I will present a joint work with V. Jaksic, Y. Pautrat and C.-A. Pillet on Hypothesis Testing for repeated quantum measurement with a focus on the Hypothesis Testing of the arrow of time.
I will present results on the rate of decrease of different characterisation of the probability of error in guessing between two hypotheses on the instruments used to repeatedly measure a quantum system. I will specialise these results to the hypothesis testing of the arrow of time for which the two probability measures are related through an involution.