On the Conservation of Information in Quantum Physics

TL;DR

This paper introduces the concept of coherent entropy to account for the conserved quantum information in pure states, addressing apparent informational discrepancies in quantum mechanics and linking it to future information conveyance.

Contribution

It defines coherent entropy as a new measure of quantum information, filling a gap in understanding information conservation in quantum systems.

Findings

Coherent entropy equals the information conveyed in the future by quantum states.

Quantum information in pure states is conserved when considering coherence.

The concept may impact foundations of quantum mechanics and black-hole physics.

Abstract

According to quantum mechanics, the informational content of isolated systems does not change in time. However, subadditivity of entropy seems to describe an excess of information when we look at single parts of a composite systems and their correlations. Moreover, the balance between the entropic contributions coming from the various parts is not conserved under unitary transformations. Reasoning on the basic concept of quantum mechanics, we find that in such a picture an important term has been overlooked: the intrinsic quantum information encoded in the coherence of pure states. To fill this gap we are led to define a quantity, that we call coherent entropy, which is necessary to account for the "missing" information and for re-establishing its conservation. Interestingly, the coherent entropy is found to be equal to the information conveyed in the future by quantum states. The perspective outlined in this paper may be of some inspiration in several fields, from foundations of quantum mechanics to black-hole physics.