Work Required for Selective Quantum Measurement

TL;DR

This paper investigates the conditions under which a measuring system in quantum mechanics can be considered independent and capable of selective measurement, revealing a fundamental link between entropy transfer and work requirement.

Contribution

It establishes the criteria for a measuring system in quantum mechanics and links entropy transfer to the work needed for selective measurement.

Findings

Existence of negative entropy transfer from measurement system to quantum system.

Negative entropy transfer can be converted into Helmholtz free energy.

An extra work of k_B T is required for selective measurement.

Abstract

In quantum mechanics, we define the measuring system $M$ in a selective measurement by two conditions. Firstly, when we define the measured system $S$ as the system in which the non-selective measurement part acts, $M$ is independent from the measured system $S$ as a quantum system in the sense that any time-dependent process in the total system $S+M$ is divisible into parts for $S$ and $M$. Secondly, when we can separate $S$ and $M$ from each other without changing the unitary equivalence class of the state of $S$ from that obtained by the partial trace of $M$, the eigenstate selection in the selective measurement cannot be realized. In order for such a system $M$ to exist, we show that in one selective measurement of an observable of a quantum system $S_0$ of particles in $S$, there exists a negative entropy transfer from $M$ to $S$ that can be directly transformed into an amount of Helmholtz free energy of $k_BT$ where $T$ is the thermodynamic temperature of the system $S$. Equivalently, an extra amount of work, $k_BT$, is required to be done by the system $M$.