A temporal analogue of quantum states for sequential measurements and time-reversal symmetry

If a quantum state distributed over regions of space provides the expectation values of observables on those regions, what object provides the expectation values of observables measured sequentially in time? We will first provide a rigorous definition of such quantum “states over time”. Using such a definition will naturally lead us to an extension of Bayes’ rule from classical probability to quantum systems. Such a quantum Bayes’ rule provides concrete predictions for the construction of processes that admit time-reversal symmetric expectation values of measurements. We will analyze the concrete example of an amplitude-damping channel on qubits.

*In-person and on Zoom*

https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09
Passcode: 657361
https://mathpicture.fas.harvard.edu/seminar