Guessing Quantum Ensemble Using Laplace Principle

TL;DR

This paper introduces a method based on the Laplace principle to derive a natural distribution of pure quantum states that compose a mixed state, emphasizing the most spread-out ensemble among infinitely many possibilities.

Contribution

The paper applies the Laplace principle to quantum ensembles, providing a novel way to select a natural distribution of pure states for a given mixed state.

Findings

Derivation of a natural distribution of pure states using Laplace principle

The distribution is more spread out than other ensembles

Provides a new perspective on quantum state decomposition

Abstract

For a mixed quantum state with density matrix $\rho$ there are infinitely many ensembles of pure quantum states, which average to $\rho$. Starting from Laplace principle of insufficient reason (not to give \emph{a priori} preference to any particular state), we derive a `natural' distribution of pure states averaging to $\rho$, which is `more spread' than all the others.