Predictability of measurements

TL;DR

This paper explores the predictability of measurements in quantum systems, linking it to entropy and examining how it evolves over time in different physical regimes.

Contribution

It introduces a method to calculate measurement predictability considering both quantum and entropic uncertainties, highlighting their relationship in various states.

Findings

Unpredictability equals entropy in semiclassical mechanics.

Unpredictability increases over time in entangled quantum states.

Quantum measurement affects the evolution of measurement unpredictability.

Abstract

The second law of thermodynamics states that entropy increases (or does not change) by time in an isolated system. As microscopic physical laws are reversible, the origin of irreversibility is not straightforward. Although the outcome of a measurement on a pure quantum state is not fully predictable due to the Heisenberg uncertainty principle, quantum and finite entropy uncertainties are thought to be fundamentally different. We propose to calculate the predictability of measurements comprising both quantum and entropic uncertainties. We show that the unpredictability of measurements is identical to entropy in case of semiclassical statistical mechanics, and it increases by time in a pure entangled quantum state as a result of quantum measurement.