Beyond Density Matrices: Geometric Quantum States

TL;DR

This paper introduces geometric quantum states as an alternative to density matrices, providing a more complete representation of quantum ensembles and their physical realizations, with implications for quantum state manipulation and thermodynamics.

Contribution

It proposes geometric quantum states to overcome density matrices' limitations in representing ensemble realizations, enhancing understanding in quantum manipulation and thermodynamics.

Findings

Geometric quantum states offer a complete description of quantum ensembles.

They have significant implications for quantum state manipulation.

They impact the understanding of quantum thermodynamics.

Abstract

A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical realization. Conveniently, when working only with the statistical outcomes of projective and positive operator-valued measurements this is not a hindrance. To track ensemble realizations and so remove the shortcoming, we explore geometric quantum states and explain their physical significance. We emphasize two main consequences: one in quantum state manipulation and one in quantum thermodynamics.