Pairs of spin-1/2 particles are prepared in a Werner state (namely, a mixture of singlet and random components). If the random component is large enough, the statistical results of spin measurements that may be performed on each pair separately can be reproduced by an algorithm involving local ``hidden'' variables. However, if several such pairs are tested simultaneously, a violation of the Clauser-Horne-Shimony-Holt inequality may occur, and no local hidden variable model is compatible with the results.
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 …
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…
Collective measurements on large quantum systems together with a majority voting strategy can lead to a violation of the CHSH Bell inequality. In presence of many entangled pairs, this violation decreases quickly with the number of pairs, and vanishes for some critical pair number that is a function of the noise present in the system. Here, we show that a different binning strategy can lead to a more substantial Bell violation when the noise is sufficiently small. Given the relation between the critical pair number and the source noise, we then present an experiment where the critical pair num…
It is argued that Hardy-type proposals assume either nonlocality at detection, and then beg the question, or "local empty waves" (local hidden variables), and then have to accept "many worlds" and cannot prove nonlocality.
We study a system represented by a Bose-Einstein condensate interacting with a cavity field in presence of a strong off-resonant pumping laser. This system can be described by a three-mode Gaussian state, where two are the atomic modes corresponding to atoms populating upper and lower momentum sidebands and the third mode describes the scattered cavity field light. We show that, as a consequence of the collective atomic recoil instability, these modes possess a genuine tripartite entanglement that increases unboundedly with the evolution time and is larger than the bipartite entanglement in an…
Entanglement, the Einstein-Podolsky-Rosen (EPR) paradox and Bell's failure of local-hidden-variable (LHV) theories are three historically famous forms of "quantum nonlocality". We give experimental criteria for these three forms of nonlocality in multi-particle systems, with the aim of better understanding the transition from microscopic to macroscopic nonlocality. We examine the nonlocality of N separated spin J systems. First, we obtain multipartite Bell inequalities that address the correlation between spin values measured at each site, and then we review spin squeezing inequalities that ad…
Quantum nonlocality has recently been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Experimentally Bell's nonlocality is usually tested by quantum violation of the Clause-Horne-Shimony-Holt (CHSH) inequality in the two-qubit system. Bell's nonlocality is the strongest type of nonlocality, also due this reason Bell-test experiments have encountered both the locality loophole and the detection loophole for a very long time. As a weaker nonlocality, EPR steering naturally escapes from the locality loophole and is corres…
Past, present and future experimental tests of quantum nonlocality are discussed. Consequences of assuming that the state-vector collapse is a real physical phenomenon in space-time are developed. These lead to experiments feasible with today's technology.
For the purpose of the nonlocality test, we propose a general correlation observable of two parties by utilizing local $d$-outcome measurements with SU($d$) transformations and classical communications. Generic symmetries of the SU($d$) transformations and correlation observables are found for the test of nonlocality. It is shown that these symmetries dramatically reduce the number of numerical variables, which is important for numerical analysis of nonlocality. A linear combination of the correlation observables, which is reduced to the Clauser-Horne-Shimony-Holt (CHSH) Bell's inequality for …
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 …
We consider a bipartite scenario where two parties hold ensembles of $1/2$-spins which can only be measured collectively. We give numerical arguments supporting the conjecture that in this scenario no Bell inequality can be violated for arbitrary numbers of spins if only first order moment observables are available. We then give a recipe to achieve a significant Bell violation with a split many-body system when this restriction is lifted. This highlights the strong requirements needed to detect bipartite quantum correlations in many-body systems device-independently.
We propose a test of nonlocality for continuous variables using a two-mode squeezed state as the source of nonlocal correlations and a measurement scheme based on conditional homodyne detection. Both the CHSH- and the CH-inequality are constructed from the conditional homodyne data and found to be violated for a squeezing parameter larger than $r\approx0.48$.
Nonlocality is a fascinating and counterintuitive aspect of Nature, revealed by the violation of a Bell inequality. The standard and easiest configuration in which Bell inequalities can be measured has been proposed by Clauser-Horne-Shimony-Holt (CHSH). However, alternative nonlocality tests can also be carried out. In particular, Bell inequalities requiring multiple measurement settings can provide deeper fundamental insights about quantum nonlocality as well as offering advantages in the presence of noise and detection inefficiency. In this article we show how these nonlocality tests can be …
The network structure offers in principle the possibility for novel forms of quantum nonlocal correlations, that are proper to networks and cannot be traced back to standard quantum Bell nonlocality. Here we define a notion of genuine network quantum nonlocality. Our approach is operational and views standard quantum nonlocality as a resource for producing correlations in networks. We show several examples of correlations that are genuine network nonlocal, considering the so-called bilocality network of entanglement swapping. In particular, we present an example of quantum self-testing which r…
We explore the possibility to manipulate massive, i.e. motional, degrees of freedom of trapped ions. In particular, we demonstrate that, if local control of the trapping frequencies is achieved, one can reproduce the full toolbox of linear optics on radial modes. Furthermore, assuming only global control of the trapping potential, we show that unprecedented degrees of continuous variable entanglement can be obtained and that nonlocality tests with massive degrees of freedom can be carried out.
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…
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 explore correlation polytopes to derive a set of all Boole-Bell type conditions of possible classical experience which are both maximal and complete. These are compared with the respective quantum expressions for the Greenberger-Horne-Zeilinger (GHZ) case and for two particles with spin state measurements along three directions.
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…
We consider Bell tests involving bipartite states shared between three parties. We show that the simple inclusion of a third part may greatly simplify the measurement scenario (in terms of the number of measurement settings per part) and allows the identification of previously unknown nonlocal resources.
We show two experimental realizations of Hardy ladder test of quantum nonlocality using energy-time correlated photons, following the scheme proposed by A. Cabello \emph{et al.} [Phys. Rev. Lett. \textbf{102}, 040401 (2009)]. Unlike, previous energy-time Bell experiments, these tests require precise tailored nonmaximally entangled states. One of them is equivalent to the two-setting two-outcome Bell test requiring a minimum detection efficiency. The reported experiments are still affected by the locality and detection loopholes, but are free of the post-selection loophole of previous energy-ti…
Incompatibility of observables, or measurements, is one of the key features of quantum mechanics, related, among other concepts, to Heisenberg's uncertainty relations and Bell nonlocality. In this manuscript we show, however, that even though incompatible measurements are necessary for the violation of any Bell inequality, some relevant Bell-like inequalities may be obtained if compatibility relations are assumed between the local measurements of one (or more) of the parties. Hence, compatibility of measurements is not necessarily a drawback and may, however, be useful for the detection of Bel…
Quantum nonlocality, one of the most important features of quantum mechanics, is normally connected in experiments with the violation of Bell-Clauser-Horne (Bell-CH) inequalities. We propose effective methods for the rearrangement and linear inequality to prove a large variety of Bell-CH inequalities. We also derive a set of Bell-CH inequalities by using these methods which can be violated in some quantum entangled states.
Two distant systems can exhibit quantum nonlocality even though the correlations between them admit a local model. This nonlocality can be revealed by testing extra correlations between successive measurements on one of the systems which do not admit a noncontextual model whatever the reduced state of this system is. This shows that quantum contextuality plays a fundamental role in quantum nonlocality, and allows an experimental test of the Kochen-Specker with locality theorem.
Relativistic causality forbids superluminal signaling between distant observers. By exploiting the non-signaling principle, we derive the exact relationship between the chained Clauser-Horne-Shimony-Holt sum of correlations CHSH_K and the success probability P_K associated with Hardy's ladder test of nonlocality for two qubits and K+1 observables per qubit. Then, by invoking the Tsirelson bound for CHSH_K, the derived relationship allows us to establish an upper limit on P_K. In addition, we draw the connection between CHSH_K and the chained version of the Clauser-Horne (CH) inequality.
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…
Self-testing protocols enable certification of quantum devices without demanding full knowledge about their inner workings. A typical approach in designing such protocols is based on observing nonlocal correlations which exhibit maximum violation in a Bell test. We show that in Bell experiment known as Hardy's test of nonlocality not only the maximally nonlocal correlation self-tests a quantum state, rather a non-maximal nonlocal behavior can serve the same purpose. We, in fact, completely characterize all such behaviors leading to self-test of every pure two qubit entangled state except the m…
An experiment has recently been performed to demonstrate quantum nonlocality by establishing contextuality in one of a pair of photons encoding four qubits; however, low detection efficiencies and use of the fair-sampling hypothesis leave these results open to possible criticism due to the detection loophole. In this Letter, a physically motivated local hidden-variable model is considered as a possible mechanism for explaining the experimentally observed results. The model, though not intrinsically contextual, acquires this quality upon post-selection of coincident detections.
Energy-time entangled biphoton source plays a great role in quantum communication, quantum metrology and quantum cryptography due to its strong temporal correlation and capability of nonlocal dispersion cancellation. As a quantum effect, nonlocal dispersion cancellation is further proposed as an alternative way for nonlocality test of continuous variable entanglement via the violation of Bell-like inequality proposed by Wasak et al. [Phys. Rev. A, 82, 052120 (2010)]. However, to date there is no experimental report either on the inequality violation or on a nonlocal detection with single-photo…
Quantum nonlocality is tested for an entangled coherent state, interacting with a dissipative environment. A pure entangled coherent state violates Bell's inequality regardless of its coherent amplitude. The higher the initial nonlocality, the more rapidly quantum nonlocality is lost. The entangled coherent state can also be investigated in the framework of $2\times2$ Hilbert space. The quantum nonlocality persists longer in $2\times2$ Hilbert space. When it decoheres it is found that the entangled coherent state fails the nonlocality test, which contrasts with the fact that the decohered enta…
Recently much interest has been directed towards designing setups that achieve realistic loss thresholds for decisive tests of local realism, in particular in the optical regime. We analyse the feasibility of such Bell tests based on a W-state shared between multiple parties, which can be realised for example by a single photon shared between spatial modes. We develop a general error model to obtain thresholds on the efficiencies required to violate local realism, and also consider two concrete optical measurement schemes.
Lately, much interest has been directed towards designing setups that achieve decisive tests of local realism. Here we present Bell tests with measurements based on linear optical displacements and single-photon detection. The scheme displays good tolerance to loss. In particular, for entangled squeezed states, we find thresholds compatible with current efficiencies of detectors and sources. Furthermore, the scheme is easily extendible to any number of observers, allowing observation of multipartite nonlocality for a single photon shared among multiple modes. We also consider the case of atom-…
We show that rejection of local realism in quantum mechanics can be tested by Bell-type inequalities for two observers and low-order moments of continuous and unbounded observables. We prove that one requires three observables for each observer for a maximally entangled state and two observables for a non-maximally entangled state and write down appropriate inequalities and show violation by quantum examples. Finding an example for quadratures or position and momentum is left as an open problem.
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.
Bell's inequality in three coupled quantum dots (QDs) within cavity QED, including Forster and exciton-phonon interactions, is investigated theoretically. For an initially entangled state, Bell's inequality is valid for certain times and violated for some other times. It is shown that the system moves from a product state to a entangled state and back again during it's time evolution.
We report the experimental realization and the characterization of polarization and momentum hyperentangled two photon states, generated by a new parametric source of correlated photon pairs. By adoption of these states an "all versus nothing" test of quantum mechanics was performed. The two photon hyperentangled states are expected to find at an increasing rate a widespread application in state engineering and quantum information. PACS: 03.65.Ud, 03.67.Mn, 42.65. Lm
Generic forms of the entangled states of two spin-1 (and spin-3/2) particles, along with the set of appropriate spin observables that together exhibit maximum nonlocality under the Hardy's nonlocality test are given; the maximum nonlocality is shown to be 0.09017. It is conjectured that this result holds good for a system of two spin-$j$ particles for all values of $j$. It is also shown that no maximally entangled state of two spin-$j$ particles responds to the Hardy's nonlocality test.
There have been studies on formation of quantum-nonlocal states in spatially separate two cavities. We suggest a nonlocal test for the field prepared in the two cavities. We couple classical driving fields with the cavities where a nonlocal state is prepared. Two independent two-level atoms are then sent through respective cavities to interact off-resonantly with the cavity fields. The atomic states are measured after the interaction. Bell's inequality can be tested by the joint probabilities of two-level atoms being in their excited or ground states. We find that quantum nonlocality can also …
There have been theoretical and experimental studies on quantum nonlocality for continuous variables, based on dichotomic observables. In particular, we are interested in two cases of dichotomic observables for the light field of continuous variables: One case is even and odd numbers of photons and the other case is no photon and presence of photons. We analyze various observables to give the maximum violation of Bell's inequalities for continuous-variable states. We discuss an observable which gives the violation of Bell's inequality for any entangled pure continuous variable state. However, …
A general method for testing essential nonlocality of nonlinear modifications of quantum mechanics is presented and applied to show the inconsistency of I. Bialynicki-Birula's and J. Mycielski's nonlinear quantum theory.
We derive a Bell inequality based on a generalized quasiprobability function which is parameterized by one non-positive real value. Two types of known Bell inequalities formulated in terms of the Wigner and Q functions are included as limiting cases. We investigate violations of our Bell inequalities for single photon entangled states and two-mode squeezed vacuum states when varying the detector efficiency. We show that the Bell inequality for the Q function allows the lowest detection efficiency for violations of local realism.
This paper is aimed to dissociate nonlocality from quantum theory. We demonstrate that the tests on violation of the Bell type inequalities are simply statistical tests of local incompatibility of observables. In fact, these are tests on violation of {\it the Bohr complementarity principle.} Thus, the attempts to couple experimental violations of the Bell type inequalities with "quantum nonlocality" is really misleading. These violations are explained in the quantum theory as exhibitions of incompatibility of observables for a single quantum system, e.g., the spin projections for a single elec…
We have experimentally tested the non local properties of the states generated by a high brilliance source of entanglement which virtually allows the direct measurement of the full set of photon pairs created by the basic QED process implied by the parametric quantum scattering. Standard Bell measurements and Bell's inequality violation test have been realized over the entire cone of emission of the degenerate pairs. By the same source we have verified the Hardy's ladder theory up to the 20th step and the contradiction between the standard quantum theory and the local realism has been tested f…
We propose a scheme to test Bell's inequalities for an arbitrary number of measurement outcomes on entangled continuous variable states. The Bell correlation functions are expressible in terms of phase-space quasiprobability functions with complex ordering parameter, which can experimentally be determined both directly via local CV-qubit interaction or indirectly via tomographic reconstructions. We demonstrate that continuous-variable systems can give stronger violations of these Bell's inequalities than of the ones developed for two-outcome observables. Thus, while keeping the feasibility of …
We report the first experimental violation of local realism in four-photon Greenberger-Horne-Zeilinger (GHZ) entanglement. In the experiment, the non-statistical GHZ conflicts between quantum mechanics and local realism are confirmed, within the experimental accuracy, by four specific measurements of polarization correlations between four photons. In addition, our experimental results not only demonstrate a violation of Mermin-Ardehali-Belinskii-Klyshko inequality by 76 standard deviations, but also for the first time provide sufficient evidence to confirm the existence of genuine four-particl…
We have investigated the quantum phase transitions in the ground states of several critical systems, including transverse field Ising and XY models as well as XY with multiple spin interactions, XXZ and the collective system Lipkin-Meshkov-Glick models, by using different quantumness measures, such as entanglement of formation, quantum discord, as well as its classical counterpart, measurement-induced disturbance and the Clauser-Horne-Shimony-Holt-Bell function. Measurement-induced disturbance is found to detect the first and second order phase transitions present in these critical systems, wh…
Bell showed 50 years ago that quantum theory is nonlocal via his celebrated inequalities, turning the issue of quantum nonlocality from a matter of taste into a matter of test. Years later, Hardy proposed a test for nonlocality without inequality, which is a kind of "something-versus-nothing" argument. Hardy's test for $n$ particles induces an $n$-partite Bell's inequality with two dichotomic local measurements for each observer, which has been shown to be violated by all entangled pure states. Our first result is to show that the Bell-Hardy inequality arising form Hardy's nonlocality test is …
A quantum system consisting of two subsystems is separable if its density matrix can be written as $ρ=\sum w_K ρ_K'\otimes ρ_K''$, where $ρ_K'$ and $ρ_K''$ are density matrices for the two subsytems, and the positive weights $w_K$ satisfy $\sum w_K=1$. A necessary condition for separability is derived and is shown to be more sensitive than Bell's inequality for detecting quantum inseparability. Moreover, collective tests of Bell's inequality (namely, tests that involve several composite systems simultaneously) may sometimes lead to a violation of Bell's inequality, even if the latter is satisf…
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）
We consider Bell tests in which the distant observers can perform local filtering before testing a Bell inequality. Notably, in this setup, certain entangled states admitting a local hidden variable model in the standard Bell scenario can nevertheless violate a Bell inequality after filtering, displaying so-called hidden nonlocality. Here we ask whether all entangled states can violate a Bell inequality after well-chosen local filtering. We answer this question in the negative by showing that there exist entangled states without hidden nonlocality. Specifically, we prove that some two-qubit We…
We investigate the robustness of multiparty nonlocality under local decoherence, acting independently and equally on each subsystems. To be specific, we consider an N-qubit GHZ state under depolarization, dephasing, or dissipation channel, and tested the nonlocality by violation of Mermin-Klyshko inequality, which is one of Bell's inequalities for multi-qubit systems. The results show that the robustness of nonlocality increases with the number of qubits, and that the nonlocality of an N-qubit GHZ state with even N is extremely persistent against dephasing.
