Nonlocality Without Nonlocality

Bell’s theorem is purported to demonstrate the impossibility of a local “hidden variable” theory underpinning quantum mechanics. It relies on the well-known assumption of ‘locality’, and also on a little-examined assumption called ‘statistical independence’ (SI). Violations of this assumption have variously been thought to suggest “backward causation”, a “conspiracy” on the part of nature, or the denial of “free will”. It will be shown here that these are spurious worries, and that denial of SI simply implies nonlocal correlation between spacelike degrees of freedom. Lorentz-invariant theories in which SI does not hold are easily constructed: two are exhibited here. It is conjectured, on this basis, that quantum-mechanical phenomena may be modeled by a local theory after all. This paper is dedicated to the memory of John A. Wheeler.     

Nonlocality in Relativistic Dynamics

Recent experiments have renewed interest in nonlocal interpretations of quantum mechanics. The experimental observation of the violation of Bell's inequalities implies the existence of nonlocality. Bohm expressed the nonlocal connection between quantum particles through the wave function and the quantum potential. This paper shows that a similar connection exists in a relativistic dynamical theory known as parametrized relativistic quantum theory (PRQT). We present an introduction to PRQT, derive the quantum potential for a system of relativistic scalar particles, and discuss alternative interpretations of nonlocality.     

Nonlocality and Entanglement

By constructing a series of mixture, which is inseparable but satisfies the Mermin-Klyshko inequality, for the N-qubit system, we prove that ＂violation of the Mermin-Klyshko inequality＂ is not equivalent to ＂the state is inseparable＂.     

Nonlocality is transitive

We show a transitivity property of nonlocal correlations: There exist tripartite nonsignaling correlations of which the bipartite marginals between A and B as well as B and C are nonlocal and any tripartite nonsignaling system between A, B, and C consistent with them must be such that the bipartite marginal between A and C is also nonlocal. This property represents a step towards ruling out certain alternative models for the explanation of quantum correlations such as hidden communication at finite speed. Whereas it is not possible to rule out this model experimentally, it is the goal of our approach to demonstrate this explanation to be logically inconsistent: either the communication cannot remain hidden, or its speed has to be infinite. The existence of a three-party system that is pairwise nonlocal is of independent interest in the light of the monogamy property of nonlocality.     

Nonlocality of relative diffusion

On the basis of numerical modeling, the hypothesis of the nonlocal character of Richardson relative diffusion is tested and confirmed. Zh. éksp. Teor. Fiz. 112, 163–166 (July 1997)     

Nonlocality for graph states

The possibility of preparing two-photon entangled states encoding three or more qubits in each photon leads to the following problem: If n quabits were distributed between two parties, which quantum pure states and qubit distributions would allow all-versus-nothing (or Greenberger-Horne-Zeilinger-like) proofs of Bell’s theorem using only single-qubit measurements? We show a necessary and sufficient condition for the existence of these proofs and provide all existing proofs up to n = 7 qubits. On the other hand, the possibility of preparing n-photon n-qubit graph states leads to the following problem: If n qubits were distributed between n parties, which would be the optimal Bell inequalities? We show all optimal n-party Bell inequalities for the perfect correlations of any graph state of n < 6 qubits. Optimal means that the ratio between the quantum violation and the bound for local hidden-variable theories is the maximum over all possible combinations of perfect correlations. This implies that the required detection efficiencies for loophole-free Bell tests are minimal.     

Realism and Single-Quanta Nonlocality

We show that local realism applied to states characterized by a single quantum equally and coherently shared between a number of qubits (so-called W states) produces predictions incompatible with quantum theory. The origin of this incompatibility is shown to originate from the destructive interference of amplitude probabilities associated with nonlocal states, a phenomenon that has no classical analog.     

Superactivation of Measurement-Induced Nonlocality

Nonlocality, as an essential, subtle and intriguing aspect of nature, has many different facets and manifestations. In quantum information theory, nonlocality is usually defined, characterized and quantified in the framework of entanglement and violation of certain Bell inequalities. An exciting phenomenon concerning entanglement-related nonlocality is the superactivation, symbolized as "0+0>0", which means that two systems, while do not possess nonlocality individually by themselves, may exhibit nonlocality when combined together in an independent fashion. In this work, we explore nonlocality from the measurement perspective and reveal the superactivation of measurement-induced nonlocality (MIN): When two bipartite states with vanishing MIN are combined together, the tensorizing state may possess non-zero MIN. Implications and applications are discussed.     

Three-Slit Experiments and Quantum Nonlocality

An interesting link between two very different physical aspects of quantum mechanics is revealed; these are the absence of third-order interference and Tsirelson’s bound for the nonlocal correlations. Considering multiple-slit experiments—not only the traditional configuration with two slits, but also configurations with three and more slits—Sorkin detected that third-order (and higher-order) interference is not possible in quantum mechanics. The EPR experiments show that quantum mechanics involves nonlocal correlations which are demonstrated in a violation of the Bell or CHSH inequality, but are still limited by a bound discovered by Tsirelson. It now turns out that Tsirelson’s bound holds in a broad class of probabilistic theories provided that they rule out third-order interference. A major characteristic of this class is the existence of a reasonable calculus of conditional probability or, phrased more physically, of a reasonable model for the quantum measurement process.     

Nonlocality in the Many-Worlds and Consistent-Histories Interpretations

The many-worlds interpretation has usually been regarded as immune to nonlocality, and similar claims have been made for the consistent-histories interpretation (1-3). However, for a thought experiment of the Hardy type, the argument for nonlocality in the usual interpretation can be extended to both these other interpretations.     

Nonlocality in the Expanding Infinite Well

According to D. Bohm's interpretation of quantum mechanics, a particle always has a well-defined spatial trajectory. A change in boundary conditions can nonlocally change that trajectory. In this note we point out a striking instance of this phenomenon that is easy to understand qualitatively.     

Single-Particle Nonlocality and Conditional Measurements

I suggest that quantum mechanical nonlocality may in a certain sense allow a particle to be in two places at the same time, without violating causality. I discuss the measurable consequences of such a feat, and speculate about possible statistical tests which could distinguish this view of quantum mechanics from a corpuscular one. In particular, I describe some experiments being set up at Toronto which will investigate atomic tunneling, looking among other things for a signature of such alkali schizophrenia.     

Measurement-induced Nonlocality for Gaussian States

We establish an analytic formula of measurement-induced nonlocality (MIN) for two-mode squeezed thermal states and mixed thermal states. Different from the quantum discord case, we show that there is no Gaussian version of MIN by Gaussian positive operator valued measurements.     

Nonlocality and the Kochen-Specker paradox

A new proof of the impossibility of reconciling realism and locality in quantum mechanics is given. Unlike proofs based on Bell's inequality, the present work makes minimal and transparent use of probability theory and proceeds by demonstrating a Kochen-Specker type of paradox based on the value assignments to the spin components of two spatially separated spin-1 systems in the singlet state of their total spin. An essential part of the argument is to distinguish carefully two commonly confused types of contextuality; we call them ontological and environmental contextuality. These in turn are associated with two quite distinct senses of nonlocality. We indicate the relevance of our treatment to other related discussions in recent literature on the philosophy of quantum mechanics.     

Nonlocality criteria for quantum teleportation

An upper bound for the fidelity of quantum teleportation explainable by local hidden variables is derived. This bound is larger than the fidelity corresponding to product states, i.e. to local quantum states. This is relevant for the study of mixed states. In particular, the fidelity of Werner's mixed state, known to be larger than the fidelity of product states, is found to be smaller than the fidelity explainable by local hidden variables. Hence the fidelity of Werner's mixed state does not exhibit nonclassical aspects.     

Nonlocality of a single particle

There has been a great deal of debate surrounding the issue of whether it is possible for a single photon to exhibit nonlocality. A number of schemes have been proposed that claim to demonstrate this effect, but each has been met with significant opposition. The objections hinge largely on the fact that these schemes use unobservable initial states and so, it is claimed, they do not represent experiments that could actually be performed. Here we show how it is possible to overcome these objections by presenting an experimentally feasible scheme that uses realistic initial states. Furthermore, all the techniques required for photons are equally applicable to atoms. It should, therefore, also be possible to use this scheme to verify the nonlocality of a single massive particle.