Post-measurement state and entropy in finite quantum systems

Abstract

We studied in this paper the bipartite quantum systems in finite Hilbert space. We applied the measurement on the first subsystem only and studied how this measurement is affecting the entropy of the second subsystem. The analytic work carried out in this paper shows that the post measurement state is factorizable when measurement is applied on the first subsystem. This result shows that the disorder of the system is reduced and hence the entropy of the whole system is reduced as expected. However, it is also shown in this work that the entropy of the second subsystem of the post-measurement state could be greater than that of the original state. Increasing entropy after measurement means that the disorder in the second subsystem is increased. The information we gain from measuring the first subsystem reduces our information about the second subsystem rather than increasing it or at least keeping it the same as expected. This means that more factors may be required in order to calculate the probability of finding the second subsystem in a certain state.