Conditional Action and Imperfect Erasure of Qubits

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.

Dilation of stochastic matrices by coarse graining

“…A stochastic matrix T can be viewed as a description of a classical "conditional action", see [23,34]. Under certain circumstances such a conditional action may decrease the Shannon entropy of the object system.…”