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.

Close to the published version. fixed typos, Comments are welcome

References in corpus (13)

• Quantum Non-Markovianity: Characterization, Quantification and Detection
• The thermodynamic meaning of negative entropy
• Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure
• Quantum Graphical Models and Belief Propagation
• Quantum Operation Time Reversal
• Quantum Dynamics as an analog of Conditional Probability
• From time-reversal symmetry to quantum Bayes' rules
• Thermodynamics of quantum switch information capacity activation
• Leggett-Garg Macrorealism and temporal correlations
• The nonequilibrium cost of accurate information processing
• Theoretical description and experimental simulation of quantum entanglement near open time-like curves via pseudo-density operators
• Unification of spatiotemporal quantum formalisms: mapping between process and pseudo-density matrices via multiple-time states
• Quantum Causal Unravelling

Cited by in corpus (8)

• Causal classification of spatiotemporal quantum correlations
• 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