Conditional Action and imperfect Erasure of Qubits

TL;DR

This paper explores how conditional actions in quantum theory, such as imperfect qubit erasure, relate to entropy and measurement, using the mathematical framework of instruments and a specific spin system example.

Contribution

It introduces a detailed mathematical analysis of conditional actions in quantum mechanics, focusing on imperfect qubit erasure via spin coupling.

Findings

Conditional actions are a special case of quantum instruments.

Imperfect qubit erasure can be modeled as a conditional action.

The paper provides a concrete example using spin systems.

Abstract

We consider state changes in quantum theory due to "conditional action" and relate these to the discussion of entropy decrease due to interventions of "intelligent beings" and the principles of Szilard and Landauer/Bennett. The mathematical theory of conditional actions is a special case of the theory of "instruments" which describes changes of state due to general measurements and will therefore be briefly outlined in the present paper. As a detailed example we consider the imperfect erasure of a qubit that can also be viewed as a conditional action and will be realized by the coupling of a spin to another small spin system in its ground state.