Multipartite quantum states over time from two fundamental assumptions
arXiv:2410.22630 · doi:10.1103/lbf3-snp8
Abstract
The theory of quantum states over time extends the density operator formalism into the temporal domain, providing a unified of treatment of timelike and spacelike separated systems in quantum theory. Although recent results have characterized quantum states over time involving two timelike separated systems, it remains unclear how to consistently extend the notion of quantum states over time to multipartite temporal scenarios, such as those considered in studies of Leggett-Garg inequalities. In this Letter, we show that two simple assumptions uniquely single out the Markovian multipartite extension of bipartite quantum states over time, namely, linearity in the initial state and a quantum analog of conditionability for multipartite probability distributions. As a direct consequence of our result, we establish a canonical correspondence between multipartite QSOTs and Kirkwood-Dirac type quasiprobability distributions, which we show opens up the possibility of experimentally verifying the temporal correlations encoded in QSOTs via the recent experimental technique of simulating quasiprobability known as quantum snapshotting.
5+9 pages, revised, comments welcome
References in corpus (30)
- Quantum correlations with no causal order
- Leggett-Garg Inequalities
- Quantum Circuits Architecture
- Non-Markovian quantum processes: complete framework and efficient characterisation
- Towards a Formulation of Quantum Theory as a Causally Neutral Theory of Bayesian Inference
- Operational Markov condition for quantum processes
- Quantum conditional mutual information and approximate Markov chains
- The quasiprobability behind the out-of-time-ordered correlator
- Quantum Advantage in Postselected Metrology
- Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables
- Can a quantum state over time resemble a quantum state at a single time?
- From time-reversal symmetry to quantum Bayes' rules
- Operational quantum theory without predefined time
- Operational formulation of time reversal in quantum theory
- Properties and Applications of the Kirkwood-Dirac Distribution
- Geometry of quantum correlations in space-time
- Quantum non-Markovianity: Overview and recent developments
- Causal limit on quantum communication
- Virtual quantum broadcasting
- Temporal teleportation with pseudo-density operators: how dynamics emerges from temporal entanglement
- Quantum Markov chains, sufficiency of quantum channels, and Renyi information measures
- Quantum space-time marginal problem: global causal structure from local causal information
- Uniqueness of quantum state over time function
- Causal classification of spatiotemporal quantum correlations
- Non-monogamy of spatio-temporal correlations and the black hole information loss paradox
- Quantum Causal Inference with Extremely Light Touch
- Quantum Bayes' rule and Petz transpose map from the minimum change principle
- Snapshotting Quantum Dynamics at Multiple Time Points
- Role of Dilations in Reversing Physical Processes: Tabletop Reversibility and Generalized Thermal Operations
- Quantum dynamics as a pseudo-density matrix