Matteo Smerlak, Carlo Rovelli
We study the EPR-type correlations from the perspective of the relational interpretation of quantum mechanics. We argue that these correlations do not entail any form of 'non-locality', when viewed in the context of this interpretation. The abandonment of strict Einstein realism implied by the relational stance permits to reconcile quantum mechanics, completeness, (operationally defined) separability, and locality.
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A new formulation of the EPR argument is presented, one which uses John Bell's mathematically precise local causality condition in place of the looser locality assumption which was used in the original EPR paper and on which Niels Bohr seems to have based his objection to the EPR argument. The new formulation of EPR bears a striking resemblance to Bell's derivation of his famous inequalities. The relation between these two arguments -- in particular, the role of EPR as part one of Bell's two-part argument for nonlocality -- is also discussed in detail.
The Einstein-locality of our EPR model has been questioned. We show that our model obeys Einstein locality and that the questions are without basis.
We prove that by adopting a strict interpretation of the Einstein-Podolsky-Rosen criterion of reality, the proofs of the known non-locality theorems fail in showing that quantum mechanics violates the principle of locality and reality.
A consistent geometrical approach to EPR non-locality as well as other non-local effects in QM like the Aharanov-Bohm effect, Berry phase, Gauge theories within Yang-Mills theory etc. is possible within the framework of sheaf cohomology. This sheds new light on our understanding on non-local correlations in QM, and provides a fundamental mathematical approach to fundamental problems in physics.
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.
It is shown that in the Rovelli relational interpretation of quantum mechanics, in which the notion of absolute or observer independent state is rejected, the conclusion of the ordinary EPR argument turns out to be frame-dependent, provided the conditions of the original argument are suitably adapted to the new interpretation. The consequences of this result for the `peaceful coexistence' of quantum mechanics and special relativity are briefly discussed.
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 …
The question has been solved whether Bell's inequalities cover all possible kinds of hidden-variable theories. It has been shown that the given nequalities can be hardly derived when the changing space position of photon-pair source together with the microscopic space structure of measuring devices are taken into account; and when corresponding impact parameters (i.e., exact impact points) of photons in individual measuring devices (polarizers) influence measured values, in addition to usually considered characteristics.
The term 'locality' is used in different contexts with different meanings. There have been claims that relational quantum mechanics is local, but it is not clear then how it accounts for the effects that go under the usual name of quantum non-locality. The present article shows that the failure of 'locality' in the sense of Bell, once interpreted in the relational framework, reduces to the existence of a common cause in an indeterministic context. In particular, there is no need to appeal to a mysterious space-like influence to understand it.
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 …
Schroedinger's principle eliminates the EPR-locality paradox
本文提出薛定谔原理，证明在哥本哈根诠释中EPR局域性悖论不存在，通过双spin1/2纠缠态的最简例子展示悖论的合理性，反驳了Araki和Yanase关于测量非局域性的观点。
The realization of the Einstein-Podolsky-Rosen effect by the correlation of spin projections of two particles created in the decay of a single scalar particle is considered for particles propagating in gravitational field. The absence of a global definition of spatial directions makes it unclear whether the correlation may exist in this case and, if yes, what directions in distant regions must be correlated. It is shown that in a gravitational field an approximate correlation may exist and the correlated directions are connected with each other by the parallel transport along the world lines o…
Most physicists agree that the Einstein-Podolsky-Rosen-Bell paradox exemplifies much of the strange behavior of quantum mechanics, but argument persists about what assumptions underlie the paradox. To clarify what the debate is about, we employ a simple and well-known thought experiment involving two correlated photons to help us focus on the logical assumptions needed to construct the EPR and Bell arguments. The view presented in this paper is that the minimal assumptions behind Bell's inequality are locality and counterfactual definiteness, but not scientific realism, determinism, or hidden …
Local realism has been knocked down by the experiments with entangled pairs of particles based on Bell's theorem(J. S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964)). However, there has been continuing debate on whether locality or realism is the problem. In this work, we analyzed the Einstein-Podolsky-Rosen thought experiment of Bohm's version using information theory and thermodynamics. The inference of non-locality from EPR experiments will be against the principle of non-realism of quantum mechanics. Therefore, the experiments about quantum entanglement cannot provide any proof to a…
We provide a detailed description of the EPR paradox (in the Bohm version) for a two qubit-state in the discrete Wigner function formalism. We compare the probability distributions for two qubit relevant to simultaneously-measurable observables (computed from the Wigner function) with the probability distributions representing two perfectly-correlated classic particles in a discrete phase-space. We write in both cases the updating formulae after a measure, thus obtaining a mathematical definition of \textit{classic collapse} and \textit{quantum collapse}. We study, with the EPR experiment, the…
Maudlin has claimed that no local theory can reproduce the predictions of standard quantum mechanics that violate Bell's inequality for Bohm's version (two spin-half particles in a singlet state) of the Einstein-Podolsky-Rosen problem. It is argued that, on the contrary, standard quantum mechanics itself is a counterexample to Maudlin's claim, because it is local in the appropriate sense (measurements at one place do not influence what occurs elsewhere there) when formulated using consistent principles in place of the inconsistent appeals to "measurement" found in current textbooks. This argum…
A recent paper [P. Martin-Dussaud, C. Rovelli, F. Zalamea, arXiv:1806.08150] has given a lucid treatment of Bell's notion of local causality within the framework of the relational interpretation of quantum mechanics. However, the authors went on to conclude that the quantum violation of Bell's notion of local causality is no more surprising than a common cause. Here, I argue that this conclusion is unwarranted by the authors' own analysis. On the contrary, within the framework outlined by the authors, I argue that the implications of the relational interpretation are much more radical.
We study the possibility of testing local realistic theory (LRT), envisioned implicitly by Einstein, Podolsky and Rosen in 1935, based on the Bell inequality for the correlations in the decay modes of entangled K or B-mesons. It is shown that such a test is possible for a restricted class of LRT, despite the passive nature of decay events and/or the non-unitary treatment of the correlations which invalidate the test for general LRT. Unfortunately, the present setup of the KEKB (Belle) experiment, where the coherence of entangled B-mesons has been confirmed recently, does not admit such a test …
The EPR argument points to the existence of additional variables that are necessary to complete standard quantum theory. It was dismissed by Bohr because it attributes physical reality to isolated microscopic systems, independently of the macroscopic measurement apparatus. Here, we transpose the EPR argument to macroscopic systems, assuming that they are in spatially extended Fock spin states and subject to spin measurements in remote regions of space. Bohr's refutation of the EPR argument does not seem to apply in this case, since the difference of scale between the microscopic measured syste…
We describe a completely general and fully non-perturbative framework for constructing dynamical reference frames in generally covariant theories, and for understanding the gauge-invariant observables that they yield. Our approach makes use of a 'universal dressing space', which contains as a subset every possible dynamical frame. We describe examples of such frames, including matter frames, a popular construction based on boundary-anchored geodesics and one using minimal surfaces -- but our formalism does not depend on the existence of a boundary. The class of observables we construct general…
Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the relational probability amplitude matrix is transformed and how mutual information is exchanged during measurement, we derive the formulation that is mathematically equivalent to the traditional quantum measurement theory. More importantly, the formulation results in significant conceptual consequences. We show that for a given quantum system, it is possible t…
We show that EPR's criterion of reality leads to contradictions in quantum mechanics. When locality is assumed, an inequality involving only one particle is violated, while when parameter and outcome dependence are assumed, EPR-realism is shown to be not Lorentz invariant. Quantum mechanics is both non-local and non-realistic.
We use a simple relational framework to develop the key notions and results on hidden variables and non-locality. The extensive literature on these topics in the foundations of quantum mechanics is couched in terms of probabilistic models, and properties such as locality and no-signalling are formulated probabilistically. We show that to a remarkable extent, the main structure of the theory, through the major No-Go theorems and beyond, survives intact under the replacement of probability distributions by mere relations.
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.
As part of a challenge to critics of Bell's analysis of the EPR argument, framed in the form of a bet, R. D. Gill formulated criteria to assure that all non-locality is precluded from simulation-algorithms used to test Bell's theorem. This is achieved in part by parceling out the subroutines for the source and both detectors to three separate computers. He argues that, in light of Bell's theorem, following these criteria absolutely precludes mimicking EPR-B correlations as computed with Quantum Mechanics and observed in experiments. Herein, nevertheless, we describe just such an local algorith…
A model for two entangled systems in an EPR setting is shown to reproduce the quantum-mechanical outcomes and expectation values. Each system is represented by a small sphere containing a point-like particle embedded in a field. A quantum state appears as an equivalence class of several possible particle-field configurations. Contrarily to Bell-type hidden variables models, the fields account for the non-commutative aspects of the measurements and deny the simultaneous reality of incompatible physical quantities, thereby allowing to escape EPR's "completeness or locality" dilemma.
Backward causation in which future events affect the past is formalized in a way consistent with Special Relativity and shown to restore locality to nonrelativistic quantum mechanics. It can explain the correlations of the EPR paradox without using hidden variables. It also restores time-symmetry to microphysics. Quantum Mechanics has the right properties to allow for backward causation. The new model is probably untestable experimentally but it has profound philosophical implications concerning reality.
Starting from the late 60's many experiments have been performed to verify the violation Bell's inequality by Einstein-Podolsky-Rosen (EPR) type correlations. The idea of these experiments being that: (i) Bell's inequality is a consequence of locality, hence its experimental violation is an indication of non locality; (ii) this violation is a typical quantum phenomenon because any classical system making local choices (either deterministic or random) will produce correlations satisfying this inequality. Both statements (i) and (ii) have been criticized by quantum probability on theoretical gro…
A model for two entangled systems in an EPR setting is shown to reproduce the quantum-mechanical outcomes and expectation values. Each system is represented by a small sphere containing a point-like particle embedded in a field. A quantum state appears as an equivalence class of several possible particle-field configurations. Contrarily to Bell-type hidden variables models, the fields account for the non-commutative aspects of the measurements and deny the simultaneous reality of incompatible physical quantities, thereby allowing to escape EPR's ``completeness or locality'' dilemma.
A classical deterministic, reversible dynamical systems, reproducing the Einstein--Podolsky--Rosen (EPR) correlations in full respect of causality and locality and without the introduction of any ad hoc selection procedure, was constructed in the paper [AIR02]. In the present paper we prove that the above mentioned model is unique (see Theorem (2) in the sense that any local causal probability measure which reproduces the EPR correlations must coincide, under natural and generic assumptions, with the one constructed in [AIR02]. [AIR02] L. Accardi, K. Imafuku and M. Regoli, "ON THE EPR--CHAMELE…
Einstein, Podolsky and Rosen (EPR) pointed out that the quantum-mechanical description of "physical reality" implied an unphysical, instantaneous action between distant measurements. To avoid such an action at a distance, EPR concluded that Quantum Mechanics had to be incomplete. However, its extensions involving additional "hidden variables", allowing for the recovery of determinism and locality, have been disproved experimentally (Bell's theorem). Here, I present an opposite solution of the paradox based on the greater indeterminism of the modern Quantum Field Theory (QFT) description of Par…
Bell's theorem is a statement by which averages obtained from specific types of statistical distributions must conform to a family of inequalities. These models, in accordance with the EPR argument, provide for the simultaneous existence of quantum mechanically incompatible quantities. We first recall several contradictions arising between the assumption of a joint distribution for incompatible observables and the probability structure of quantum-mechanics, and conclude that Bell's theorem is not expected to be relevant to quantum phenomena described by non-commuting observables, irrespective …
A critical reconsideration of the EPR (Einstein-Podolsky-Rosen) paper shows that the EPR argument can be developed without using the concept of `element of physical reality', thus eliminating any philosophical element in the logical chains of the paper. Deprived of its philosophical ornament, the EPR argument plainly reduces to require what quantum mechanics can not do: to assign definite values to two incompatible physical quantities. Hidden variables theories built up according to Bell - type theorems are formulated on the basis of the assumption that the locality condition implies the stati…
It is currently believed that the local causality of Quantum Field Theory (QFT) is destroyed by the measurement process. This belief is also based on the Einstein-Podolsky-Rosen (EPR) paradox and on the so-called Bell's theorem, that are thought to prove the existence of a mysterious, instantaneous action between distant measurements. However, I have shown recently that the EPR argument is removed, in an interpretation-independent way, by taking into account the fact that the Standard Model of Particle Physics prevents the production of entangled states with a definite number of particles. Thi…
The aim of the paper is to investigate the characterization of an unambiguous notion of causation linking single space-llike separated events in EPR-Bell frameworks. This issue is investigated in ordinary quantum mechanics, with some hints to no collapse formulations of the theory such as Bohmian mechanics.
Quantum mechanics is very odd. It presents both an immensely practical and a deeply troubling conception of the physical world. As such, its uses stretch from optimizing nanoelectronics to examining the very nature of reality. In this article we will see how quantum mechanics forces us into a dramatic rethinking of one of the most fundamental tenets of modern science, locality. The article is written in a popular style for anyone interested in this subject.
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…
The emergence of the generalized uncertainty principle and the existence of a non-zero minimal length are intertwined. On the other hand, the Heisenberg uncertainty principle forms the core of the EPR paradox. Subsequently, here, the implications of resorting to the generalized uncertainty principle (or equally, the minimal length) instead of the Heisenberg uncertainty principle on the quantum non-locality are investigated through focusing on the Franson experiment in which the uncertainty relation is the backbone of understanding and explaining the results.
We describe an experiment in which two non communicating computers, starting from a common input in the form of sequences of pseudo--random numbers in the interval $[0,2π]$, and computing deterministic $\{\pm 1\}$--valued functions, chosen at random and independently, produce sequences of numbers whose correlations coincide with the EPR correlations and therefore violate Bell's inequality. The experiment is the practical implementation of a mathematical model of a classical, deterministic system whose initial state is chosen at random from its state space, with a known initial probability dist…
According to Bell's theorem, the degree of correlation between spatially separated measurements on a quantum system is limited by certain inequalities if one assumes the condition of locality. Quantum mechanics predicts that this limit can be exceeded, making it nonlocal. We analyse the effect of an environment modelled by a fluctuating magnetic field on the quantum correlations in an EPR singlet as seen in the Bell inequality. We show that in an EPR setup, the system goes from the usual 'violation' of Bell inequality to a 'non-violation' for times larger than a characteristic time scale which…
We review the computation of correlations of successive projections of the spin onto axes for spin-1/2 particles and EPRB pairs (in the Singlet state). We assume forms of Realism (at least as general as the Predictive Hidden Variables in the classical Bell's Theory), to review one particle correlations before we further assume Locality and analyze EPRB pairs. To our surprise, we find that the Abstract Bell Inequalities with three or four axes cannot have physical meaning i.e., two spin projections cannot belong to one particle or some correlations that one would need cannot be evaluated. A rec…
We argue that the so-called entangled states in quantum theory are not something exceptional, deserving a special attention in our efforts to understand conceptual foundations of quantum world. They appear by constructing the basis states of a compound system via the basis states of entering subsystems and describe it as a wholeness. While a system is considered as a wholeness, the individual members, forming the entangled state, have no physical meaning. In consequence, there is no physical ground for Einstein, Podolsky and Rosen (EPR) correlations arising in a process of decaying the system,…
The quantum theory (QT) and new stochastic approaches have no deterministic prediction for a single measurement or for a single time -series of events observed for a trapped ion, electron or any other individual physical system. The predictions of QT being of probabilistic character apply to the statistical distribution of the results obtained in various experiments. The probability distribution is not an attribute of a dice but it is a characteristic of a whole random experiment : '' rolling a dice''. and statistical long range correlations between two random variables X and Y are not a proof…
Einstein, Podolsky and Rosen (EPR) argued that the quantum-mechanical probabilistic description of physical reality had to be incomplete, in order to avoid an instantaneous action between distant measurements. This suggested the need for additional "hidden variables", allowing for the recovery of determinism and locality, but such a solution has been disproved experimentally. Here, I present an opposite solution, based on the greater indeterminism of the modern quantum theory of Particle Physics, predicting that the number of photons is always uncertain. No violation of locality is allowed for…
Recently it has been shown that transformations of Heisenberg-picture operators are the causal mechanism which allows Bell-theorem-violating correlations at a distance to coexist with locality in the Everett interpretation of quantum mechanics. A calculation to first order in perturbation theory of the generation of EPRB entanglement in nonrelativistic fermionic field theory in the Heisenberg picture illustrates that the same mechanism leads to correlations without nonlocality in quantum field theory as well. An explicit transformation is given to a representation in which initial-condition in…
Non-locality and quantum measurement are two fundamental topics in quantum theory and theirinterplay attracts intensive focus since the discovery of Bell theorem. Non-locality sharing amongmultiple observers is predicted and experimentally observed. However, only one-sided sequentialcase, i.e., one Alice and multiple Bobs is widely discussed and little is known about two-sided case.Here, we theoretically and experimentally explore the non-locality sharing in two-sided sequentialmeasurements case in which one entangled pair is distributed to multiple Alices and Bobs. Weexperimentally observed d…
I purport to show why old and new claims on the role of counterfactual reasoning for the EPR argument and the Bell theorem are unjustified: once the logical relation between locality and counterfactual reasoning is clarified, the use of the latter does no harm and the nonlocality result can well follow from the EPR premises. To show why, I critically review (i) incompleteness arguments that Einstein developed before the EPR paper, and (ii) more recent claims that equate the use of counterfactual reasoning with the assumption of a strong form of realism.
It is shown that a criterion used to demonstrate realization of the 1935 Einstein-Podolsky-Rosen (EPR) gedanken experiment is sufficient to demonstrate quantum entanglement. A further set of measurable criteria sufficient to demonstrate EPR gedanken experiment is proposed, these being the set of criteria sufficient to demonstrate entanglement, by way of a measured violation of a necessary condition of separability. In this way, provided the spatial separation of systems is sufficient to ensure EPR's locality hypothesis, it is shown how a measured demonstration of entanglement will, at least, b…
A large number of physicists now admit that quantum mechanics is a non local theory. The EPR argument and the many experiments (including recent loop-hole free tests) showing the violation of Bell's inequalities seem to have confirmed convincingly that quantum mechanics cannot be local. Nevertheless, this conclusion can only be drawn inside a standard realist framework assuming an ontic interpretation of the wave function and viewing the collapse of the wave function as a real change in the physical state of the system. We show that this standpoint is not mandatory and that if the collapse is …
We derive a Bell-like inequality involving all correlations in local observables with uncertainty free states and show that the inequality is violated in quantum mechanics for EPR and GHZ states. If the uncertainties are allowed in local observables then the statistical predictions of hidden variable theory is well respected in quantum world. We argue that the uncertainties play a key role in understanding the non-locality issues in quantum world. Thus we can not rule out the possibility that a local, realistic hidden variable theory with statistical uncertainties in the observables might repr…
Actual realisations of EPR experiments do {\em not} demonstrate non-locality. A model is presented that should enable non-specialists as well as specialists to understand how easy it is to find realistic explanations for the observations. The model also suggests new areas where realistic (``hidden-variable'') models can give valid predictions whilst quantum mechanics fails. It offers straightforward explanations for some anomalies that Aspect was unable to account for, providing perhaps the first experimental evidence that a hidden-variable theory can be {\em superior} to quantum mechanics. Th…
Activation of post-quantum steering
本文展示了如何通过更大网络激活后量子引导，使其在贝尔场景中表现为后量子相关性，同时展示了在假设后量子资源下如何自我测试双方面量子集合。
Quantum inseparabilities can be classified into three inequivalent forms: entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Bell-nonlocal states form a strict subset of EPR steerable states which also form a strict subset of entangled states. Recently, EPR steerable states are shown to be fundamental resources for one-sided device-independent quantum information processing tasks and, hence, identification of EPR steerable states becomes important from foundational as well as informational theoretic perspectives. In the present study we propose a new criteria to dete…
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.
Einstein-Podolsky-Rosen (EPR) steering demonstrates that two parties share entanglement even if the measurement devices of one party are untrusted. Here, going beyond this bipartite concept, we develop a novel formalism to explore a large class of EPR steering from generic multipartite quantum systems of arbitrarily high dimensionality and degrees of freedom, such as graph states and hyperentangled systems. All of these quantum characteristics of genuine high-order EPR steering can be efficiently certified with few measurement settings in experiments. We faithfully demonstrate for the first ti…
It is shown that the quantum theory can be formulated on homogeneous spaces of generalized coherent states in a manner that accounts for interference, entanglement, and the linearity of dynamics without using the superposition principle. The coherent state labels, which are essentially instructions for preparing states, make it unnecessary to identify properties with projectors in Hilbert space. This eliminates the so called "eigenvalue-eigenstate" link, and the theory thereby escapes the measurement problem. What the theory allows us to predict is the distribution in the outcomes of tests of …
We discuss quantum non-locality and contextuality using the notion of transition sets. This approach provides a way to obtain a direct logical contradiction with locality/non-contextuality in the EPRB gedanken experiment as well as a clear graphical illustration of what violations of Bell inequalities quantify. In particular, we show graphically how these violations are related to measures of non-local transition sets. We also introduce a new form of contextuality, {\em measurement ordering contextuality}, i.e. there exists commuting operators $\hat{\mathcal{A}}$ and $\hat{\mathcal{B}}$ such t…
An elementary topological error in Bell's representation of the EPR elements of reality is identified. Once recognized, it leads to a topologically correct local-realistic framework that provides exact, deterministic, and local underpinning of at least the Bell, GHZ-3, GHZ-4, and Hardy states. The correlations exhibited by these states are shown to be exactly the classical correlations among the points of a 3 or 7-sphere, both of which are closed under multiplication, and hence preserve the locality condition of Bell. The alleged non-localities of these states are thus shown to result from mis…
EPR correlations exist and can be observed independently of any a priori given frame of reference. We can even construct a frame of reference that is based on these correlations. This observation-based frame of reference is equivalent to the customary a priori given frame of reference of the laboratory when describing real EPR experiments. J.S. Bell has argued that local hidden parameter theories that reproduce the predictions of Quantum Mechanics cannot exist, but the counterfactual reasoning leading to Bell's conclusion is physically meaningless if the frame of reference that is based on EPR…
I report on the discovery of quantum compatible local variables that are shared between subsystems of quantum-conventionally entangled physical systems such that they determine the correlations of spatially separated systems while preserving strict Einstein locality. This puts an end to the mystery of spooky action at a distance and alleged collapse at a distance, answering vital questions, first raised in the EPR paper, on the behaviour of spatially separated entangled systems. The solution helps to understand quantitative measures of entanglement in a transparent way. It also provides new in…
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