Petz map recovery in quantum many-body systems


Zou, Y. (2023). Petz map recovery in quantum many-body systems. Perimeter Institute. https://pirsa.org/23090053


Zou, Yijian. Petz map recovery in quantum many-body systems. Perimeter Institute, Sep. 12, 2023, https://pirsa.org/23090053


          @misc{ pirsa_PIRSA:23090053,
            doi = {10.48660/23090053},
            url = {https://pirsa.org/23090053},
            author = {Zou, Yijian},
            keywords = {Condensed Matter},
            language = {en},
            title = {Petz map recovery in quantum many-body systems},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {sep},
            note = {PIRSA:23090053 see, \url{https://pirsa.org}}

Yijian Zou Perimeter Institute for Theoretical Physics

Talk Type Scientific Series


We study the Petz map, which is a universal recovery channel of a tripartite quantum state upon erasing one party, in quantum many-body systems. The fidelity of the recovered state with the original state quantifies how much information shared by the two parties is not mediated by one of the party, and has a universal lower bound in terms of the conditional mutual information (CMI). I will study this quantity in two different contexts. First, in a CFT ground state, we show that the fidelity is universal, which means it only depends on the central charge and the cross ratio. We compute this universal function numerically and show that it is consistently better than the naive CMI bound. Secondly, we show that for two broad classes of the states, the CMI lower bound is saturated. These include stabilizer states (in any dimensions) and the ground state of 2+1D topological order.

Zoom link: https://pitp.zoom.us/j/92623435839?pwd=N1JIdkUwWHFkZGpqb1p1V3NKYy91QT09