Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox

The concept of steering was introduced by Schr?dinger in 1935 as a generalization of the Einstein-Podolsky-Rosen 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. For arbitrary bipartite Gaussian states we derive a linear matrix inequality that decides the question of steerability via Gaussian measurements, and we relate this to the original Einstein-Podolsky-Rosen paradox.     

Einstein-Podolsky-Rosen correlations of ultracold atomic gases

We demonstrate that collective continuous variables of two species of trapped ultracold bosonic gases can be Einstein-Podolsky-Rosen-correlated (entangled) via inherent interactions between the species. We propose two different schemes for creating these correlations--a dynamical scheme and a static scheme analogous to two-mode squeezing in quantum optics. We quantify the correlations by using known measures of entanglement and study the effect of finite temperature on these quantum correlations.     

Continuous variable tripartite entanglement and Einstein-Podolsky-Rosen correlations from triple nonlinearities

We develop three-mode generalizations of the Einstein-Podolsky-Rosen paradox, allowing us to define inequalities which may be used to indicate continuous-variable tripartite entanglement. We use these inequalities and an appropriate version of the previously developed van Loock-Furusawa inequalities to theoretically compare the continuous-variable tripartite entanglement available from the use of three concurrent x ⁽²⁾ nonlinearities and from three independent squeezed states mixed on beamsplitters. The text was submitted by the authors in English.     

Quantum causal structure and the Einstein-Podolsky-Rosen experiment

In earlier papers—independently of the EPR problem—the author suggested a causal structure, which was intrinsically based on quantum theory. In this paper the causal relations of the crucial EPR events are analyzed in the light of the new conception of causality.     

Quantum nonlocality and beyond: limits from nonlocal computation

We address the problem of "nonlocal computation," in which separated parties must compute a function without any individual learning anything about the inputs. Surprisingly, entanglement provides no benefit over local classical strategies for such tasks, yet stronger nonlocal correlations allow perfect success. This provides intriguing insights into the limits of quantum information processing, the nature of quantum nonlocality, and the differences between quantum and stronger-than-quantum nonlocal correlations.     

On the relation between the Einstein-Podolsky-Rosen paradox and the problem of nonlocality in quantum mechanics

The EPR problem is studied both from an instrumentalistic and from a realistic point of view. Bohr's reply to the EPR paper is analyzed and demonstrated to be not completely representative of Bohr's general views on the possibility of defining properties of a microscopic object. A more faithful Bohrian answer would not have led Einstein to the conclusion that Bohr's completeness claim of quantum mechanics implies nonlocality. The projection postulate, already denounced in 1936 by Margenau as the source of the EPR paradox, is found to be also at the origin of the nonlocality conundrum. Its unobservability in EPR-like experiments is demonstrated, thus showing the redundancy of the idea of nonlocality in the instrumentalist interpretation of quantum mechanics. It is argued that also from a realist point of view there is no reason to assume nonlocality. The relevance of Bohm's quantum potential and of Bell's inequalities with respect to the (non)locality problem is discussed.     

Quantum correlations from classical Gaussian correlations

Already Schrödinger tried to proceed towards a purely wave theory of quantum phenomena. However, he should give up and accept Born’s probabilistic interpretation of the wave function. A simple mathematical fact was behind this crucial decision. The wave function of a composite system S = (S ₁, S ₂) belongs to the tensor product of two L2 spaces and not to their Cartesian product. It was impossible to consider it as a vector function ψ(x) = (ψ ₁(x), ψ ₂(x)), x ∈ R ³. Here we solved this problem. It is shown that there exists a mathematical formalism that provides a possibility to describe composite quantum systems without appealing to the tensor product of the Hilbert state space, and one can proceed with their Cartesian product. It may have important consequences for the understanding of entanglement and applications to quantum information theory. It seems that “quantum algorithms” can be realized on the basis of classical wave mechanics. However, the interpretation of the proposed mathematical formalism is a difficult problem and needs additional studies.     

Solving the Einstein-Podolsky-Rosen puzzle: the origin of non-locality in Aspect-type experiments

So far no mechanism is known, which could connect the two measurementsin an Aspect-type experiment. Here, we suggest such a mechanism, basedon the phase of a photon’s field during propagation. We showthat two polarization measurements are correlated, even if no signalpasses from one point of measurement to the other. The non-local connectionof a photon pair is the result of its origin at a common source, wherethe two fields acquire a well defined phase difference. Therefore,it is not actually a non-local effect in any conventional sense. Weexpect that the model and the detailed analysis it allows will havea major impact on quantum cryptography and quantum computation.     

Popescu-Rohrlich correlations as a unit of nonlocality

A set of nonlocal correlations that have come to be known as a Popescu-Rohrlich (PR) box suggest themselves as a natural unit of nonlocality, much as a singlet is a natural unit of entanglement. We present two results relevant to this idea. One is that a wide class of multipartite correlations can be simulated using local operations on PR boxes only. We show this with an explicit scheme, which has the interesting feature that the number of PR boxes required is related to the computational resources necessary to represent a function defining the multipartite box. The second result is that there are quantum multipartite correlations, arising from measurements on a cluster state, that cannot be simulated with n PR boxes, for any n.     

Quantum nonlocality and interference in frequency domain

The experiment is proposed which should demonstrate that if the filter providing the spectral selection is placed in the route of one photon of the entangled pair produced by spontaneous down-conversion and the photon is detected behind it then the interference appears in the (distant) Mach-Zehnder interferometer placed in the route of the other photon of the pair even if the optical path difference through the interferometer greatly exceeds the coherence length of the light and if the spectra of these two photons do not overlap. The theoretical analysis is carried out and physical interpretation is discussed.     

An analysis of the Einstein-Podolsky-Rosen correlations in terms of events

It is shown that Bell's inequalities can be derived from two general assumptions bearing on events, namely the possibility of their retrodiction and their locality. The meaning of a possible violation of the retrodiction principle is interpreted by making use of the many-worlds formulation of quantum mechanics.     

On some frequent but controversial statements concerning the Einstein-Podolsky-Rosen correlations

Quite often the compatibility of the EPR correlations with the relativity theory has been questioned; it has been stated that the first in time of two correlated measurements instantaneously collapses the other subsystem; it has been suggested that a causal asymmetry is built into the Feynman propagator. However, the EPR transition amplitude, as derived from the S matrix, is Lorentz andCPT invariant; the correlation formula is symmetric in the two measurements irrespective of their time ordering, so that the link of the correlations is the Feynman zigzag, and that causality isCPT invariant at the microlevel; finally, although the Feynman propagator has theP andCT symmetries, no causal asymmetry follows from that. As for Stapp's views concerning process and becoming, and his Whiteheadean concept of an advancing front, I object that they belong to factlike macrophysics, and are refuted at the microlevel by the EPR phenomenology, which displays direct Fokker-like space-time connections. The reason for this is a radical one. The very blending of a space-time picture and of a probability calculus is a paradox. The only adequate paradigm is one denying objectivity to space-time—but this, of course, is also required by the complementary of the x and the k pictures, which only look compatible at the macrolevel. Therefore, the classical objectivity must yield in favor of intersubjectivity. Only the macroscopic preparing and measuring devices have factlike objectivity; the transition of the quantal system takes place beyond both thex and thek 4-spaces. Then, the intrinsic symmetries between retarded and advanced waves, and statistical prediction and retrodiction, entails that the future has no less (but no more) existence than the past. It is the future that is significant in creative process, the elementary forms of which should be termed precognition or psychokinesis—respectively symmetric to the factlike taboos that we can neither know into the future nor act into the past. It is gratifying that Robert Jahn, at the Engineering School of Princeton University, is conducting (after others) conclusive experiments demonstrating low level psychokinesis—a phenomenon implied by the very symmetry of the negentropy-information transition. So, what pierces the veil of maya is the (rare) occurrence of paranormal phenomena. The essential severance between act and potentia is not a spacelike advancing front, but the out of and the into factlike space-time. Finally, I do not feel that an adequate understanding of the EPR phenomenology requires going beyond the present status of relativistic quantum mechanics. Rather, I believe that the potentialities of this formalism have not yet been fully exploited.     

Quantum nonlocality effect and radiative damping of the Dirac electron

Quantum spacetime nonlocality, i.e., retardation of the interaction between an electron and its own radiation field at distances of about the Compton wavelength, is established. By taking into account a finite variance of the electron-coordinate increment in the intrinsic coordinate system, the radiative damping coefficient is obtained as a divergence-free function of frequency not subject to the well-known paradoxes of the classical theory of radiative damping. A relation between radiative damping, the Lamb shift, and the electromagnetic mass of the electron is found.     

Einstein-Podolsky-Rosen correlations via dissociation of a molecular Bose-Einstein condensate

Recent experimental measurements of atomic intensity correlations through atom shot noise suggest that atomic quadrature phase correlations may soon be measured with a similar precision. We propose a test of local realism with mesoscopic numbers of massive particles based on such measurements. Using dissociation of a Bose-Einstein condensate of diatomic molecules into bosonic atoms, we demonstrate that strongly entangled atomic beams may be produced which possess Einstein-Podolsky-Rosen (EPR) correlations in field quadratures in direct analogy to the position and momentum correlations originally considered by EPR.     

Dynamics of Einstein-Podolsky-Rosen Steering in Quantum Spin Environment

We explore the dynamics of Einstein-Podolsky-Rosen steering (EPR), measured by steering robustness, for two spin-qubits coupled to a general XY spin chain environment. The evolution process is numerically investigated in the vicinity of critical point for the spin environment. The results show an obvious suppression of steering robustness when the environment undergoes a quantum phase transition. The scaling behavior for the dynamics of EPR steering is also revealed and analyzed around the critical point. Furthermore, we find that steering robustness power (i.e. the average value of steering robustness within a certain time) can indicate the quantum criticality of the environment directly.

     

Quantum nonlocality and partial transposition for continuous-variable systems

A continuous-variable Bell inequality, valid for an arbitrary number of observers measuring observables with an arbitrary number of outcomes, was recently introduced [Cavalcanti, Phys. Rev. Lett. 99, 210405 (2007)10.1103/PhysRevLett.99.210405]. We prove that any n-mode quantum state violating this inequality with quadrature measurements necessarily has a negative partial transposition. Our results thus establish the first link between nonlocality and bound entanglement for continuous-variable systems.     

Quantum transfer functions,weak nonlocality and relativity

The method of transfer functions is developed as a tool for studying Bell inequalities, alternative quantum theories and the associated physical properties of quantum systems. Non-negative probabilities for transfer functions result in Bell-type inequalities. The method is used to show that all realistic Lorentz-invariant quantum theories, which give unique results and have no preferred frame, can be ruled out on the grounds that they lead to weak backward causality.     

Multinomial Distribution,Quantum Statistics and Einstein-Podolsky-Rosen Like Phenomena

Bose-Einstein statistics may be characterized in terms of multinomial distribution. From this characterization, an information theoretic analysis is made for Einstein-Podolsky-Rosen like situation; using Shannon’s measure of entropy.