We examine the time reversal symmetry of quantum measurement sequences by introducing a forward and backward Janus sequence of measurements. If the forward sequence of measurements creates a sequence of quantum states in time, starting from an initial state and ending in a final state, then the backward sequence begins with the time-reversed final state, exactly retraces the intermediate states, and ends with the time-reversed initial state. We prove that such a sequence can always be constructed, showing that unless the measurements are ideal projections, it is impossible to tell if a given sequence of measurements is progressing forward or backward in time. A statistical arrow of time emerges only because typically the forward sequence is more probable than the backward sequence.
Jordan, A.N., Chantasri, A., Murch, K., Dressel, J., Korotkov, A.N., 2017. Janus sequences of quantum measurements and the arrow of time. AIP Conference Proceedings 1841: 020003. doi:10.1063/1.4982767
American Institute of Physics