The long-standing puzzle of the nonlocal Einstein-Podolsky-Rosen correlations is resolved. The correct quantum mechanical correlations arise for the case of entangled particles when strict locality is assumed for the probability amplitudes instead of locality for probabilities. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state.
The present standard interpretation of quantum mechanics invokes nonlocality and state reduction at space-like separated points during measurements on entangled systems. While there is no understanding of the physical mechanism of such nonlocal state reduction, the experimental verifications of quantum correlations different from that predicted by local realistic theories have polarized the physicists' opinion in favour of nonlocality. I show conclusively that there is no such spooky state reduction, vindicating the strong views against nonlocality held by Einstein and Popper. Experimental sup…
We begin with a review of the famous thought experiment that was proposed by Einstein, Podolsky and Rosen (EPR) and mathematically formulated by Bell; the outcomes of which challenge the completeness of quantum mechanics and the locality of Nature. We then suggest a reinterpretation of the EPR experiment that utilizes observer complementarity; a concept from quantum gravity which allows spatially separated observers to have their own, independent reference frames. The resulting picture provides a self-consistent resolution of the situation that does not jeopardize causality nor unitarity, nor …
Quantum non-local correlations and the acausal, spooky action at a distance suggest a discord between quantum theory and special relativity. We propose a resolution for this discord by first observing that there is a problem of time in quantum theory. There should exist a reformulation of quantum theory which does not refer to classical time. Such a reformulation is obtained by suggesting that space-time is fundamentally non-commutative. Quantum theory without classical time is the equilibrium statistical thermodynamics of the underlying non-commutative relativity. Stochastic fluctuations abou…
Whence Nonlocality? Removing spooky action at a distance from the de Broglie Bohm pilot-wave theory using a time-symmetric version of de Broglie double solution
In the well-known EPR paper, Einstein et al. called the nonlocal correlation in quantum entanglement as `spooky action at a distance'. If the spooky action does exist, what is its speed? All previous experiments along this direction have locality loopholes and thus can be explained without having to invoke any `spooky action' at all. Here, we strictly closed the locality loopholes by observing a 12-hour continuous violation of Bell inequality and concluded that the lower bound speed of `spooky action' was four orders of magnitude of the speed of light if the Earth's speed in any inertial refer…
It is proved in the frame of standard quantum mechanics that selection of different ensembles emerging from measurements of an observable leads to identification of corresponding reductions of the initial, premeasured state. This solves the problem of ``nonlocality`` observed in EPR-Bohm-type experiments.
Henry Stapp's commentary (quant-ph/9711060) does not capture the point I was trying to make in my essay (quant-ph/9711052) on how a subtle flaw in his ``proof of quantum nonlocality'' clearly illustrates a central issue in Bohr's reply to EPR. I therefore wish to emphasize what I do and do not say in that essay and even, with some trepidation, what Bohr did and did not say in his reply to EPR.
A new way of understanding the non local correlation effects observed in the 'Twin Photon' EPR experiment is presented. The theory is based on a vector version of the Kuramoto sychronisation for coupled non linear oscillators. EPR correlation is obtained without the use of superluminal signals. Bell's inequality is used to confirm that the local theory developed can still violate the inequality resolving the non local nature of the correlation.
The enigmatic nonlocal quantum correlation that was famously derided by Einstein as "spooky action at a distance" has now been experimentally demonstrated to be authentic. The quantum entanglement and nonlocal correlations emerged as inevitable consequences of John Bell's epochal paper on Bell's inequality. However, in spite of some extraordinary applications as well as attempts to explain the reason for quantum nonlocality, a satisfactory account of how Nature accomplishes this astounding phenomenon is yet to emerge. A cogent mechanism for the occurrence of this incredible event is presented …
We give a conceptually simple proof of nonlocality using only the perfect correlations between results of measurements on distant systems discussed by Einstein, Podolsky and Rosen---correlations that EPR thought proved the incompleteness of quantum mechanics. Our argument relies on an extension of EPR by Schrödinger.
It is shown that classical electrodynamics in its alternative Kemmer-Duffin-Petiau-Harish-Chandra formulation surprisingly reveals a Hilbert space structure leading to the possibility of entangled states of classical radiation, and this in turn implies the violation of Einstein-Bell locality in spite of Lorentz invariance.
Relativistic bipartite entangled quantum states is studied to show that Nature doesn't favor nonlocality for massive particles in the ultra-relativistic limit. We found that to an observer (Bob) in a moving frame S', the entangled Bell state shared by Alice and Bob appears as the superposition of the Bell bases in the frame S' due to the requirement of the special relativity. It is shown that the entangled pair satisfies the Bell's inequality when the boost speed approaches the speed of light, thus providing a counter example for nonlocality of Einstein-Podolsky-Rosen(EPR) paradox.
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.
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…
It is shown that the Einstein, Podolsky and Rosen (EPR) correlations for arbitrary spin-s and the Greenberger, Horne and Zeilinger (GHZ) correlations for three particles can be described by nonlocal joint and conditional quantum probabilities. The nonlocality of these probabilities makes the Bell's inequalities void. A description that exhibits the relation between the randomness and the nonlocality of entangled correlations is introduced. Entangled EPR and GHZ correlations are studied using the Gibbs-Shannon entropy. The nonlocal character of the EPR correlations is tested using the informati…
Quantum trajectories are used to investigate the EPR-Bohr debate in a modern sense by examining entanglement and nonlocality. We synthesize a single "entanglement molecule" from the two scattered particles of the EPR experiment. We explicitly investigate the behavior of the entanglement molecule rather than the behaviors of the two scattered particles to gain insight into the EPR-Bohr debate. We develop the entanglement molecule's wave function in polar form and its reduced action, both of which manifest entanglement. We next apply Jacobi's theorem to the reduced action to generate the equatio…
The concept of steering was introduced by Schrodinger in 1935 as a generalization of the EPR paradox for arbitrary pure bipartite entangled states and arbitrary measurements by one party. Until now, it has never been rigorously defined, so it has not been known (for example) what mixed states are steerable (that is, can be used to exhibit steering). We provide an operational definition, from which we prove (by considering Werner states and Isotropic states) that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell-nonlocality. …
We discuss the problem of finding a Lorentz invariant extension of Bohmian mechanics. Due to the nonlocality of the theory there is (for systems of more than one particle) no obvious way to achieve such an extension. We present a model invariant under a certain limit of Lorentz transformations, a limit retaining the characteristic feature of relativity, the non-existence of absolute time resp. simultaneity. The analysis of this model exemplifies an important property of any Bohmian quantum theory: the quantum equilibrium distribution $ρ= |ψ|^2$ cannot simultaneously be realized in all Lorentz …
We show that the projection postulate plays a crucial role in the discussion on the so called "quantum nonlocality", in particular in the EPR-argument. We stress that the original von Neumann projection postulate was crucially modified by extending it to observables with degenerate spectra (the Lüders postulate) and we show that this modification is highly questionable from a physical point of view, and it is the real source of "quantum nonlocality". The use of the original von Neumann postulate eliminates this problem: instead of "action at the distance"-nonlocality, we obtain a classical mea…
Bell nonlocality and Einstein-Podolsky-Rosen (EPR) steering are every important quantum correlations of a composite quantum system. Bell nonlocality of a bipartite state is a quantum correlation demonstrated by some local quantum measurements, while EPR steering is another form of quantum correlations, observed firstly by Schrodinger in the context of famous EPR paradox. In this paper, we give some remarks on Bell nonlocality and EPR steering of bipartite states, including mathematical definitions and characterizations of these two quantum correlations, the convexity and closedness of the set …
Bell's theorem has fascinated physicists and philosophers since his 1964 paper, which was written in response to the 1935 paper of Einstein, Podolsky, and Rosen. Bell's theorem and its many extensions have led to the claim that quantum mechanics and by inference nature herself are nonlocal in the sense that a measurement on a system by an observer at one location has an immediate effect on a distant "entangled" system (one with which the original system has previously interacted). Einstein was repulsed by such "spooky action at a distance" and was led to question whether quantum mechanics coul…
In a recent work [Phys. Rev. Lett. {\bf 98}, 140402 (2007)] we defined ``steering'', a type of quantum nonlocality that is logically distinct from both nonseparability and Bell-nonlocality. In the bipartite setting, it hinges on the question of whether Alice can affect Bob's state at a distance through her choice of measurement. More precisely and operationally, it hinges on the question of whether Alice, with classical communication, can convince Bob that they share an entangled state, under the circumstances that Bob trusts nothing that Alice says. We argue that if she can, then this demonst…
We develop criteria to detect three classes of nonlocality that have been shown by Wiseman et al. [Phys. Rev. Lett. 98, 140402 (2007)] to be nonequivalent: entanglement, EPR steering, and the failure of local hidden-variable theories. We use the approach of Cavalcanti et al. [Phys. Rev. Lett. 99, 210405 (2007)] for continuous variables to develop the nonlocality criteria for arbitrary spin observables defined on a discrete Hilbert space. The criteria thus apply to multisite qudits, i.e., systems of fixed dimension d, and take the form of inequalities. We find that the spin moment inequalities …
In terms of a suitable variant of the EPR-Bohm example, we argue that the quantum mechanically predicted and experimentally verified violation of a Bell-type path-spin noncontextual realist inequality for an `intraparticle' path-spin entanglement involving single neutrons can be used to infer a form of nonlocality, distinct from Bell-type nonlocality, that is required for any relevant hidden variable model to be compatible with the quantum mechanical treatment of an EPR-Bohm-type `interparticle' entanglement.
David Mermin's recent paper with the same title as this one makes it clear that his claim to have found a gap in my reasoning rests on his claim that my argument violates a criterion for meaningfulness of counterfactual statements that I myself had set down. I set down no such requirement. But I am willing to accept it as a conservative sufficient condition. This already entails, within my proof, that nature must have a deep structure that extends beyond what actually occurs. It imposes, without appeal to the notion of determinism or hidden variables, constraints connecting, at the macroscopic…
I have been arguing that quantum nonlocality, deeply entrenched in the present formalism of quantum mechanics and widely believed as a reality by physicists, is in fact absent. Spooky nonlocal state reduction is the most, and perhaps the only irrational feature of present day physics. There are experimental results that reject nonlocal state reduction at a distance. Also, there are arguments that show that signal locality itself can be violated if there is true nonlocal collapse of the wavefunction. The Bell's inequalities, the violation of which polarized physicists in favour of nonlocality, …
A single photon incident on a beam splitter produces an entangled field state, and in principle could be used to violate a Bell-inequality, but such an experiment (without post-selection) is beyond the reach of current experiments. Here we consider the somewhat simpler task of demonstrating EPR-steering with a single photon (also without post-selection). That is, of demonstrating that Alice's choice of measurement on her "half" of a single photon can affect the other "half" of the photon in Bob's lab, in a sense rigorously defined by us and Doherty [Phys. Rev. Lett. 98, 140402 (2007)]. Previou…
In this paper, we propose a continuous measurement and feedback scheme to achieve strong Einstein-Podolsky-Rosen (EPR) steering and Bell nonlocality of two macroscopic mechanical oscillators in cavity optomechanics. Our system consists of two optomechanical cavities in which two cavity fields are coupled to each other via a nondegenerate parametric downconversion. The two cavity output fields are subject to continuous Bell-like homodyne detection and the detection currents are fed back to drive the cavity fields. It is found that when the feedback is absent, the two mechanical oscillators can …
We discuss violation of Bell inequalities by the regularized Einstein-Podolsky-Rosen (EPR) state, which can be produced in a quantum optical parametric down-conversion process. We propose an experimental photodetection scheme to probe nonlocal quantum correlations exhibited by this state. Furthermore, we show that the correlation functions measured in two versions of the experiment are given directly by the Wigner function and the Q function of the EPR state. Thus, the measurement of these two quasidistribution functions yields a novel scheme for testing quantum nonlocality.
Based on his extension of the classical argument of Einstein, Podolsky and Rosen, Schrödinger observed that, in certain quantum states associated with pairs of particles that can be far away from one another, the result of the measurement of an observable associated with one particle is perfectly correlated with the result of the measurement of another observable associated with the other particle. Combining this with the assumption of locality and some "no hidden variables" theorems, we showed in a previous paper [11] that this yields a contradiction. This means that the assumption of localit…
It is shown how a "meddlesome" photon indistinguishable from another photon of an entangled pair can affect the result of an Einstein- Podolsky-Rosen (EPR) experiment. This makes it clear the importance of the notion of field over that of particle.
Models are developed to estimate properties of relic cosmic perturbations with "spooky" nonlocal correlations on the inflationary horizon, analogous to those previously posited for information on black hole event horizons. Scalar curvature perturbations are estimated to emerge with a dimensionless power spectral density $Δ_S^2\approx H t_P$, the product of inflationary expansion rate $H$ with Planck time $t_P$, larger than standard inflaton fluctuations. Current measurements of the spectrum are used to derive constraints on parameters of the effective potential in a slow-roll background. It is…
This note is a part of my efforts for getting rid of nonlocality from quantum mechanics (QM). Quantum nonlocality is two faced Janus, one face is Lüders projection nonlocality, another face is Bell nonlocality. This paper is devoted to disillusion of the latter. The main casualty of Bell's model with hidden variables is that it straightforwardly contradicts to the Heinsenberg's uncertainty and generally Bohr's complementarity principles. Thus, we do not criticize the derivation or interpretation of the Bell inequality (as was done by numerous authors). Our critique is directed against the mode…
Quantum correlations of observables for two particle states have demonstrated the nonlocal character of the quantum mechanics. However nonlocality can be exhibited even for noncommuting observables of a single particle system. In this paper we show nonlocality of position-momentum correlations of a single particle in the double-slit experiment modeled by an initially correlated Gaussian wavepacket. The positivity or negativity of the Wigner function for the state of the particle at the detection screen is related with the $σ_{xp}$ covariances. A Bell's inequality is constructed from the Wigner…
Einstein-Podolsky-Rosen (EPR) steering exhibits an inherent asymmetric feature that differs from both entanglement and Bell nonlocality, which leads to one-way EPR steering. Although this one-way EPR steering phenomenon has been experimentally observed, the schemes to manipulate the direction of EPR steering have not been investigated thoroughly. In this paper, we propose and experimentally demonstrate three schemes to manipulate the direction of EPR steering, either by varying the noise on one party of a two-mode squeezed state (TMSS) or transmitting the TMSS in a noisy channel. The dependenc…
The Einstein-Podolsky-Rosen (EPR) paradox is one of the milestones in quantum foundations, arising from the lack of local realistic description of quantum mechanics. The EPR paradox has stimulated an important concept of "quantum nonlocality", which manifests itself by three different types: quantum entanglement, quantum steering, and Bell nonlocality. Although Bell nonlocality is more often used to show the "quantum nonlocality", the original EPR paradox is essentially a steering paradox. In this work, we formulate the original EPR steering paradox into a contradiction equality,thus making it…
Recent experiments have perfectly verified the fact that quantum correlations between two entangled particles are stronger than any classical, local pre-quantum worldview allows. This is famously called the EPR paradox first conceived as a thought experiment and decades later realized in the lab. We discuss in depth the nature of the paradox and show that the problematics it presents is first and foremost epistemological. After briefly exploring resolutions to the paradox that after many decades of discourse still remain controversial, we argue that the paradox is rooted in the failure of our …
Einstein-Podolsky-Rosen (EPR) steering is a form of quantum nonlocality which is intermediate between entanglement and Bell nonlocality. EPR steering is a resource for quantum key distribution that is device independent on only one side in that it certifies bipartite entanglement when one party's device is not characterized while the other party's device is fully characterized. In this work, we introduce two types of genuine tripartite EPR-steering, and derive two steering inequalities to detect them. In a semi-device-independent scenario where only the dimensions of two parties are assumed, t…
We formally link the concept of steering (a concept created by Schrodinger but only recently formalised by Wiseman, Jones and Doherty [Phys. Rev. Lett. 98, 140402 (2007)] and the criteria for demonstrations of Einstein-Podolsky-Rosen (EPR) paradox introduced by Reid [Phys. Rev. A, 40, 913 (1989)]. We develop a general theory of experimental EPR-steering criteria, derive a number of criteria applicable to discrete as well as continuous-variables observables, and study their efficacy in detecting that form of nonlocality in some classes of quantum states. We show that previous versions of EPR-ty…
We investigate the complexity cost of demonstrating the key types of nonclassical correlations --- Bell inequality violation, EPR-steering, and entanglement --- with independent agents, theoretically and in a photonic experiment. We show that the complexity cost exhibits a hierarchy among these three tasks, mirroring the recently-discovered hierarchy for how robust they are to noise. For Bell inequality violations, the simplest test is the well-known CHSH test, but for EPR-steering and entanglement the tests that involve the fewest number of detection patterns require non-projective measuremen…
Quantum nonlocality is a kind of significant quantum correlation that is stronger than quantum entanglement and EPR steering. The standard tripartite nonlocality can be detected by the violation of the Mermin inequality. By using local filtering operations, we give a tight upper bound on the maximal expected value of the Mermin operators. By detailed examples we show that the hidden standard nonlocality can be revealed by local filtering which can enhance the robustness of the noised entangled states.
In a recent paper [arXiv:1703.11003] on this journal Stephen Boughn argued that quantum mechanics does not require nonlocality of any kind and that the common interpretation of Bell theorem as a nonlocality result is based on a misunderstanding. In this note I argue that the Boughn arguments, that summarize views widespread in certain areas of the foundations of quantum mechanics, are based on an incorrect reading of the presuppositions of the EPR argument and the Bell theorem and, as a consequence, are totally unfounded.
This paper is a new step towards getting rid of nonlocality from quantum physics. This is an attempt to structure the nonlocality mess. "Quantum nonlocality" is Janus faced. One its face is projection (Einstein-Lüders) nonlocality and another Bell nonlocality. The first one is genuine quantum nonlocality, the second one is subquantum nonlocality. Recently it was shown that Bell "nonlocality" is a simple consequence of the complementarity principle. We now show that projection nonlocality has no connection with physical space. Projection state update is generalization of the well known operatio…
It is argued that the Heisenberg picture of standard quantum mechanics does not save Einstein locality as claimed in Deutsch and Hayden (2000). In particular, the EPR-type correlations that DH obtain by comparing two qubits in a local manner are shown to exist before that comparison. In view of this result, the local comparison argument would appear to ineffective in supporting their locality claim.
We review some of our experiments performed over the past few years on two-photon interference. These include a test of Bell's inequalities, a study of the complementarity principle, an application of EPR correlations for dispersion-free time-measurements, and an experiment to demonstrate the superluminal nature of the tunneling process. The nonlocal character of the quantum world is brought out clearly by these experiments. As we explain, however, quantum nonlocality is not inconsistent with Einstein causality.
We propose an EPR inequality based on an entropic uncertainty relation for complementary continuous variable observables. This inequality is more sensitive than the previously established EPR inequality based on inferred variances, and opens up the possibility of EPR tests of quantum nonlocality in a wider variety of quantum states. We experimentally test the inequality using spatially entangled photons. For a particular quantum state, our experimental results show a violation of the entropic EPR inequality, while the variance EPR inequality is not violated.
By filtering out the philosophic component we can be said that the EPR-paper was directed against the straightforward interpretation of the Heisenberg's uncertainty principle or more generally the Bohr's complementarity principle. The latter expresses contextuality of quantum measurements: dependence of measurement's output on the complete experimental arrangement. However, Bell restructured the EPR-argument against complementarity to justify nonlocal theories with hidden variables of the Bohmian mechanics' type. Then this Bell's kind of nonlocality - {\it subquantum nonlocality} - was lifted …
The Einstein-Podolsky-Rosen (EPR) steering is an intermediate quantum nonlocality between entanglement and Bell nonlocality, which plays an important role in quantum information processing tasks. In the past few years, the investigations concerning EPR steering have been demonstrated in a series of experiments. However, these studies rely on the relevant steering inequalities and the choices of measurement settings. Here, we experimentally verify the EPR steering via entanglement detection without using any steering inequality and measurement setting. By constructing two new states from a two-…
For the Abner Shimony (AS) inequalities, the simplest unified forms of directions attaining the maximum quantum violation are investigated. Based on these directions, a family of Einstein-Podolsky-Rosen (EPR) steering inequalities is derived from the AS inequalities in a systematic manner. For these inequalities, the local hidden state (LHS) bounds are strictly less than the local hidden variable (LHV) bounds. This means that the EPR steering is a form of quantum nonlocality strictly weaker than Bell-nonlocality.
In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell's nonlocality does not go through for bipartite Einstein-Podolsky-Rosen (EPR) state. Recent study on quantum nonlocality has shown that the more precise description of EPR's original scenario is "steering", i.e., the no…
Einstein-Podolsky-Rosen (EPR) steering is an intermediate type of quantum nonlocality which sits between entanglement and Bell nonlocality. A set of correlations is Bell nonlocal if it does not admit a local hidden variable (LHV) model, while it is EPR nonlocal if it does not admit a local hidden variable-local hidden state (LHV-LHS) model. It is interesting to know what states can generate EPR-nonlocal correlations in the simplest nontrivial scenario, that is, two projective measurements for each party sharing a two-qubit state. Here we show that a two-qubit state can generate EPR-nonlocal fu…
