Bayesian Retrodiction Approach to Reverse Processes

Defining the reverse of a physical process may not always be straightforward. However, by using Bayesian reasoning, such a reverse process can be defined for a general scenario [1-2]. Moreover, Bayesian retrodiction can also be extended into quantum theory by using the Petz recovery map. In this talk, I will describe the intuition behind Bayesian retrodiction and its applications. While we originally used this framework to approach the fluctuation relations in thermodynamics [2-3], there are also other applications, one of them being the recovery of information from a toy black hole as modeled by Hayden and Preskill [4].
 
[1] F. Buscemi, V. Scarani, PRE 103, 052111 (2021) https://arxiv.org/abs/2009.02849
[2] C.C. Aw, F. Buscemi, V. Scarani, AVS Quantum Sci. 3, 045601 (2021) https://arxiv.org/abs/2106.08589
[3] A.F. Ducuara et al., https://arxiv.org/abs/2306.00449
[4] Hayden, P. and Preskill, J., JHEP09(2007)120 (2007) https://arxiv.org/abs/0708.4025