Inferring the arrow of time in quantum spatiotemporal correlations

Abstract

We consider how to tell the time-ordering associated with measurement data from quantum experiments at two times and any number of qubits. We define an arrow of time inference problem. We consider conditions on the initial and final states that are symmetric or asymmetric under time reversal. We represent the spatiotemporal measurement data via the pseudo density matrix space-time state. There is a forward process which is CPTP and a reverse process which is obtained via a novel recovery map based on inverting unitary dilations. For asymmetric conditions, the protocol determines whether the data is consistent with the unitary dilation recovery map or the CPTP map. For symmetric conditions, the recovery map yields a valid CPTP map and the experiment may have taken place in either direction. We also discuss adapting the approach to the Leifer-Spekkens or Process matrix space-time states.

arXiv commentClose to the published version. fixed typos, Comments are welcome

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Cited by in corpus (8)

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• Unification of spatiotemporal quantum formalisms: mapping between process and pseudo-density matrices via multiple-time states
• Experimental Validation of Enhanced Information Capacity by Quantum Switch in Accordance with Thermodynamic Laws
• Quantum Causal Inference with Extremely Light Touch
• Certifying Quantum Temporal Correlation via Randomized Measurements: Theory and Experiment
• Quantum dynamics as a pseudo-density matrix
• Experimental Virtual Quantum Broadcasting
• Bipartite quantum states admitting a causal explanation