It is shown that the correlations between two qubits selected from a trio prepared in a W state violate the Clauser-Horne-Shimony-Holt inequality more than the correlations between two qubits in any quantum state. Such a violation beyond Cirel'son's bound is smaller than the one achieved by two qubits selected from a trio in a Greenberger-Horne-Zeilinger state [A. Cabello, Phys. Rev. Lett. 88, 060403 (2002)]. However, it has the advantage that all local observers can know from their own measurements whether their qubits belongs or not to the selected pair.
Cirel'son inequality states that the absolute value of the combination of quantum correlations appearing in the Clauser-Horne-Shimony-Holt (CHSH) inequality is bound by $2 \sqrt 2$. It is shown that the correlations of two qubits belonging to a three-qubit system can violate the CHSH inequality beyond $2 \sqrt 2$. Such a violation is not in conflict with Cirel'son's inequality because it is based on postselected systems. The maximum allowed violation of the CHSH inequality, 4, can be achieved using a Greenberger-Horne-Zeilinger state.
An EPR-Bell type experiment carried out on an entangled quantum system can produce correlations stronger than allowed by local realistic theories. However there are correlations that are no-signaling and are more non local than the quantum correlations. Here we show that any correlations more non local than those achievable in an EPR-Bell type experiment necessarily allow -in the context of the quantum formalism- both for signaling and for generation of entanglement. We use our approach to rederive Cirel'son bound for the CHSH expression, and we derive a new Cirel'son type bound for qutrits. W…
The correlations between two qubits belonging to a three-qubit system can violate the Clauser-Horne-Shimony-Holt-Bell inequality beyond Cirel'son's bound [A. Cabello, Phys. Rev. Lett. 88, 060403 (2002)]. We experimentally demonstrate such a violation by 7 standard deviations by using a three-photon polarization-entangled Greenberger-Horne-Zeilinger state produced by Type-II spontaneous parametric down-conversion. In addition, using part of our results, we obtain a violation of the Mermin inequality by 39 standard deviations.
Kochen-Specker (KS) theorem lies at the heart of the foundations of quantum mechanics. It establishes impossibility of explaining predictions of quantum theory by any noncontextual ontological model. Spekkens generalized the notion of KS contextuality in [Phys. Rev. A 71, 052108 (2005)] for arbitrary experimental procedures (preparation, measurement, and transformation procedure). Interestingly, later on it was shown that preparation contextuality powers parity-oblivious multiplexing [Phys. Rev. Lett. 102, 010401 (2009)], a two party information theoretic game. Thus, using resources of a given…
We present the results of two tests where a sample of human participants were asked to make judgements about the conceptual combinations {\it The Animal Acts} and {\it The Animal eats the Food}. Both tests significantly violate the Clauser-Horne-Shimony-Holt version of Bell inequalities (`CHSH inequality'), thus exhibiting manifestly non-classical behaviour due to the meaning connection between the individual concepts that are combined. We then apply a quantum-theoretic framework which we developed for any Bell-type situation and represent empirical data in complex Hilbert space. We show that …
Quantum theory violates Bell's inequality, but not to the maximum extent that is logically possible. We derive inequalities (generalizations of Cirel'son's inequality) that quantify the upper bound of the violation, both for the standard formalism and the formalism of generalized observables (POVMs). These inequalities are quantum analogues of Bell inequalities, and they can be used to test the quantum version of locality. We discuss the nature of this kind of locality. We also go into the relation of our results to an argument by Popescu and Rohrlich (Found. Phys. 24, 379 (1994)) that there i…
We present a non-linear inequality that completely characterizes the set of correlation functions obtained from bipartite quantum systems, for the case in which measurements on each subsystem can be chosen between two arbitrary dichotomic observables. This necessary and sufficient condition is the maximal strengthening of Cirel'son's bound.
We implemented the experiment proposed by Cabello [arXiv:quant-ph/0309172] to test the bounds of quantum correlation. As expected from the theory we found that, for certain choices of local observables, Cirel'son's bound of the Clauser-Horne-Shimony-Holt inequality ($2\sqrt{2}$) is not reached by any quantum states.
Shortcomings of experimental techniques are usually assumed to diminish nonclassical properties of quantum systems. Here it is demonstrated that this standard assumption is not true in general. It is theoretically shown that the inability to resolve different photon numbers in photodetection may pseudo-increase a measured Bell parameter. Under proper conditions one even pseudo-violates the quantum Cirel'son bound of the Bell parameter, the corresponding density operator fails to be positive semi-definite. This paradox can be resolved by appropriate squash models.
Multi-component correlation functions are developed by utilizing d-outcome measurements. Based on the multi-component correlation functions, we propose a Bell inequality for bipartite d-dimensional systems. Violation of the Bell inequality for continuous variable (CV) systems is investigated. The violation of the original Einstein-Podolsky-Rosen state can exceed the Cirel'son bound, the maximal violation is 2.96981. For finite value of squeezing parameter, violation strength of CV states increases with dimension d. Numerical results show that the violation strength of CV states with finite squ…
We study Bell inequality tests with entanglement between a coherent-state field in a cavity and a two-level atom. In order to detect the cavity field for such a test, photon on/off measurements and photon number parity measurements, respectively, are investigated. When photon on/off measurements are used, at least 50% of detec- tion efficiency is required to demonstrate violation of the Bell inequality. Photon number parity measurements for the cavity field can be effectively performed using ancillary atoms and an atomic detector, which leads to large degrees of Bell violations up to Cirel'son…
We show that a Bell inequality test using an optical hybrid state between a polarized single photon and a coherent field can be highly robust against detection inefficiency. The Bell violation occurs until the efficiency becomes as low as 67% even though its degree becomes small as the detection efficiency degrades. We consider on/off and photon number parity measurements, respectively, for the Bell test and they result in the similar conditions. If the detection efficiency is higher than 98.68%, parity measurements give larger Bell violations close to Cirel'son's bound, while on/off measureme…
Non-locality without inequality is an elegant argument introduced by L. Hardy for two qubit systems, and later generalised to $n$ qubits, to establish contradiction of quantum theory with local realism. Interestingly, for $n=2$ this argument is actually a corollary of Bell-type inequalities, viz. the CH-Hardy inequality involving Bell correlations, but for $n$ greater than 2 it involves $n$-particle probabilities more general than Bell-correlations. In this paper, we first derive a chain of completely new local realistic inequalities involving joint probabilities for $n$ qubits, and then, asso…
We study a recently proposed Einstein-Podolsky-Rosen steering inequality [arXiv- 1412.8178 (2014)]. Analogous to Clauser-Horne-Shimony-Holt (CHSH) inequality for Bell nonlocality, in the simplest scenario, i.e., 2 parties, 2 measurements per party and 2 outcomes per measurement, this newly proposed inequality has been proved to be necessary and sufficient for steering. In this article, using an equivalence between measurement incompatibility (non joint measurability) and steering, we find the optimal violation amount of this inequality in quantum theory. Interestingly, the optimal violation am…
Tests are essential in Information Retrieval (IR), in order to evaluate the effectiveness of a query. Tests intended to exhibit the sense of words in con-text were undertaken and linked with Quantum Mechanics (QM). Poll tests were undertaken on heterogeneous media such as music and polysemy in foreign languages. Interference effects are shown in the results. Bell inequality was used leading to a significant spread in the results of the poll tests but without violating the classical limit. Then an automatic pertinence measure tool on texts has been developed using the HAL algorithm using an ort…
Bell's inequalities are defined by sums of correlations involving non-commuting observables in each of the two systems. Violations of Bell's inequalities are only possible because the precision of any joint measurement of these observables will be limited by quantum mechanical uncertainty relations. In this paper we explore the relation between the local measurement uncertainties and the magnitude of the correlations by preparing polarization entangled photon pairs and performing joint measurements of non-commuting polarization components at different uncertainty trade-offs. The change in meas…
Nonlocality is one of the main characteristic features of quantum systems involving more than one spatially separated subsystems. It is manifested theoretically as well as experimentally through violation of some local realistic inequality. On the other hand, classical behavior of all physical phenomena in the macroscopic limit gives a general intuition that any physical theory for describing microscopic phenomena should resemble classical physics in the macroscopic regime-- the so-called macro-realism. In the 2-2-2 scenario (two parties, each performing two measurements, each measurement with…
Entanglement is one of the most intriguing features of quantum mechanics. It gives rise to peculiar correlations which cannot be reproduced by a large class of alternative theories, the so-called hidden-variable models, that use parameters in addition to the wave-function. This incompatibility was quantified through the celebrated Bell inequalities, and more recently through new inequalities due to Leggett. Experiments confirm the predictions of quantum mechanics. However, this does not imply that quantum mechanics is the ultimate theory, unsusceptible of improvement, nor that quantum mechanic…
We propose a generalized Bell inequality for two three-dimensional systems with three settings in each local measurement. It is shown that this inequality is maximally violated if local measurements are configured to be mutually unbiased and a composite state is maximally entangled. This feature is similar to Clauser-Horne-Shimony-Holt inequality for two qubits but is in contrast with the two types of inequalities, Collins-Gisin-Linden-Massar-Popescu and Son-Lee-Kim, for high-dimensional systems. The generalization to aribitrary prime-dimensional systems is discussed.
A Necessary and Sufficient Condition for Quantum Realizability of Correlations for Arbitrary Normalized Observables in the Clauser--Horne--Shimony--Holt Setup
Recently, it was demonstrated by Son et al., Phys. Rev. Lett. \textbf{102}, 110404 (2009), that a separable bipartite continuous variable quantum system can violate the Clauser-Horne-Shimony-Holt (CHSH) inequality via operationally local transformations. Operationally local transformations are parameterized only by local variables, however in order to allow violation of the CHSH inequality a maximally entangled ancilla was necessary. The use of the entangled ancilla in this scheme caused the state under test to become dependent on the measurement choice one uses to calculate the CHSH inequalit…
