# Quantum spatiotemporal correlations and Bayes' rule

### APA

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

### MLA

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

### BibTex

@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}} }

**Collection**

**Subject**

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].