Recent experimental studies on human cognition, particularly where non-separable or entangled cognitive states have been found, show that in many such cases Bell or CHSH inequalities have been violated. The implications are that greater non-local correlations than allowed in quantum mechanics (often known as the Tsirelson bound), are found in human cognition. However, it is also evident that surpassing of Tsirelson limit within relativistic physical Spacetime seems impossible. Tsirelson limit is not guaranteed by no-signaling condition, but some deeper feature like indistinguishability of identical quantum particles might be related to such an upper bound in quantum physics, within relativistic Spacetime. We propose in the current paper that a non-local theory of mind is needed in order to account for the empirical findings. This requires a foundationally different approach than the extant ‘quantum-like’ approach to human mind. To account for the surpassing of the Tsirelson bound we propose abandoning the constraint of no-signaling that depends upon spacetime. Thus, we ask; ‘Is mind outside spacetime?’ We discuss a candidate theory of quantum gravity based on nonlocality as fundamental that may accord with our proposal. We are led to suggest a new 6 - part ontological framework linking Mind, Matter, and Cosmos.
Recent experimental studies on human cognition, particularly where non-separable or entangled cognitive states have been found, show that in many such cases Bell or CHSH inequalities have been violated. The implications are that greater non-local correlations than allowed in quantum mechanics (often known as the Tsirelson bound), are found in human cognition. However, it is also evident that surpassing of Tsirelson limit within relativistic physical Spacetime seems impossible. Tsirelson limit is not guaranteed by no-signaling condition, but some deeper feature like indistinguishability of identical quantum particles might be related to such an upper bound in quantum physics, within relativistic Spacetime. We propose in the current paper that a non-local theory of mind is needed in order to account for the empirical findings. This requires a foundationally different approach than the extant ‘quantum-like’ approach to human mind. To account for the surpassing of the Tsirelson bound we propose abandoning the constraint of no-signaling that depends upon spacetime. Thus, we ask; ‘Is mind outside spacetime?’ We discuss a candidate theory of quantum gravity based on nonlocality as fundamental that may accord with our proposal. We are led to suggest a new 6 - part ontological framework linking Mind, Matter, and Cosmos.
A physical explanation for quantum bounds to nonlocality (Tsirelson's bound) is a fundamental problem in quantum theory, for it is known that no-signaling alone fails to reproduce this limit. Here, information indistinguishability is presented as the indistinguishability of qubits or more general bits, and it suggests an answer to the nonlocality conundrum, ultimately placing it as the origin to quantum limits. Indistinguishability is also connected to exclusivity principle, and it is shown that indistinguishability leads to quantum correlation bounds. This suggests indistinguishability be as fundamental as non-locality and relativistic causality for nonlocal realism.
The term Bell's theorem refers to a set of closely related results which imply that quantum mechanics is incompatible with local hidden variable theories. Bell's inequality is the statement that if measurements are performed independently on two space-like separated particles of an entangled pair, the assumption that outcomes depend on hidden variables implies an upper bound on the correlations between the outcomes. Quantum mechanics predicts correlations which violate this upper bound. The CHSH inequality is a specific Bell inequality in which classical correlation (i.e. if local hidden variables exist) can take the maximum value of 2. Quantum mechanics violates this bound, allowing for a higher bound on the correlation, which can take the maximum value 22, known as the Tsirelson bound. Popescu and Rohrlich showed that the assumption of relativistic causality allows for an even higher bound on the CHSH correlation, this value being 4. Why is the bound coming from causality higher than the Tsirelson bound? Are there relativistic causal dynamical theories which violate the Tsirelson bound? In the present paper we answer this question in the affirmative. We show that the pre-quantum theory of trace dynamics, from which quantum theory is emergent as a thermodynamic approximation, permits the CHSH correlation to take values higher than 22. We interpret our findings to suggest that quantum theory is approximate, and emergent from the more general theory of trace dynamics.
Quantum mechanics is nonlocal, meaning it cannot be described by any classical local hidden variable model. In this thesis we study two aspects of quantum nonlocality. Part I addresses the question of what classical resources are required to simulate nonlocal quantum correlations. We start by constructing new local models for noisy entangled quantum states. These constructions exploit the connection between nonlocality and Grothendieck's inequality, first noticed by Tsirelson. Next, we consider local models augmented by a limited amount of classical communication. After generalizing Bell inequalities to this setting, we show that (i) one bit of communication is sufficient to simulate the correlations of projective measurements on a maximally entangled state of two qubits, and (ii) five bits of communication are sufficient to simulate the joint correlation of two-outcome measurements on any bipartite quantum state. The latter result can be interpreted as a stronger (constrained) version of Grothendieck's inequality. In part II, we investigate the monogamy of nonlocal correlations. In a setting where three parties, A, B, and C, share an entangled quantum state of arbitrary dimension, we: (i) bound the trade-off between AB's and AC's violation of the CHSH inequality, obtaining an intriguing generalization of Tsirelson's bound, and (ii) demonstrate that forcing B and C to be classically correlated prevents A and B from violating certain Bell inequalities. We study not only correlations that arise within quantum theory, but also arbitrary correlations that do not allow signaling between separate groups of parties. These results are based on new techniques for obtaining Tsirelson bounds, or bounds on the quantum value of a Bell inequality, and have applications to interactive proof systems and cryptography.
Abstract Bell’s theorem renders quantum correlations distinct from those of any local-realistic model. Although being stronger than classical correlations, quantum correlations are limited by the Tsirelson bound. This bound, however, applies for Hermitian, commutative operators corresponding to non-signaling observables in Alice’s and Bob’s spacelike-separated labs. As an attempt to explore theories beyond quantum mechanics and analyze the uniqueness of the latter, we examine in this work the extent of non-local correlations when relaxing these fundamental assumptions, which allows for theories with non-local signaling. We prove that, somewhat surprisingly, the Tsirelson bound in the Bell–Clauser–Horne–Shimony–Holt scenario, and similarly other related bounds on non-local correlations, remain effective as long as we maintain the Hilbert space structure of the theory. Furthermore, in the case of Hermitian observables we find novel relations between non-locality, local correlations, and signaling. We demonstrate that such non-local signaling theories are naturally simulated by quantum systems of parafermionic zero modes. We numerically study the derived bounds in parafermionic systems, confirming the bounds’ validity yet finding a drastic difference between correlations of ‘signaling’ and ‘non-signaling’ sets of observables. We also propose an experimental procedure for measuring the relevant correlations.
Bell's theorem renders quantum correlations distinct from those of any local-realistic model. Although being stronger than classical correlations, quantum correlations are limited by the Tsirelson bound. This bound, however, applies for Hermitian, commutative operators corresponding to non-signaling observables in Alice's and Bob's spacelike-separated labs. As an attempt to explore theories beyond quantum mechanics and analyze the uniqueness of the latter, we examine in this work the extent of non-local correlations when relaxing these fundamental assumptions, which allows for theories with non-local signaling. We prove that, somewhat surprisingly, the Tsirelson bound in the Bell-Clauser-Horne-Shimony-Holt scenario, and similarly other related bounds on non-local correlations, remain effective as long as we maintain the Hilbert space structure of the theory. Furthermore, in the case of Hermitian observables we find novel relations between non-locality, local correlations, and signaling. We demonstrate that such non-local signaling theories are naturally simulated by quantum systems of parafermionic zero modes. We numerically study the derived bounds in parafermionic systems, confirming the bounds' validity yet finding a drastic difference between correlations of 'signaling' and 'non-signaling' sets of observables. We also propose an experimental procedure for measuring the relevant correlations.
Tsirelson's bound is the upper bound for a Bell inequality which is valid for all quantum mechanical systems. We discuss why Tsirelson's bound was developed by looking at some historical arguments in quantum physics, such as the Einstein-Podolsky-Rosen (EPR) paradox, an argument for the quantum mechanical description of physical reality being incomplete, and local hidden variables. We present the counterargument to those theories, Bell's inequality, which later expanded to include any inequality that a local system fulfills, but that an entangled quantum system can violate. We present the proof of two specific Bell inequalities: the Clauser-Horne-Shimony-Holt (CHSH) inequality and the I3322 inequality. Then the Tsirelson's bound for the CHSH inequality is proven with a simple system of two entangled spin-1/2 particles and with a general argument that is valid for all entangled systems. We give the upper quantum bound for the generalized CHSH inequality, which describes the situation that we have more than two measurement options, by using semidefinite programming. We prove the Tsirelson's bound for the I3322 inequality by using maximally entangled systems and semidefinite programming. Finally, we discuss the upper bounds that are obtained from these different methods.