Non-classicality of temporal correlations

Abstract

The results of space-like separated measurements are independent of distant measurement settings, a property one might call two-way no-signalling. In contrast, time-like separated measurements are only one-way no-signalling since the past is independent of the future but not vice-versa. For this reason temporal correlations that are formally identical to non-classical spatial correlations can still be modelled classically. We define non-classical temporal correlations as the ones which cannot be simulated by propagating in time a classical information content of a quantum system. We first show that temporal correlations between results of any projective quantum measurements on a qubit can be simulated classically. Then we present a sequence of POVM measurements on a single $m$-level quantum system that cannot be explained by propagating in time $m$-level classical system and using classical computers with unlimited memory.

6 pages, 1 figure

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• Memory cost of temporal correlations
• Memory cost for simulating all quantum correlations of the Peres-Mermin scenario
• Quantum correlations in composite systems
• Probing the Non-Classicality of Temporal Correlations
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• Multitime correlation functions in nonclassical stochastic processes
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• Semi-device-independently characterizing quantum temporal correlations
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• Structure of dimension-bounded temporal correlations
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• The spatiotemporal doubled density operator: a unified framework for analyzing spatial and temporal quantum processes
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• Scalable noncontextuality inequalities and certification of multiqubit quantum systems
• Quantifiable simulation of quantum computation beyond stochastic ensemble computation
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• Role of nonclassical temporal correlation in powering quantum random access codes
• Exploiting Faraday Rotation to Jam Quantum Key Distribution via Polarized Photons
• The essence of nonclassicality: non-vanishing signal deficit
• Quantum Entanglement in Time
• Certification of multi-qubit quantum systems with temporal inequalities