Source independent quantum networks are considered as a natural generalization to the Bell scenario where we investigate the nonlocal properties of quantum states distributed and measured in a network. Considering the simplest network of entanglement swapping, recently Gisin et. al. and Andreoli et. al. independently provided a systematic characterization of the set of quantum states leading to violation of the so-called 'bilocality' inequality. In this work, we consider the complexities in the quantum networks with an arbitrary number of parties distributed in chain-shaped and star-shaped networks. We derive the maximal violation of the 'n-local' inequality that can be achieved by arbitrary two-qubit states for such chain and star-shaped networks. This would further provide us deeper understanding of quantum correlations in complex structures.
We present a set of Bell inequalities for multiqubit quantum systems. These Bell inequalities are shown to be able to detect multiqubit entanglement better than previous Bell inequalities such as Werner-Wolf-Zukowski- Brukner ones. Computable formulas are presented for calculating the maximal violations of these Bell inequalities for any multiqubit states.
We study a class of Bell inequalities and find their maximum quantum violation. These inequalities involve n parties, two measurements per party, with each measurement having two outcomes. The n=2 case corresponds to the CH inequality. We use the method of Jordan bases to find the maximum quantum violations. Results are found for the cases n=2 through n=7.
We investigate the violation of Leggett-Garg (LG) inequalities inquantum dots with the stationarity assumption. By comparing two types of LG inequalities, we find a better one which is easier to be tested in experiment. In addition, we show that the fine-structure splitting, background noise and temperature of quantum dots all influence the violation of LG inequalities.
We construct steering inequalities which exhibit unbounded violation. The concept was to exploit the relationship between steering violation and uncertainty relation. To this end we apply mutually unbiased bases and anti-commuting observables, known to exibit the strongest uncertainty. In both cases, we are able to procure unbounded violations. Our approach is much more constructive and transparent than the operator space theory approach employed to obtain large violation of Bell inequalities. Importantly, using anti-commuting observables we are able to obtain a {\it dichotomic} steering inequ…
The Suppes-Zanotti inequalities involving the joint expectations of just three binary quantum observables are (re-)derived by the hull computation of the respective correlation polytope. A min-max calculation reveals its maximal quantum violations correspond to a generalized Tsirelson bound. Notions of "contextuality" motivated by such violations are critically reviewed.
Violation of Mermin's and Svetlichny's inequalities can rule out the predictions of local hidden variable theory and can confirm the existence of true nonlocal correlation for n-particle pure quantum systems. Here we demonstrate the experimental violation of the above inequalities for W- and GHZ-class of states. We use IBM's five-qubit quantum computer for experimental implementation of these states and illustration of inequalities' violations. Our results clearly show the violations of both Mermin's and Svetlichny's inequalities for W and GHZ states respectively. Being a superconducting qubit…
Local systems may appear to violate Bell's inequalities if they are observed through suitable filters. The nonlocality leading to violation is outside the system and comprises the observer comparing the outcomes of the typical two wing Bell experiment. An example based on a well known gedanken experiment by Mermin is presented, and implications for the interpretation of Bell tests are discussed.
In this paper, it is proved that the maximal violation of Mermin's inequalities of $n$ qubits occurs only for GHZ's states and the states obtained from them by local unitary transformations. The key point of our argument involved here is by using the certain algebraic properties that Pauli's matrices satisfy, which is based on the determination of local spin observables of the associated Bell-Mermin operators.
We report the experimental violation of Leggett-type inequalities for a hybrid entangled state of spin and orbital angular momentum of a single photon. These inequalities give a physical criterion to verify the possible validity of a class of hidden-variable theories, originally named "crypto non-local", that are not excluded by the violation of Bell-type inequalities. In our case, the tested theories assume the existence of hidden variables associated with independent degrees of freedom of the same particle, while admitting the possibility of an influence between the two measurements, i.e. th…
We show that the state-independent violation of inequalities for noncontextual hidden variable theories introduced in [Phys. Rev. Lett. 101, 210401 (2008)] is universal, i.e., occurs for any quantum mechanical system in which noncontextuality is meaningful. We describe a method to obtain state-independent violations for any system of dimension d > 2. This universality proves that, according to quantum mechanics, there are no "classical" states.
We report on the experimental violation of multipartite Bell inequalities by entangled states of trapped ions. First we consider resource states for measurement-based quantum computation of between 3 and 7 ions and show that all strongly violate a Bell-type inequality for graph states, where the criterion for violation is a sufficiently high fidelity. Second we analyze GHZ states of up to 14 ions generated in a previous experiment using stronger Mermin-Klyshko inequalities, and show that in this case the violation of local realism increases exponentially with system size. These experiments rep…
The chained Bell inequalities of Braunstein and Caves involving N settings per observer have some interesting applications. Here we obtain the minimum detection efficiency required for a loophole-free violation of the Braunstein-Caves inequalities for any N > 2. We discuss both the case in which both particles are detected with the same efficiency and the case in which the particles are detected with different efficiencies.
We estimate the probability of random $N$-qudit pure states violating full-correlation Bell inequalities with two dichotomic observables per site. These inequalities can show violations that grow exponentially with $N$, but we prove this is not the typical case. For many-qubit states the probability to violate any of these inequalities by an amount that grows linearly with $N$ is vanishingly small. If each system's Hilbert space dimension is larger than two, on the other hand, the probability of seeing \emph{any} violation is already small. For the qubits case we discuss furthermore the conseq…
The famous Clauser-Horne-Shimony-Holt (CHSH) inequality certifies a quantum violation, by a factor $\sqrt{2}$, of correlations predicted by the classical view of the world in the simplest possible nontrivial measurement setup (two systems with two dichotomic measurements each). In such setting, this is the largest possible violation, which is known as the \emph{Tsirelson bound}. In this paper we calculate the exact values of quantum violations for the other Bell correlation inequalities that appear in the setups involving up to four measurements; they are all smaller than $\sqrt{2}$. While var…
We investigate the violation of Bell-type inequalities for two-qubit Werner-like states parametrized by the positive parameter 0<p<1. We use an unbalanced homodyne detection scheme to obtain the quantum mechanical probabilities. A violation of the Bell-Wigner and Janssens inequalities is obtained for a large range of the parameter p. The range given by these inequalities is greater than the one given by the Clauser-Horne inequality. The range in which a violation is attained actually coincides with the range where the Werner-like states are known to be nonseparabel, i.e., for p>1/3. However, t…
The possibility of observing violations of temporal Bell inequalities, originally proposed by Leggett as a mean of testing the quantum mechanical delocalization of suitably chosen macroscopic bodies, is discussed by taking into account the effect of the measurement process. A general criterion quantifying this possibility is defined and shown not to be fulfilled by the various experimental configurations proposed so far to test inequalities of different forms.
The violation of Leggett-Garg type inequalities (LGtIs) is studied on a two level atom, driven by an external field in the presence of a squeezed thermal reservoir. The violations are observed in the underdamped regime where the spontaneous transition rate is much smaller compared to the Rabi frequency. Increase in thermal effects is found to decrease the extent of violation as well as the time over which the violation lasts. With increase in the value squeezing parameter the extent of violation of LGtIs is seen to reduce. The violation of LGtIs is favored by increase in the driving frequency.…
Geometrical Bell Inequalities (GBIs) are the strongest known Bell inequalities for collections of qubits. However, their generalizations to other systems is not yet fully understood. We formulate GBIs for an arbitrary number $N$ of observers, each of which possesses a particle of an arbitrary dimension $d$. The whole $(d-1)$-parameter family of local observables with eigenbases unbiased to the computational basis is used, but it is immediate to use a discrete subset of them. We argue analytically for qutrits and numerically for other systems that the violations grows exponenetially with $N$. W…
In an article published in 2010, Kiukas and Werner claim to have shown that Bohmian Mechanics does not make the same empirical predictions as ordinary Quantum Mechanics. We explain that such claim is wrong.
We consider quantum systems composed of $N$ qubits, and the family of all Bell's correlation inequalities for two two-valued measurements per site. We show that if a $N$-qubit state $ρ$ violates any of these inequalities, then it is at least bipartite distillable. Indeed there exists a link between the amount of Bell's inequality violation and the degree of distillability. Thus, we strengthen the interpretation of Bell's inequalities as detectors of useful entanglement.
Photomultiplier tubes and avalanche photodiodes, which are commonly used in quantum optic experiments, are sometimes referred to as threshold detectors because, in photon counting mode, they cannot discriminate the number of photoelectrons initially extracted from the absorber in the detector. We argue that they can be called threshold detectors on more account than that. We point out that their their functioning principle relies on two thresholds that are usually thought unimportant individually in the context of EPR-Bell discussion. We show how the combined effect of these threshold can lead…
Entanglement witnesses such as Bell inequalities are frequently used to prove the non-classicality of a light source and its suitability for further tasks. By demonstrating Bell inequality violations using classical light in common experimental arrangements, we highlight why strict locality and efficiency conditions are not optional, particularly in security-related scenarios.
Leggett-Garg inequalities are tests of macroscopic realism that can be violated by quantum mechanics. In this letter, we realise photonic Leggett-Garg tests on a three-level system and implement measurements that admit three distinct measurement outcomes, rather than the usual two. In this way we obtain violations of three- and four-time Leggett-Garg inequalities that are significantly in excess of those obtainable in standard Leggett-Garg tests. We also report violations the quantum-witness equality up to the maximum permitted for a three-outcome measurement. Our results highlight differences…
We generalize the derivation of Leggett-Garg inequalities to systematically treat a larger class of experimental situations by allowing multi-particle correlations, invasive detection, and ambiguous detector results. Furthermore, we show how many such inequalities may be tested simultaneously with a single setup. As a proof of principle, we violate several such two-particle inequalities with data obtained from a polarization-entangled biphoton state and a semi-weak polarization measurement based on Fresnel reflection. We also point out a non- trivial connection between specific two-party Legge…
We derive N-particle Bell-type inequalities under the assumption of partial separability, i.e. that the N-particle system is composed of subsystems which may be correlated in any way (e.g. entangled) but which are uncorrelated with respect to each other. These inequalities provide, upon violation, experimentally accessible sufficient conditions for full N-particle entanglement, i.e. for N-particle entanglement that cannot be reduced to mixtures of states in which a smaller number of particles are entangled. The inequalities are shown to be maximally violated by the N-particle Greenberger-Horne…
A Franson-type test of Bell inequalities by photons 10.9 km apart is presented. Energy-time entangled photon-pairs are measured using two-channel analyzers, leading to a violation of the inequalities by 16 standard deviations without subtracting accidental coincidences. Subtracting them, a 2-photon interference visibility of 95.5% is observed, demonstrating that distances up to 10 km have no significant effect on entanglement. This sets quantum cryptography with photon pairs as a practical competitor to the schemes based on weak pulses.
We discuss the use of inequalities of the Leggett-Garg type (LGtI) to witness quantum coherence and present the first experimental violation of this type of inequalities using a light-matter interfaced system. By separately benchmarking the Markovian character of the evolution and the translational invariance of the conditional probabilities, the observed violation of a LGtI is attributed to the quantum coherent character of the process. These results provide a general method to benchmark `quantumness' when the absence of memory effects can be independently certified and confirm the persistenc…
The strength of classical correlations is subject to certain constraints, commonly known as Bell inequalities. Violation of these inequalities is the manifestation of nonlocality---displayed, in particular, by quantum mechanics, meaning that quantum mechanics can outperform classical physics at tasks associated with such Bell inequalities. Interestingly, however, there exist situations in which this is not the case. We associate an intriguing class of bound entangled states, constructed from unextendable product bases (UPBs) with a wide family of tasks, for which (i) quantum correlations do no…
The 60 real vectors derived from the vertices of a 600-cell are shown to yield a number of pentagon inequalities that are satisfied by realistic noncontextual theories but violated by quantum mechanics. The replicas of these inequalities cover Hilbert space so densely that every real four-dimensional vector violates at least one of them. It is pointed out that this set of 60 vectors contains numerous "N-gons" (generalizations of pentagons) that may be of interest in connection with demonstrations of contextuality.
In the present article, based on the formalism introduced in [Loubenets, J. Math. Phys. 53, 022201 (2012)], we derive for a pure bipartite quantum state a new upper bound on its maximal violation of general Bell inequalities. This new bound indicates that, for an infinite dimensional pure bipartite state with a finite sum of its Schmidt coefficients, violation of any general Bell inequality is bounded from above by the value independent on a number of settings and a type of outcomes, continuous or discrete, specific to this Bell inequality. As an example, we apply our new general results to sp…
The tomographic method is employed to investigate the presence of quantum correlations in two classes of parameter-dependent states of two qutrits. The violation of some Bell's inequalities in a wide domain of the parameter space is shown. A comparison between the tomographic approach and a recent method elaborated by Wu, Poulsen and Molmer shows the better adequacy of the former method with respect to the latter one.
At first sight, the use of an everywhere positive Wigner function as a probability density to perform stochastic simulations in quantum optics seems equivalent to the introduction of local hidden variables, thus preventing any violation of Bell inequalities. However, because of the difference between symmetrically and normally ordered operators, some trajectories in stochastic simulations can imply negative intensities, despite a positive mean. Hence, Bell inequalities do not apply. Here, we retrieve for a weakly squeezed Gaussian state the maximum violation on polarization states allowed by q…
Since the experimental observation of the violation of the Bell-CHSH inequalities, much has been said about the non-local and contextual character of the underlying system. But the hypothesis from which Bell's inequalities are derived differ according to the probability space used to write them. The violation of Bell's inequalities can, alternatively, be explained assuming that the hidden variables do not exist at all, or that they exist but their values cannot be simultaneously assigned, or that the values can be assigned but joint probabilities cannot be properly defined, or that averages ta…
We exhibit a local-hidden-variable model in agreement with the results of the two-photon coincidence experiment made by Torgerson et al. [Phys. Lett. A 204 (1995) 323]. The existence of any such model shows that the experiment does not exclude local realism.
The phenomenon of monogamy of Bell inequality violations is interesting both from the fundamental perspective as well as in cryptographic applications such as the extraction of randomness and secret bits. In this article, we derive new and stronger monogamy relations for violations of Bell inequalities in general no-signaling theories. These relations are applicable to the class of binary output correlation inequalities known as XOR games, and to a restricted set of unique games. In many instances of interest, we show that the derived relation provides a significant strengthening over previous…
A multipartite quantum state violates a Bell inequality asymptotically if, after jointly processing by general local operations an arbitrarily large number of copies of it, the result violates the inequality. In the bipartite case we show that asymptotic violation of the CHSH-inequality is equivalent to distillability. Hence, bound entangled states do not violate it. In the multipartite case we consider the complete set of full-correlation Bell inequalities with two dichotomic observables per site, also called WWZB-inequalities. We show that asymptotic violation of any of these inequalities by…
Despite the great success of quantum mechanics, questions regarding its application still exist and the boundary between quantum and classical mechanics remains unclear. Based on the philosophical assumptions of macrorealism and noninvasive measurability, Leggett and Garg devised a series of inequalities (LG inequalities) involving a single system with a set of measurements at different times. Introduced as the Bell inequalities in time, the violation of LG inequalities excludes the hidden-variable description based on the above two assumptions. We experimentally investigated the single photon…
The connection between quantum optical nonclassicality and the violation of Bell's inequalities is explored. Bell type inequalities for the electromagnetic field are formulated for general states(arbitrary number or photons, pure or mixed) of quantised radiation and their violation is connected to other nonclassical properties of the field. Classical states are shown to obey these inequalities and for the family of centered Gaussian states the direct connection between violation of Bell-type inequalities and squeezing is established.
In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order $\sqrt{n}$ (up to a logarithmic factor) when observables with n possible outcomes are used. A central tool in the analysis is a close relation between this problem and operator space theory and, in particular, the very recent noncommutative $L_p$ embedding theory. As a consequence of this result, we obtain better Hilbert space dimension witnesses and quantum violations of Bell inequalities with better resistance to noise.
We propose a new type of attack on Ekert protocol in which, rather surprisingly, Eve drives a violation of Bell inequalities in Alice's and Bob's detectors with a mixture of separable states. She does so by sending correlated pulses containing several photons at frequencies where only multiple-photon absorptions are possible in their detectors. Whenever the photons stemming from a same pulse are dispatched in such a way that the number of photons is insufficient to trigger a multiple-photon absorption in either channel, the pulse remains undetected. We show that this simple feature leads to vi…
We explore the challenges posed by the violation of Bell-like inequalities by $d$-dimensional systems exposed to imperfect state-preparation and measurement settings. We address, in particular, the limit of high-dimensional systems, naturally arising when exploring the quantum-to-classical transition. We show that, although suitable Bell inequalities can be violated, in principle, for any dimension of given subsystems, it is in practice increasingly challenging to detect such violations, even if the system is prepared in a maximally entangled state. We characterize the effects of random pertur…
We show that it is possible to find maximal violations of the CHSH-Bell inequality using only position measurements on a pair of entangled non-relativistic free particles. The device settings required in the CHSH inequality are done by choosing one of two times at which position is measured. For different assignments of the "+" outcome to positions, namely to an interval, to a half line, or to a periodic set, we determine violations of the inequalities, and states where they are attained. These results have consequences for the hidden variable theories of Bohm and Nelson, in which the two-time…
We propose a Bell inequality for high-dimensional bipartite systems obtained by binning local measurement outcomes and show that it is tight. We find a binning method for even d-dimensional measurement outcomes for which this Bell inequality is maximally violated by maximally entangled states. Furthermore, we demonstrate that the Bell inequality is applicable to continuous variable systems and yields strong violations for two-mode squeezed states.
We investigate the relation between unextendible product bases (UPB) and Bell inequalities found recently in [R. Augusiak et al., Phys. Rev. Lett. 107, 070401 (2011)]. We first review the procedure introduced there that associates to any set of mutually orthogonal product vectors in a many-qubit Hilbert space a Bell inequality. We then show that if a set of mutually orthogonal product vectors can be completed to a full basis, then the associated Bell inequality is trivial, in the sense of not being violated by any nonsignalling correlations. This implies that the relevant Bell inequalities tha…
We investigate the behavior of the maximal violations of the CHSH inequality and V$\grave{e}$rtesi's inequality under the local filtering operations. An analytical method has been presented for general two-qubit systems to compute the maximal violation of the CHSH inequality and the lower bound of the maximal violation of V$\acute{e}$rtesi's inequality over the local filtering operations. We show by examples that there exist quantum states whose non-locality can be revealed after local filtering operation by the V$\acute{e}$rtesi's inequality instead of the CHSH inequality.
We show that nonlocal correlation experiments on the two spatially separated modes of a maximally path-entangled number state may be performed and lead to a violation of a Clauser-Horne Bell inequality for any finite photon number N. We present also an analytical expression for the two-mode Wigner function of a maximally path-entangled number state and investigate a Clauser-Horne-Shimony-Holt Bell inequality for such states. We test other Bell-type inequalities. Some are violated by a constant amount for any N.
We prove that for a three-qubit system in the Greenberger-Horne-Zeilinger (GHZ) state, locality per se is in conflict with the perfect GHZ correlations. The proof does not in any way use the realism assumption and can lead to a refutation of locality. We also provide inequalities that are imposed by locality. The experimental confirmation of the present reasoning may imply a genuine quantum nonlocality and will deepen our understanding of nonlocality of nature.
Bell inequalities have traditionally been used to demonstrate that quantum theory is nonlocal, in the sense that there exist correlations generated from composite quantum states that cannot be explained by means of local hidden variables. With the advent of device-independent quantum information protocols, Bell inequalities have gained an additional role as certificates of relevant quantum properties. In this work we consider the problem of designing Bell inequalities that are tailored to detect maximally entangled states. We introduce a class of Bell inequalities valid for an arbitrary number…
We discuss models that attempt to provide an explanation for the violation of Bell inequalities at a distance in terms of hidden influences. These models reproduce the quantum correlations in most situations, but are restricted to produce local correlations in some configurations. The argument presented in [Bancal et al. Nature Physics 8, 867 (2012)] applies to all of these models, which can thus be proved to allow for faster-than-light communication. In other words, the signalling character of these models cannot remain hidden.
We demonstrate that different kind of mesoscopic quantum states of light can be efficiently generated from a simple iterative scheme using homodyne heralding. These states exhibit strong non-classical features, and are of great interest for many applications such as quantum error-correcting codes or fundamental testings. On this basis we propose a protocol allowing a large loophole-free violation of a CHSH-type Bell inequality with a remarkable robustness to line losses.
Bell's theorem has been widely argued to show that some of the predictions of quantum mechanics which are obtained by applying the {\it Born's rule} to a class of {\it entangled states}, are {\it not} compatible with {\it any} local-causal statistical model, via the violation of Bell's inequalities. On the other hand, in the previous work, we have shown that quantum dynamics and kinematics are {\it emergent} from a statistical model that is singled out {\it uniquely} by the principle of Locality. Here we shall show that the local-causal model supports entangled states and give the statistical …
We investigate the maximal violations for both sides of the $d$-dimensional CGLMP inequality by using the Bell operator method. It turns out that the maximal violations have a decelerating increase as the dimension increases and tend to a finite value at infinity. The numerical values are given out up to $d=10^6$ for positively maximal violations and $d=2\times 10^5$ for negatively maximal violations. Counterintuitively, the negatively maximal violations tend to be a little stronger than the positively maximal violations. Further we show the states corresponding to these maximal violations and…
We suggest to test the premise of ``macroscopic local realism'' which is sufficient to derive Bell inequalities when measurements of photon number are only accurate to an uncertainty of order $n$ photons, where $n$ is macroscopic. Macroscopic local realism is only sufficient to imply, in the context of the original Einstein-Podolsky-Rosen argument, fuzzy ``elements of reality'' which have a macroscopic indeterminacy. We show therefore how the violation of local realism in the presence of macroscopic uncertainties implies the failure of ``macroscopic local realism''. Quantum states violating th…
In this paper, we characterize the maximal violation of Ardehali's inequality of $n$ qubits by showing that GHZ's states and the states obtained from them by local unitary transformations are the unique states that maximally violate the Ardehali's inequalities. This concludes that Ardehali's inequalities can be used to characterize maximally entangled states of $n$ qubits, as the same as Mermin's and Bell-Klyshko's inequalities.
In a scenario where two parties share, act on and exchange some physical resource, the assumption that the parties' actions are ordered according to a definite causal structure yields constraints on the possible correlations that can be established. We show that the set of correlations that are compatible with a definite causal order forms a polytope, whose facets define causal inequalities. We fully characterize this causal polytope in the simplest case of bipartite correlations with binary inputs and outputs. We find two families of nonequivalent causal inequalities; both can be violated in …
Bell inequalities (BIs) derived in terms of quantum probability statistics are extended to general bipartite-entangled states of arbitrary spins with parallel polarization. The original formula of Bell for the two-spin singlet is slightly modified in the parallel configuration, while, the inequality for- mulated by Clauser-Horne-Shimony-Holt remains not changed. The violation of BIs indeed resulted from the quantum non-local correlation for spin-1=2 case. However, the inequalities are always satisfied for the spin-1 entangled states regardless of parallel or antiparallel polarizations of two s…
