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Do neural activities of binocular rivalry follow a quantum probability model? A test of temporal Bell inequalities

Hirao Takahiro, Naotsugu Tsuchiya, Emmanuel Pothos, Jerome R. Busemeyer, Peter Bruza, Yamada Makiko

Published Dec 8, 2021• 0 citations
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Abstract

Binocular rivalry refers to a phenomenon in which the perceived image changes spontaneously over time when the two eyes are presented with different images. The purpose of this study is to test whether the violation of temporal Bell inequality can be experimentally observed in binocular rivalry. If the temporal Bell inequality is violated (under no-signaling in time: NSIT), it implies that the perception of the rival stimuli cannot be assumed to be definite at each point in time (i.e., “realism” in the corresponding mental representations is violated), which is a key indication of non-classical behavior (as in, for example, quantum-like systems). Here, to test the violation of the inequality, we used binocular rivalry and measured both subjective reports and electroencephalogram (EEG). With EEG, we used frequency-tagging technique to track the cortical signal driven by each eye’s stimulus, known as the steady-state visual evoked potential (SSVEP). We present the conceptual and methodological approaches to test the temporal Bell inequality.

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Binocular rivalry refers to a phenomenon in which the perceived image changes spontaneously over time when the two eyes are presented with different images. The purpose of this study is to test whether the violation of temporal Bell inequality can be experimentally observed in binocular rivalry. If the temporal Bell inequality is violated (under no-signaling in time: NSIT), it implies that the perception of the rival stimuli cannot be assumed to be definite at each point in time (i.e., “realism” in the corresponding mental representations is violated), which is a key indication of non-classical behavior (as in, for example, quantum-like systems). Here, to test the violation of the inequality, we used binocular rivalry and measured both subjective reports and electroencephalogram (EEG). With EEG, we used frequency-tagging technique to track the cortical signal driven by each eye’s stimulus, known as the steady-state visual evoked potential (SSVEP). We present the conceptual and methodological approaches to test the temporal Bell inequality.
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.
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.
In this paper we applied for the first time the no-signaling in time (NSIT) formalism discussed by Kofler and Brukner (2013) to investigate temporal entanglement between binary human behavioral unconscious choices at t1 with binary random outcomes at t2. NSIT consists of a set of inequalities and represents mathematical conditions for macro-realism which require only two measurements in time. The analyses of three independent experiments show a strong violation of NSIT in two out of three of them, suggesting the hypothesis of a quantum-like temporal entanglement between human choices at t1 with binary random outcomes at t2. We discuss the potentialities of using NSIT to test temporal entanglement with behavioral measures.
There is widespread evidence that human memory is constructive, so that recollective processes may alter the information retrieved or impact on subsequent recollections. We examine a framework for narrowing down the nature of such processes, from physics. In Physics, the Temporal Bell (TB) inequality offers a general test of the sensitivity of the context of previous measurements in sequential measurement scenarios, as predicted by quantum theory. We present an empirical memory paradigm that allows a test of the TB inequality, using a novel kind of "change judgment," whereby participants are asked to decide whether there has been a change in a question across different time points of a scenario. Across two experiments, we were able to observe evidence for the violation of a TB inequality in one case, offering evidence for quantum-like processes in memory. The present results complement other recent work purporting the relevance of quantum-like representations in memory and raise questions regarding the adaptive value of such representations.
For the first time we perform an experiment to test the possibility of Bell's inequality violation in mental states, during perception-cognition in humans. We study under a theoretical and experimental framework, a Bell-type test for human perception-cognition of ambiguous figures. It is performed a detailed analysis which demonstrates that, although we have not yet been able to violate Bell's inequality in the present performed experiment, there are strong theoretical arguments supporting our expectation to violate it by a simple articulation of the same experiment. In this framework we introduce for the first time what we retain to represent quantum cognitive observables. We consider that our analysis provides a solid ground for further investigations on quantum behaviour of cognitive systems. Therefore we reaffirm that quantum mechanics is a Giano Bifronte theory (two-faced Giano, a mythological God of the past), looking from one hand to physical reality and from the other hand to the sphere of mental reality and cognitive dynamics.
Bell-inequality violation is one of the most widely known manifestations of entanglement in quantum mechanics; indicating that experiments on physically separated quantum mechanical systems cannot be given a local realistic description. However, despite the importance of Bell inequalities, it is not known in general how to determine whether a given entangled state will violate a Bell inequality. This is because one can choose to make many different measurements on a quantum system to test any given Bell inequality and the optimization over measurements is a high-dimensional variational problem. In order to better understand this problem we present algorithms that provide, for a given quantum state and Bell inequality, both a lower bound and an upper bound on the maximal violation of the inequality. In many cases these bounds determine measurements that would demonstrate violation of the Bell inequality or provide a bound that rules out the possibility of a violation. Both bounds apply techniques from convex optimization and the methodology for creating upper bounds allows them to be systematically improved. Examples are given to illustrate how these algorithms can be used to conclude definitively if some quantum states violate a given Bell inequality.