PIRSA:24060019 Scientific Series Quantum Foundations

DOI10.48660/24060019

Series: Quantum Foundations

Parzygnat, A. (2024). Quantum spatiotemporal correlations and Bayes' rule. Perimeter Institute. https://pirsa.org/24060019

Parzygnat, Arthur. Quantum spatiotemporal correlations and Bayes' rule. Perimeter Institute, Jun. 06, 2024, https://pirsa.org/24060019 

@misc{ pirsa_PIRSA:24060019,
  doi = {10.48660/24060019},
  url = {https://pirsa.org/24060019},
  author = {Parzygnat, Arthur},
  keywords = {Quantum Foundations},
  language = {en},
  title = {Quantum spatiotemporal correlations and Bayes{\textquoteright} rule},
  publisher = {Perimeter Institute},
  year = {2024},
  month = {jun},
  note = {PIRSA:24060019 see, \url{https://pirsa.org}}
}

Abstract

While quantum correlations between two spacelike-separated systems are fully encoded by the bipartite density operator associated with the joint system, what operator encodes quantum correlations across space and time? I will describe the general theory of such "quantum states over time" as well as a canonical example that encodes the expectation values of certain observables measured sequentially in time. The latter extends the theory of pseudo-density matrices to arbitrary dimensions, not necessarily restricted to multi-qubit systems. In addition, quantum states over time admit a natural proposal for a general-purpose quantum Bayes' rule. Our results specialize to many well-studied examples, such as the state-update rule, the two-state vector formalism and weak values, and the Petz recovery map. This talk is based on joint work with James Fullwood and the two papers: arXiv: 2212.08088 [quant-ph] and 2405.17555 [quant-ph].

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