Entropy Change in Quantum Measurements for Infinite-Dimensional Quantum Systems

In this paper, first, we prove the projective measurement increases the entropy in infinite-dimensional quantum systems, and discuss some useful properties for the study of entropy changes in quantum measurement. Next, we introduce a joint purification framework which keeps track of all the information transfer in a quantum measurement. Based on this joint purification which encodes the various entropies arising from the most general quantum measurement, we establish several information conservation and entropic relations in infinite-dimensional case.