Violation Of Local Realism Research Articles

Two-player quantum pseudotelepathy based on recent all-versus-nothing violations of local realism

We introduce two two-player quantum pseudo-telepathy games based on two recently proposed all-versus-nothing (AVN) proofs of Bell's theorem [A. Cabello, Phys. Rev. Lett. 95, 210401 (2005); Phys. Rev. A 72, 050101(R) (2005)]. These games prove that Broadbent and Methot's claim that these AVN proofs do not rule out local-hidden-variable theories in which it is possible to exchange unlimited information inside the same light-cone (quant-ph/0511047) is incorrect.

All-Versus-Nothing Violation of Local Realism by Two-Photon, Four-Dimensional Entanglement

We develop and exploit a source of two-photon, four-dimensional entanglement to report the first two-particle all-versus-nothing test of local realism with a linear optics setup, but without resorting to a noncontextuality assumption. Our experimental results are in good agreement with quantum mechanics while in extreme contradiction to local realism. Potential applications of our experiment are briefly discussed.

“Local Realism”, Bell’s Theorem and Quantum “Locally Realistic” Inequalities

Based on the new general framework for the probabilistic description of experiments, introduced in quant-ph/0305126, quant-ph/0312199, we analyze in mathematical terms the link between the validity of Bell-type inequalities under joint experiments upon a system of any type and the physical concept of local realism. We prove that the violation of Bell-type inequalities in the quantum case has no connection with the violation of local realism. In a general setting, we formulate in mathematical terms a condition on local realism under a joint experiment and consider examples of quantum locally realistic joint experiments. We, in particular, show that quantum joint experiments of the Alice/Bob type are locally realistic. For an arbitrary bipartite quantum state, we derive quantum analogs of the original Bell inequality. In view of our results, we argue that the violation of Bell-type inequalities in the quantum case cannot be a valid argument in the discussion on locality or non-locality of quantum interactions.

Stronger Two-Observer All-Versus-Nothing Violation of Local Realism

We introduce a two-observer all-versus-nothing proof of Bell's theorem which reduces the number of required quantum predictions from 9 to 4, provides a greater amount of evidence against local realism, reduces the detection efficiency requirements for a conclusive experimental test of Bell's theorem, and leads to a Bell inequality which resembles Mermin's inequality for three observers but requires only two observers.

Loophole-free Bell’s experiments and two-photon all-versus-nothing violations of local realism

We introduce an all-versus-nothing proof of impossibility of Einstein-Podolsky-Rosen's local elements of reality for two photons entangled both in polarization and path degrees of freedom, which leads to a Bell's inequality where the classical bound is 8 and the quantum prediction is 16. A simple estimation of the detection efficiency required to close the detection loophole using this proof gives eta > 0.69. This efficiency is lower than that required for previous proposals.

Entanglement swapping of noisy states: A kind of superadditivity in nonclassicality

We address the question as to whether an entangled state that satisfies local realism will give a violation of the same, after entanglement swapping in a suitable scenario. We consider such possibility as a kind of superadditivity in nonclassicality. Importantly, it will indicate that checking for violation of local realism, in the state obtained after entanglement swapping, can be a method for detecting entanglement in the input state of the swapping procedure. We investigate various entanglement swapping schemes, which involve mixed initial states. The strength of violation of local realism by the state obtained after entanglement swapping, is compared with the one for the input states. We obtain a kind of superadditivity of violation of local realism for Werner states, consequent upon entanglement swapping involving Greenberger-Horne-Zeilinger state measurements. We also discuss whether entanglement swapping of specific states may be used in quantum repeaters with a substantially reduced need to perform the entanglement distillation step.

Noncommuting observables and local realism

A standard approach in the foundations of quantum mechanics studies local realism and hidden variables models exclusively in terms of violations of Bell-like inequalities. Thus quantum nonlocality is tied to the celebrated no-go theorems, and these comprise a long list that includes the Kochen–Specker and Bell theorems, as well as elegant refinements by Mermin, Peres, Hardy, GHZ, and many others. Typically entanglement or carefully prepared multipartite systems have been considered essential for violations of local realism and for understanding quantum nonlocality. Here we show, to the contrary, that sharp violations of local realism arise almost everywhere without entanglement. The pivotal fact driving these violations is just the noncommutativity of quantum observables. We demonstrate how violations of local realism occur for arbitrary noncommuting projectors, and for arbitrary quantum pure states. Finally, we point to elementary tests for local realism, using single particles and without reference to entanglement, thus avoiding experimental loopholes and efficiency issues that continue to bedevil the Bell inequality related tests.

Asymmetric multipartite Greenberger-Horne-Zeilinger states and Bell inequalities

We study the multiparticle generalized GHZ states. It has been shown that for an odd number of qubits and for a specific range of parameters, they do not violate any Bell inequality for correlation functions. We show here both analytically and numerically that, nevertheless, such states violate local realism, once a more detailed analysis of the correlations is made than the one allowed by correlation functions. The results imply that multiparticle Clauser-Horne-type inequalities involving probabilities are stronger tools for analyzing violations of local realism in multiparticle systems than inequalities involving the correlation functions.

Entanglement with classical fields

We experimentally demonstrate a simple classical-field optical heterodyne method which employs postselection to reproduce the polarization correlations of a four-particle entangled state. We give a heuristic argument relating this method to the measurement of multiple quantum fields by correlated homodyne detection. We suggest that using multiple classical fields and postselection, one can reproduce the polarization correlations obtained in quantum experiments which employ multiple single-photon sources and linear optics to prepare multiparticle entangled states. Our experimental scheme produces four spatially separated beams which are separately detected by mixing with four independent optical local oscillators (LO) of variable polarization. Analog multiplication of the four beat signals enables projection onto a four-particle polarization-state basis. Appropriate band pass filtering is used to produce a signal proportional to the projections of the maximally entangled four-field polarization state, $\ensuremath{\mid}{H}_{1})\ensuremath{\mid}{H}_{2})\ensuremath{\mid}{H}_{3})\ensuremath{\mid}{H}_{4})+\ensuremath{\mid}{V}_{1})\ensuremath{\mid}{V}_{2})\ensuremath{\mid}{V}_{3})\ensuremath{\mid}{V}_{4})$, onto the product of the four LO polarizations. Since the data from multiple observers is combined prior to postselection, this method does not constitute a test of nonlocality. However, we reproduce the polarization correlations of the 32 elements in the truth table from the quantum mechanical Greenberger-Horne-Zeilinger experiments on the violation of local realism. We also demonstrate a form of classical entanglement swapping in a four-particle basis.

Violation of local realism versus detection efficiency

We put bounds on the minimum detection efficiency necessary to violate local realism in Bell experiments. These bounds depend on simple parameters like the number of measurement settings or the dimensionality of the entangled quantum state. We derive them by constructing explicit local hidden variable models which reproduce the quantum correlations for sufficiently small detectors efficiency.

MultiqubitWstates lead to stronger nonclassicality than Greenberger-Horne-Zeilinger states

The N-qubit states of the W class, for $N>10,$ lead to more robust (against noise admixture) violations of local realism, than the Greenberger-Horne-Zeilinger (GHZ) states. These violations are most pronounced for correlations for a pair of qubits, conditioned on specific measurement results for the remaining $N\ensuremath{-}2$ qubits. The considerations provide us with a qualitative difference between the W state and GHZ state in the situation when they are separately sent via depolarizing channels. For sufficiently high amount of noise in the depolarizing channel, the GHZ states cannot produce a distillable state between two qubits, whereas the W states can still produce a distillable state in a similar situation.

Experimental violation of local realism by four-photon Greenberger-Horne-Zeilinger entanglement.

We report the first experimental violation of local realism by four-photon Greenberger-Horne-Zeilinger (GHZ) entanglement. In the experiment, the nonstatistical 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 also demonstrate a strong violation of Mermin-Ardehali-Belinskii-Klyshko inequality by 76 standard deviations. Such a violation can only be attributed to genuine four-photon entanglement.

Violation of local realism by a system withNspin-12particles

Recently, it was found that Mermin's inequalities may not always be optimal for the refutation of a local realistic description [Phys. Rev. Lett. 88, 210402 (2002)]. To complete this work, we derive an inequality for the Greenberger-Horne-Zeilinger-type pure state for a system with N spin-$\frac{1}{2}$ particles and the violation of the inequality can be shown for all the non product pure states. Mermin's inequality for a system of N spin-$\frac{1}{2}$ particles and Gisin's theorem for a system of two spin-$\frac{1}{2}$ particles are both included in our inequality.

Unified criterion for security of secret sharing in terms of violation of Bell inequalities

In secret sharing protocols, a secret is to be distributed among several partners so that leaving out any number of them, the rest do not have the complete information. Strong multiqubit correlations in the state by which secret sharing is carried out, had been proposed as a criterion for security of such protocols against individual attacks by an eavesdropper. However we show that states with weak multiqubit correlations can also be used for secure secret sharing. That our state has weak multiqubit correlations, is shown from the perspective of violation of local realism, and also by showing that its higher order correlations are described by lower ones. We then present a unified criterion for security of secret sharing in terms of violation of local realism, which works when the secret sharing state is the Greenberger-Horne-Zeilinger state (with strong multiqubit correlations), as well as states of a different class (with weak multiqubit correlations).

All-versus-nothing violation of local realism for two entangled photons.

It is shown that the Greenberger-Horne-Zeilinger theorem can be generalized to the case with only two entangled particles. The reasoning makes use of two photons which are maximally entangled both in polarization and in spatial degrees of freedom. In contrast to Cabello's argument of "all versus nothing" nonlocality with four photons [Phys. Rev. Lett. 87, 010403 (2001)]], our proposal to test the theorem can be implemented with linear optics and thus is well within the reach of current experimental technology.

Three Qubit GHZ Correlations and Generalized Bell Experiments

We present a brief historical introduction to the topic of Bell's theorem. Next we present the surprising features of the three-particle Greenberger—Horne—Zeilinger (GHZ) states. Finally we shall present a method of analysis of the GHZ correlations, which is based on a numerical approach, which is effectively equivalent to the full set of Bell inequalities for correlation functions for the given problem. The aim of our numerical approach is to answer the following question: Do additional possible local settings lead for the GHZ states to more pronounced violation of local realism (measured by the resistance of the quantum nature of the correlations with respect to “white” noise admixtures)?

Nonlocality of Hardy type in experiments using independent particle sources

By applying Hardy's argument, we demonstrate the violation of local realism in a gedanken experiment using independent and separated particle sources.

Clauser-Horne inequality for three-state systems

We show a new Bell-Clauser-Horne inequality for two entangled three-dimensional quantum systems (so-called qutrits). This inequality is not violated by a maximally entangled state of two qutrits observed through a symmetric three-input- and three-output-port beam splitter only if the amount of noise in the system is greater than $(11\ensuremath{-}6\sqrt{3})/2\ensuremath{\approx}0.308.$ This result is in a perfect agreement with the previous numerical calculations presented in Kaszlikowski et al. [Phys. Rev. Lett. 85, 4418 (2000)]. Moreover, we prove that for noiseless case, the necessary and sufficient condition for the threshold quantum efficiency of detectors below which there is no violation of local realism for the optimal choice of observables is equal to $6(15\ensuremath{-}4\sqrt{3})/59\ensuremath{\approx}0.821.$ This efficiency result again agrees with the numerical predictions.

Bell’s theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger andWstates

A proof of Bell's theorem without inequalities valid for both inequivalent classes of three-qubit entangled states under local operations assisted by classical communication, namely Greenberger-Horne-Zeilinger (GHZ) and W, is described. This proof leads to a Bell inequality that allows more conclusive tests of Bell's theorem for three-qubit systems. Another Bell inequality involving both tri- and bipartite correlations is introduced which illustrates the different violations of local realism exhibited by the GHZ and W states.

Violation of a Bell-type inequality in the homodyne measurement of light in an Einstein-Podolsky-Rosen state

An optical Einstein-Podolsky-Rosen (EPR) state is produced in the spontaneous parametric down-conversion of an ultrashort classical pump pulse. It is shown both theoretically and experimentally that this results in the violation of a Bell-type inequality of the kind proposed by Grangier et al. The experiment is based on measuring interference between the light in the EPR state and weak light pulses in a coherent state. The maximum observed visibility of the interference pattern was $(89\ifmmode\pm\else\textpm\fi{}4)%.$ This interference can be regarded as a manifestation of nonlocality in the sense described by Banaszek and Wodkiewicz, even though the EPR state has a positive Wigner function. We develop the theory of two-channel homodyne detection with ultrafast pulses and then apply it to the EPR state generated in a type-II collinear geometry. Particular attention is paid to the investigation of how dispersion and phase matching influence the violation of local realism.