Temporal Bell Inequalities Research Articles

Semi-Device-Independently Characterizing Quantum Temporal Correlations.

We develop a framework for characterizing quantum temporal correlations in a general temporal scenario, in which an initial quantum state is measured, sent through a quantum channel, and finally measured again. This framework does not make any assumptions on the system nor on the measurements, namely, it is device independent. It is versatile enough, however, to allow for the addition of further constraints in a semi-device-independent setting. Our framework serves as a natural tool for quantum certification in a temporal scenario when the quantum devices involved are uncharacterized or partially characterized. It can hence also be used for characterizing quantum temporal correlations when one assumes an additional constraint of no-signalling in time, there are upper bounds on the involved systems' dimensions, rank constraints-for which we prove genuine quantum separations over local hidden variable models-or further linear constraints. We present a number of applications, including bounding the maximal violation of temporal Bell inequalities, quantifying temporal steerability, and bounding the maximum successful probability in quantum randomness access codes.

Quantum Markov blankets for meta-learned classical inferential paradoxes with suboptimal free energy

Abstract Quantum active Bayesian inference and quantum Markov blankets enable robust modeling and simulation of difficult-to-render natural agent-based classical inferential paradoxes interfaced with task-specific environments. Within a non-realist cognitive completeness regime, quantum Markov blankets ensure meta-learned irrational decision making is fitted to explainable manifolds at optimal free energy, where acceptable incompatible observations or temporal Bell-inequality violations represent important verifiable real-world outcomes.

Temporal Bell inequalities in cognition

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.

Quantifying Quantumness of Channels Without Entanglement

Quantum channels breaking entanglement, incompatibility, or nonlocality are defined as such because they are not useful for entanglement-based, one-sided device-independent, or device-independent quantum information processing, respectively. Here, we show that such breaking channels are related to complementary tests of macrorealism i.e., temporal separability, channel unsteerability, temporal unsteerability, and the temporal Bell inequality. To demonstrate this we first define a steerability-breaking channel, which is conceptually similar to entanglement and nonlocality-breaking channels and prove that it is identical to an incompatibility-breaking channel. A hierarchy of quantum non-breaking channels is derived, akin to the existing hierarchy relations for temporal and spatial quantum correlations. We then introduce the concept of channels that break temporal correlations, explain how they are related to the standard breaking channels, and prove the following results: (1) A robustness-based measure for non-entanglement-breaking channels can be probed by temporal nonseparability. (2) A non-steerability-breaking channel can be quantified by channel steering. (3) Temporal steerability and non-macrorealism can be used for, respectively, distinguishing unital steerability-breaking channels and nonlocality-breaking channels for a maximally entangled state. Finally, a two-dimensional depolarizing channel is experimentally implemented as a proof-of-principle example to demonstrate the hierarchy relation of non-breaking channels using temporal quantum correlations

Hidden nonmacrorealism: Reviving the Leggett-Garg inequality with stochastic operations

The Leggett-Garg inequality (LGI) distinguishes nonmacrorealistic channels from macrorealistic ones by constraining the experimental outcomes of the underlying system. In this work, we propose a class of channels which, initially, cannot violate the LGI (in the form of the temporal Bell inequality) but can violate it after the application of stochastic pre- and post- operations (SPPOs). As a proof-of-principle experiment, we demonstrate the stochastic pre- and post- operations in an amplitude-damping channel with photonic qubits. We denote the above phenomenon as hidden nonmacrorealistic channels. We also discuss the relationship between this hidden nonmacrorealistic channels (in terms of the temporal Clauser-Horne-Shimony-Holt (CHSH) inequality) and the strongly nonlocality-breaking channel, which breaks the hidden spatial CHSH nonlocality for arbitrary states. In general, if the channel satisfies hidden nonmacrorealism, it is not a strongly CHSH nonlocality-breaking channel.

Bipartite temporal Bell inequalities for two-mode squeezed states

Bipartite temporal Bell inequalities are similar to the usual Bell inequalities except that, instead of changing the direction of the polariser at each measurement, one changes the time at which the measurement is being performed. By doing so, one is able to test for realism and locality, but relying on position measurements only. This is particularly useful in experimental setups where the momentum direction cannot be probed (such as in cosmology for instance). We study these bipartite temporal Bell inequalities for continuous systems placed in two-mode squeezed states, and find some regions in parameter space where they are indeed violated. We highlight the role played by the rotation angle, which is one of the three parameters characterising a two-mode squeezed state (the other two being the squeezing amplitude and the squeezing angle). In single-time measurements, it only determines the overall phase of the wavefunction and can therefore be discarded, but in multiple-time measurements, its time dynamics becomes relevant and crucially determines when bipartite temporal Bell inequalities can be violated. Our study opens up the possibility of new experimental designs for the observation of Bell inequality violations.

Testing violation of the Leggett\u2013Garg-type inequality in neutrino oscillations of the Daya Bay experiment

The Leggett–Garg inequality (LGI), derived under the assumption of realism, acts as the temporal Bell inequality. It is studied in electromagnetic and strong interaction like photonics, superconducting qubits and nuclear spin. The weak interaction two-state oscillations of neutrinos affirmed the violation of Leggett–Garg-type inequalities (LGtI). We make an empirical test for the deviation of experimental results with the classical limits by analyzing the survival probability data of reactor neutrinos at a distinct range of baseline dividing energies, as an analog to a single neutrino detected at different times. A study of the updated data of the Daya Bay experiment unambiguously depicts an obvious cluster of data over the classical bound of LGtI and shows a 6.1sigma significance of the violation of them.

Leggett-Garg inequalities for squeezed states

Temporal Bell inequalities, or Leggett-Garg Inequalities (LGI), are studied for continuous-variable systems placed in a squeezed state. The importance of those systems lies in their broad applicability which allows the description of many different physical settings in various branches of physics, ranging from cosmology to condensed matter physics and from optics to quantum information theory. LGI violations are explored and systematically mapped in squeezing parameter space. Configurations for which LGI violation occurs are found but it is shown that no violation can be obtained if all squeezing angles vanish, contrary to what happens for the spatial Bell inequalities. We also assess the effect of decoherence on the detectability of such violations. Our study opens up the possibility of new experimental designs for the observation of LGI violation.

Editorial: Quantum Structures in Cognitive and Social Science.

Editorial: Quantum Structures in Cognitive and Social Science.

Challenging the classical notion of time in cognition: a quantum perspective

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.

Leggett-Garg inequalities for the statistics of electron transport

We derive a set of Leggett-Garg inequalities (temporal Bell's inequalities) for the moment generating function of charge transferred through a conductor. Violation of these inequalities demonstrates the absence of a macroscopic-real description of the transport process. We show how these inequalities can be violated by quantum-mechanical systems and consider transport through normal and superconducting single-electron transistors as examples.

Publisher’s Note: Violation of a Temporal Bell Inequality for Single Spins in a Diamond Defect Center [Phys. Rev. Lett.107, 090401 (2011)

Publisher’s Note: Violation of a Temporal Bell Inequality for Single Spins in a Diamond Defect Center [Phys. Rev. Lett.<b>107</b>, 090401 (2011)

Violation of a Temporal Bell Inequality for Single Spins in a Diamond Defect Center

Quantum nonlocality has been experimentally investigated by testing different forms of Bell's inequality, yet a loophole-free realization has not been achieved up to now. Much less explored are temporal Bell inequalities, which are not subject to the locality assumption, but impose a constraint on the system's time correlations. In this Letter, we report on the experimental violation of a temporal Bell's inequality using a nitrogen-vacancy (NV) defect in diamond and provide a novel quantitative test of quantum coherence. Such a test requires strong control over the system, and we present a new technique to initialize the electronic state of the NV with high fidelity, a necessary requirement also for reliable quantum information processing and/or the implementation of protocols for quantum metrology.

Hardy’s Paradox and Violation of a State-Independent Bell Inequality in Time

Tests such as Bell's inequality and Hardy's paradox show that joint probabilities and correlations between distant particles in quantum mechanics are inconsistent with local realistic theories. Here we experimentally demonstrate these concepts in the time domain, using a photonic entangling gate to perform nondestructive measurements on a single photon at different times. We show that Hardy's paradox is much stronger in time and demonstrate the violation of a temporal Bell inequality independent of the quantum state, including for fully mixed states.

A proposed test of temporal nonlocality in bistable perception

The concept of temporal nonlocality is used to refer to states of a (classical) system that are not sharply localized in time but extend over a time interval of non-zero duration. We investigate the question whether, and how, such a temporal nonlocality can be tested in mental processes. For this purpose we exploit the empirically supported Necker–Zeno model for bistable perception, which uses formal elements of quantum theory but does not refer to anything like quantum physics of the brain. We derive so-called temporal Bell inequalities and demonstrate how they can be violated in this model. We propose an experimental realization of such a violation and discuss some of its consequences for our understanding of mental processes.

Information-theoretic temporal Bell inequality and quantum computation

An information-theoretic temporal Bell inequality is formulated to contrast classical and quantum computations. Any classical algorithm satisfies the inequality, while quantum ones can violate it. Therefore, the violation of the inequality is an immediate consequence of the quantumness in the computation. Furthermore, this approach suggests a notion of temporal nonlocality in quantum computation.

The quantum self-eraser

A scheme for an atomic beam quantum self-eraser is presented. The proposal is based on time reversal invariance on a quantum optical Ramsey fringes experiment, where a realization of complementarity for atomic coherence can be achieved. It consists of two high finesse resonators that are pumped and probed by the same atom. This property relates quantum erasing with time reversal symmetry, allowing for a full quantum erasing of the which-way information stored in the cavity fields. The outlined scheme also prepares and observes a non-local state in the fields of the resonators: a coherent superposition between correlated states of macroscopically separated quantum systems. The proposed scheme emphasizes the role of entanglement swapping in delayed-choice experiments. Finally, we show that the quantum self-eraser violates temporal Bell inequalities and analyze the relation between this violation and the erasability of which-way information.

Delayed-choice Measurement and Temporal Nonlocality

Abstract We study for a composite quantum system with a quantum Turing architecture the temporal non-locality of quantum mechanics by using the temporal Bell inequality, which will be derived for a discretized network dynamics by identifying the subsystem indices with (discrete) parameter time. However, the direct “observation” of the quantum system will lead to no violation of the temporal Bell inequality and to consistent histories of any subsystem. Its violation can be demonstrated, though, for a delayedchoice measurement

Tunneling in rf-SQUIDs and Tests of Quantum Mechanics at the Macroscopic Level

Superconducting devices such as rf-SQUIDs have been proposed to test the validity of quantum mechanics by means of Bell-like inequalities involving different-time correlation probabilities for measurements of magnetic flux. We calculate the quantum mechanical violations to such temporal Bell inequalities taking into account the effect of the measurement process on the probability distribution for the outcomes. We define a general criterion quantifying the observability of the violations and show that it is not fulfilled for the various experimental configurations proposed so far.

Quantum nondemolition measurements on two-level atomic systems and temporal Bell inequalities

The evolution of a two-level system subjected to stimulated transitions which is undergoing a sequence of measurements of the level occupation probability is evaluated. Its time correlation function is compared to the one obtained through the pure Schrödinger evolution. Systems of this kind have been recently proposed for testing the quantum mechanical predictions against those of macrorealistic theories, by means of temporal Bell inequalities. The classical requirement of noninvasivity, needed to define correlation functions in the realistic case, finds a quantum counterpart in the quantum nondemolition condition. The consequences on the observability of quantum mechanically predicted violations to temporal Bell inequalities are drawn and compared to the already dealt case of the rf-SQUID dynamics.