable and nonlocal states can be obtained with respect to the tripartite Werner-type state established initially. GMS and GMN are very fragi…
The construction of nonlocal sets of quantum states has attracted much attention in recent years. We first introduce two Lemmas related to the triviality of orthogonality-preserving local measurements. Then we propose a general construction of nonlocal set of $n(d-1)+1$ orthogonal product states in $(\mathbb{C}^{d})^{\otimes n}$. The sets of nonlocal orthogonal product states are also put forward for the multipartite quantum systems with arbitrary dimensions. Our novel construction gives rise to nonlocal sets of orthogonal product states with much less members and thus reveals the phenomenon o…
The generation and verification of genuine multipartite nonlocality (GMN) is of central interest for both fundamental research and quantum technological applications, such as quantum privacy. To demonstrate GMN in measurement data, the statistics are commonly postselected by neglecting undesired data. Until now, valid postselection strategies have been restricted to local postselection. A general postselection that is decided after communication between parties can mimic nonlocality, even though the complete data are local. Here, we establish conditions under which GMN is demonstrable even if …
Recently, Halder \emph{et al.} [S. Halder \emph{et al.}, Phys. Rev. Lett. \textbf{122}, 040403 (2019)] present two sets of strong nonlocality of orthogonal product states based on the local irreducibility. However, for a set of locally indistinguishable orthogonal entangled states, the remaining question is whether the states can reveal strong quantum nonlocality. Here we present a general definition of strong quantum nonlocality based on the local indistinguishability. Then, in $2 \otimes 2 \otimes 2$ quantum system, we show that a set of orthogonal entangled states is locally reducible but l…
We propose an optimal numerical test for genuine multipartite nonlocality based on linear programming. In particular, we consider two non-equivalent models of local hidden variables, namely the Svetlichny and the no-signaling bilocal model. While our knowledge concerning these models is well established for Bell scenarios involving two measurement settings per party, the general case based on an arbitrary number of settings is a considerably more challenging task and very little work has been done in this field. In this paper, we applied such general tests to detect and characterize genuine $n…
We present an exhaustive numerical analysis of violations of local realism by families of multipartite quantum states. As an indicator of nonclassicality we employ the probability of violation for randomly sampled observables. Surprisingly, it rapidly increases with the number of parties or settings and even for relatively small values local realism is violated for almost all observables. We have observed this effect to be typical in the sense that it emerged for all investigated states including some with randomly drawn coefficients. We also present the probability of violation as a witness o…
The nonlocal correlations of multipartite entangled states can be reproduced by a classical model if sufficiently many parties join together or if sufficiently many parties broadcast their measurement inputs. The maximal number m of groups and the minimal number k of broadcasting parties that allow for the reproduction of a given set of correlations quantify their multipartite nonlocal content. We show how upper-bounds on m and lower-bounds on k can be computed from the violation of the Mermin-Svetlichny inequalities. While n-partite GHZ states violate these inequalities maximally, we find tha…
We study the nonlocal properties of two-qubit maximally-entangled and N-qubit Greenberger-Horne-Zeilinger states under local decoherence. We show that the (non)resilience of entanglement under local depolarization or dephasing is not necessarily equivalent to the (non)resilience of Bell-inequality violations. Apart from entanglement and Bell-inequality violations, we consider also nonlocality as quantified by the nonlocal content of correlations, and provide several examples of anomalous behaviors, both in the bipartite and multipartite cases. In addition, we study the practical implications o…
Genuine multipartite nonlocality detection in graph states
Universiteit Leiden（莱顿大学）；Università degli Studi di Padova（帕多瓦大学）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Center for Quantum-Enabled Computing, Center for Theoretical Physics, Polish Academy of Sciences（波兰科学院理论物理中心量子赋能计算中心）
The celebrated Einstein-Podolsky-Rosen quantum steering has a complex structure in the multipartite scenario. We show that a naively defined criterion for multipartite steering allows, like in Bell nonlocality, for a contradictory effect whereby local operations could create steering seemingly from scratch. Nevertheless, neither in steering nor in Bell nonlocality has this effect been experimentally confirmed. Operational consistency is reestablished by presenting a suitable redefinition: there is a subtle form of steering already present at the start, and it is only exposed -- as opposed to c…
In a multipartite setting, it is possible to distinguish quantum states that are genuinely $n$-way entangled from those that are separable with respect to some bipartition. Similarly, the nonlocal correlations that can arise from measurements on entangled states can be classified into those that are genuinely $n$-way nonlocal, and those that are local with respect to some bipartition. Svetlichny introduced an inequality intended as a test for genuine tripartite nonlocality. This work introduces two alternative definitions of $n$-way nonlocality, which we argue are better motivated both from th…
Genuine multipartite nonlocality (GMN), the strongest form of multipartite nonlocality that describes fully collective nonlocal correlations among all experimental parties, can be observed when different distant parties each locally measure a particle from a shared entangled many-particle state. For the demonstration of GMN, the experimentally observed statistics are typically postselected: Events for which some parties do not detect a particle must be discarded. This coincidence postselection generally leads to the detection loophole that invalidates a proper nonlocality demonstration. In thi…
The maximally entangled state can be in a mixed state as well as the well-known pure state. Taking the negativity as a measure of entanglement, we study the entanglement dynamics of bipartite, mixed maximally entangled states (MMESs) in multipartite cavity-reservoir systems. It is found that the MMES can exhibit the phenomenon of entanglement sudden death, which is quite different from the asymptotic decay of the pure-Bell-state case. We also find that maximal entanglement cannot guarantee maximal nonlocality and the MMES does not correspond to the state with maximal measurement-induced nonloc…
There are multipartite entangled states in many-body systems which may be potential resources in various quantum applications. There are lots of methods to witness specific entangled systems. However, no efficient method is available to explore many-body systems without multipartite entanglement. It may provide necessary restrictions for experimental preparations of multipartite entanglement. Our goal is to solve this problem for spin systems. The maximal effective velocity with propagation of information is bounded in quantum spin systems with short-range interactions from Lieb-Robinson's ine…
We assess quantum non-locality of multiparty entangled thermal states by studying, quantitatively, both tripartite and quadripartite states belonging to the Greenberger-Horne-Zeilinger (GHZ), W and linear cluster-state classes and showing violation of relevant Bell-like inequalities. We discuss the conditions for maximizing the degree of violation against the local thermal character of the states and the inefficiency of the detection apparatuses. We demonstrate that such classes of multipartite entangled states can be made to last quite significantly, notwithstanding adverse operating conditio…
We show that arbitrary functions of continuous variables, e.g. position and momentum, can be used to generate tests that distinguish quantum theory from local hidden variable theories. By optimising these functions, we obtain more robust violations of local causality than obtained previously. We analytically calculate the optimal function and include the effect of nonideal detectors and noise, revealing that optimized functional inequalities are resistant to standard forms of decoherence. These inequalities could allow a loophole-free Bell test with efficient homodyne detection.
Multipartite quantum states may exhibit different types of quantum entanglement in that they cannot be converted into each other by local quantum operations only, and fully understanding mathematical structures of different types of multipartite entanglement is a very challenging task. In this paper, from the viewpoint of Hardy's nonlocality, we compare W and GHZ states and show a couple of crucial different behaviors between them. Particularly, by developing a geometric model for the Hardy's nonlocality problem of W states, we derive an upper bound for its maximal violation probability, which…
In this paper, we generalize the concept of strong quantum nonlocality from two aspects. Firstly in $\mathbb{C}^d\otimes\mathbb{C}^d\otimes\mathbb{C}^d$ quantum system, we present a construction of strongly nonlocal quantum states containing $6(d-1)^2$ orthogonal product states, which is one order of magnitude less than the number of basis states $d^3$. Secondly, we give the explicit form of strongly nonlocal orthogonal product basis in $\mathbb{C}^3\otimes \mathbb{C}^3\otimes \mathbb{C}^3\otimes \mathbb{C}^3$ quantum system, where four is the largest known number of subsystems in which there …
Quantum technologies are enjoying an unprecedented popularity, and some applications are already in the market. This thesis studies two phenomena that are behind a lot of quantum technologies: entanglement and nonlocality. We focus on multipartite systems, and ask what configurations of those systems are more useful than others. 'Usefulness' takes on different meanings depending on the context, but, roughly speaking, we aim for more entanglement or more nonlocality. Chapter 2 develops a resource theory of entanglement with a unique multipartite maximally entangled state. Chapter 3 shows that a…
Understanding the relation between nonlocality and entanglement is one of the fundamental problems in quantum physics. In the bipartite case, it is known that the correlations observed for some entangled quantum states can be explained within the framework of local models, thus proving that these resources are inequivalent in this scenario. However, except for a single example of an entangled three-qubit state that has a local model, almost nothing is known about such relation in multipartite systems. We provide a general construction of genuinely multipartite entangled states that do not disp…
Recently, Halder \emph{et al.} [Phys. Rev. Lett. \textbf{122}, 040403 (2019)] proposed the concept strong nonlocality without entanglement: an orthogonal set of fully product states in multipartite quantum systems that is locally irreducible for every bipartition of the subsystems. As the difficulty of the problem, most of the results are restricted to tripartite systems. Here we consider a weaker form of nonlocality 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 …
Local measurements acting on entangled quantum states give rise to a rich correlation structure in the multipartite scenario. We introduce a versatile technique to build families of Bell inequalities witnessing different notions of multipartite nonlocality for any number of parties. The idea behind our method is simple: a known Bell inequality satisfying certain constraints, for example the Clauser-Horne-Shimony-Holt inequality, serves as the $seed$ to build new families of inequalities for more parties. The constructed inequalities have a clear operational meaning, capturing an essential feat…
The characterization of quantum correlations in terms of information-theoretic resource has been a fruitful approach to understand the power of quantum correlations as a resource. While bipartite entanglement and Bell inequality violation in this setting have been extensively studied, relatively little is known about their multipartite counterpart. In this paper, we apply and adapt the recently proposed definitions of multipartite nonlocality [Phys. Rev. A 88, 014102] to the three- and four-partite scenario to gain new insight on the resource aspect of multipartite nonlocal quantum correlation…
In this work we investigate the probability of violation of local realism under random measurements in parallel with the strength of these violations as described by resistance to white noise admixture. We address multisetting Bell scenarios involving up to 7 qubits. As a result, in the first part of this manuscript we report statistical distributions of a quantity reciprocal to the critical visibility for various multipartite quantum states subjected to random measurements. The statistical relevance of different classes of multipartite tight Bell inequalities violated with random measurements…
We study how conditional photon operations can affect multipartite quantum correlations, specifically nonlocality and entanglement, of the continuous variable GHZ states. We find that the violation of the Mermin-Klyshko inequality revealing the multipartite nonlocality can be made stronger with photon subtraction applied on each mode of the original GHZ states, particularly in a weak squeezing regime. Photon addition applied on local modes also turns out to enhance the degree of multipartite nonlocality in a broad range of parameters. We further investigate the effects of the photon operations…
The quantum entanglement as one of very important resources has been widely used in quantum information processing. In this work, we present a new kind of genuine multipartite entanglement. It is derived from special geometric feature of entangled systems compared with quantum multisource networks. We prove that any symmetric entangled pure state shows stronger nonlocality than the genuinely multipartite nonlocality in the biseparable model. Similar results hold for other entangled pure states with local dimensions no larger than $3$. We further provide computational conditions for witnessing …
