A correlation measure relating to measured and unmeasured local quantities in quantum mechanics is introduced, and is then applied to assess the locality implications for Bell/CHSH and similar set-ups. This leads to some interesting results, and the scheme is extended to the generalized no-signalling boxes framework. Some questions are raised about the use of counterfactual reasoning in quantum mechanics.
A correlation measure relating to measured and unmeasured local quantities in quantum mechanics is introduced, and is then applied to assess the locality implications for Bell/CHSH and similar set-ups. This leads to some interesting results, and the scheme is extended to the generalized no-signalling boxes framework. Some questions are raised about the use of counterfactual reasoning in quantum mechanics.
Nonlocal correlations are usually understood through the outcomes of alternative measurements (on two or more parts of a system) that cannot altogether actually be carried out in an experiment. Indeed, a joint input-output --- e.g., measurement-setting--outcome --- behavior is nonlocal if and only if the outputs for all possible inputs cannot coexist consistently. It has been argued that this counterfactual view is how Bell's inequalities and their violations are to be seen. I propose an alternative perspective which refrains from setting into relation the results of mutually exclusive measurements, but that is based solely on data actually available. My approach uses algorithmic complexity instead of probability and randomness, and implies that nonlocality has consequences similar to those in the probabilistic view. Our view is conceptually simpler than the traditional reasoning.
We introduce a framework in which a variety of theories can be defined that share two features with quantum mechanics: the no-signalling principle for states, and the fact that the global state of a multi-partite system can be completely specified by correlations between local measurements on the individual subsystems. The aim is to investigate the relationships between the physical properties of these theories and the information processing possibilities that each one offers. One of these theories, which we call Generalised Non-Signalling Mechanics, includes states that can give rise to arbitrary non-signalling correlations, including the super-quantum correlations that have become known in the literature as non-local machines or PR boxes. By investigating these correlations in the context of a theory with well-defined dynamics, we hope to make further progress with a question raised by Popescu and Rohrlich: why does quantum mechanics not allow these strongly non-local correlations? We show that the existence of strongly non-local correlations forces much of the dynamics in this theory to be, in a certain sense, trivial, with consequences for teleportation, cryptography and computation. We also investigate another theory, which we call Generalised Local Mechanics, since all states in this theory are local. This has its own consequences for cryptography and computation. Finally, we raise the question of what further axiom(s) could be added to our framework in order uniquely to identify quantum mechanics.
Scientific inquiry seeks causal explanations of observed phenomena. The Bell experiment provides a paradigmatic case, revealing correlations between spatially separated systems that no local model can reproduce. Such correlations, known as Bell non-locality, are typically analyzed under the non-signaling assumption, which requires that local statistics be independent of distant measurement choices. Yet real experiments, as well as applications beyond physics, often involve signaling, raising the question of how non-locality should be characterized without this constraint. We introduce a general method for quantifying Bell non-locality in the presence of signaling, designed to relax locality as little as necessary. Our approach is guided by the question: how often can locality be preserved across repeated trials in explaining the observed correlations? The task reduces to finding the optimal convex decomposition of the observed correlations into local and genuinely non-local components. We solve this problem within the linear-programming framework, obtaining a closed-form solution valid for arbitrary correlations. We further evaluate a corresponding measure of signaling, demonstrating the generality of the method and the non-trivial character of the results. By extending the notion of non-locality beyond the non-signaling regime, our framework reshapes the basis for experimental analysis in physics and offers tools applicable outside physics.
Counterfactual reasoning plays a crucial role in exploring hypothetical scenarios, by comparing some consequent under conditions identical except as results from a differing antecedent. David Lewis' well-known analysis evaluates counterfactuals using a hierarchy of desiderata. These were, however, built upon a deterministic classical framework, and whether it could be generalized to indeterministic quantum theory has been an open question. In this paper, we propose a formalism for quantum counterfactuals in which antecedents are measurement settings. Unlike other approaches, it non-trivially answers questions like: "Given that a photon-detector, observing an atom's fluorescence, clicked at a certain time, what would a field-quadrature detector have measured, if it had been used instead?"
This book uses the formal semantics of counterfactual conditionals to analyze the problem of non-locality in quantum mechanics. Counterfactual conditionals (subjunctive conditionals) enter the analysis of quantum entangled systems in that they enable us to precisely formulate the locality condition that purports to exclude the existence of causal interactions between spatially separated parts of a system. They also make it possible to speak consistently about alternative measuring settings, and to explicate what is meant by quantum property attributions. The book develops the possible-world semantics of quantum counterfactuals using David Lewis’s famous approach as a starting point but modifying it significantly in order to achieve compatibility with the demands of the special theory of relativity as well as quantum mechanics. There have been several attempts to use counterfactual semantics to strengthen Bell’s theorem and its cognates such as the GHZ and Hardy theorems. These are critically evaluated in the book. Finally, a counterfactual reconstruction of the EPR argument and Bell’s theorem is proposed that sheds a new light on their philosophical consequences regarding the relations between realism and local causation.
We analyze the structure of the so called non-signaling theories respecting relativistic causality but allowing correlations violating bounds imposed by quantum mechanics such as CHSH inequality. We discuss relations among such theories, quantum mechanics, and classical physics. In particular we reconstruct the probability theory adequate for the simplest instance of a non-signaling theory, the two non-signaling boxes world, and exhibit its differences in comparison with classical and quantum probabilities. We show that the question whether such a theory can be treated as a kind of "generalization" of the quantum theory of the two-qubit system cannot be answered positively. Some of its features put it closer to the quantum world, for example measurements must be destructive, on the other hand the Heisenberg uncertainty relations are not satisfied. Another interesting property contrasting it from quantum mechanics is that the subset of "classically correlated states," i.e.\ the states with only classical correlations, does not reproduce the classical world of two two-state systems. Our results establish a new link between quantum information theory and the well-developed theory of quantum logics and can shed new light on the problem why quantum mechanics is distinguished among non-signaling theories.