Temporally non-local measurements – single measurements yielding information about the state of a system at different instances – may provide a way to observe non-classical behavior in mental systems. The signature for such behavior is a violation of temporal Bell inequalities. We present such inequalities applicable to scenarios with two alternating mental states, such as in the perception of ambiguous figures. We indicate empirical options for testing temporal Bell inequalities, and speculate about possible explanations in case these inequalities are indeed violated.
Temporally non-local measurements – single measurements yielding information about the state of a system at different instances – may provide a way to observe non-classical behavior in mental systems. The signature for such behavior is a violation of temporal Bell inequalities. We present such inequalities applicable to scenarios with two alternating mental states, such as in the perception of ambiguous figures. We indicate empirical options for testing temporal Bell inequalities, and speculate about possible explanations in case these inequalities are indeed violated.
Introduction The purpose of the present study is to investigate quantum-like properties of mental states in bistable perception. In order to do this, we tested whether the temporal Bell inequality applied to bistable perception experiments[1] can be violated. In the present study, we used visual stimuli [2], where we can continuously and systematically manipulate two types of ambiguities in the perceived rotation of dots. When the rotation angle is large, the stimuli induce bistable percept. When the angle is small, the direction of rotation of the stimuli becomes difficult to judge. We use the stimuli to test if the temporal Bell inequality can be violated, and if so, under what parameter regime, it can be violated. Method Two patterns were presented alternately: a visual stimulus consisting of four disks, and one in which the disks were rotated by a specific angle (5-45 degrees) in each trial [FIG. 1(A)]. When the angle of rotation was close to 45 degrees, stimuli were perceived to rotate in one of the two directions for a while with occasional reversals at random times (i.e., bistable perception). When the angle of rotation was close to 5 degrees, no rotation was perceived beyond the angle of rotation of the stimulus, and left and right rotations were perceived alternately, but the angle of rotation was so small that it was difficult to determine the direction of rotation [FIG. 1(B)]. At two time points after the beep, the participants responded by pressing a button in the direction of rotation that they saw at that time [FIG. 1(C)]. Reference 1H. Atmanspacher, and T. Filk, J. Math. Psychol. 54, 314-321 (2010). 2S. Takei and S. Nishida, J. Vision. 10, 23 (2010). 3M. M. Wilde and A. Mizel, Found. Phys. 42, 256 (2012). Acknowledgement This work was supported by JSPS KAKENHI JP20H05711 and MEXT Q-LEAP Grant Number JPMXS0120330644.
Quantum nonlocality is often judged by violations of Bell-type inequalities for a given state. The computation of such violations is a global task, requiring evaluation of global correlations and subsequent testing against a Bell functional. We ask instead: when is a given state local (classical)? We formalize this question via local perception operators (LPOs) that compress global observables into locally accessible statistics, and we derive two complementary witnesses -- one implementable by a single party with classical side information, one intrinsically two-sided. These tools revisit familiar Bell scenarios from a new operational angle. We show how the witness leads to state-aware constraints that depend on local marginals and measurement geometry, with natural specializations to canonical scenarios. The resulting criteria are built from first moments and standard projective measurements and provide a way to certify compatibility with local hidden variable explanations for the LPO-processed data in regimes where conventional Bell violations may be inconclusive.
All mental representations change with time. A baseline intuition is that mental representations have specific values at different time points, which may be more or less accessible, depending on noise, forgetting processes, etc. We present a radical alternative, motivated by recent research using the mathematics from quantum theory for cognitive modelling. Such cognitive models raise the possibility that certain possibilities or events may be incompatible, so that perfect knowledge of one necessitates uncertainty for the others. In the context of time-dependence, in physics, this issue is explored with the so-called temporal Bell (TB) or Leggett-Garg inequalities. We consider in detail the theoretical and empirical challenges involved in exploring the TB inequalities in the context of cognitive systems. One interesting conclusion is that we believe the study of the TB inequalities to be empirically more constrained in psychology than in physics. Specifically, we show how the TB inequalities, as applied to cognitive systems, can be derived from two simple assumptions: cognitive realism and cognitive completeness. We discuss possible implications of putative violations of the TB inequalities for cognitive models and our understanding of time in cognition in general. Overall, this paper provides a surprising, novel direction in relation to how time should be conceptualized in cognition.
Abstract Analyzing the spreading of information in many-body systems is crucial to understanding their quantum dynamics. At the most fundamental level, this task is accomplished by Bell inequalities, whose violation by quantum mechanics implies that information cannot always be stored locally. While Bell-like inequalities, such as the one of Clauser and Horne, envisage a situation in which two parties perform measurements on systems at different positions, one could formulate temporal inequalities, in which the two parties measure at different times. However, for causally-connected measurement events, these extensions are compatible with a local description, so that no intrinsically-quantum information spreading is involved in such temporal correlations. Here we show that a temporal Clauser–Horne inequality for two spins is violated for a nonzero time interval between the measurements if the two measured parties are connected by a spin chain. Since the chain constitutes the sole medium for the spreading of quantum information, it prevents the immediate vanishing of Bell correlations after the first measurement and it induces violation revivals. The dynamics we analyze shows that, as expected in a non-relativistic setup, the spreading of information is fundamentally limited by the Lieb–Robinson bound. New insights on many-body quantum dynamics could emerge through future applications of our temporal Bell inequality to more general systems.
Nonlocality and contextuality are at the root of conceptual puzzles in quantum mechanics, and they are key resources for quantum advantage in information-processing tasks.Bell nonlocality is best understood as the incompatibility between quantum correlations and the classical theory of causality, applied to relativistic causal structure.Contextuality, on the other hand, is on a more controversial foundation.In this work, I provide a common conceptual ground between nonlocality and contextuality as violations of classical causality.First, I show that Bell inequalities can be derived solely from the assumptions of no signaling and no fine-tuning of the causal model.This removes two extra assumptions from a recent result from Wood and Spekkens and, remarkably, does not require any assumption related to independence of measurement settings-unlike all other derivations of Bell inequalities.I then introduce a formalism to represent contextuality scenarios within causal models and show that all classical causal models for violations of a Kochen-Specker inequality require fine-tuning.Thus, the quantum violation of classical causality goes beyond the case of spacelike-separated systems and already manifests in scenarios involving single systems.
Bell inequalities reveal the fundamentally nonlocal character of quantum mechanics. In this regard, one of the interesting problems is to explore all possible Bell inequalities that demonstrate a gap between local and nonlocal quantum behaviour. This is useful for the geometric characterisation of the set of nonlocal correlations achievable within quantum theory. Moreover, it provides a systematic way to construct Bell inequalities that are tailored to specific quantum information processing tasks. This characterisation is well understood in the simplest (2,2,2) scenario, namely two parties performing two binary outcome measurements. However, beyond this setting, relatively few Bell inequalities are known, and the situation becomes particularly scarce in scenarios involving a greater number of outcomes. Here, we consider the (2,2,3) scenario, or two parties performing two three-outcome measurements, and characterise all Bell inequalities that can arise from the simplest sum-of-squares decomposition and are maximally violated by the maximally entangled state of local dimension three. We then utilise them to self-test this state, along with a class of three-outcome measurements.