On quantum states over time

In 2017, D. Horsman, C. Heunen, M. Pusey, J. Barrett, and R. Spekkens proved that there is no physically reasonable assignment takes a quantum channel an initial state produces joint on the tensor product of input output spaces. The interpretation was clear distinction between space time in setting not visible classically, where latter, one can freely use Bayes' theorem to go states marginals with noisy channels. this paper, we prove actually such assignment, bypassing no-go result Horsman et al., illustrate achievable by restricting domain their which represents given data more faithfully.