Unitary evolution and the distinguishability of quantum states

TL;DR

This paper investigates how quantum states evolve into distinguishable states under unitary evolution, revealing that the maximum distinguishability depends on the Hamiltonian and the system's Hilbert space dimension.

Contribution

It provides a numerical analysis of the proportion of quantum states evolving to nearly orthogonal states and highlights the role of the Hamiltonian in this process.

Findings

Maximum distinguishability depends on the Hamiltonian.

The proportion of states evolving to orthogonal states varies with Hilbert space dimension.

Speed of evolution influences state distinguishability.

Abstract

The study of quantum systems evolving from initial states to distinguishable, orthogonal final states is important for information processing applications such as quantum computing and quantum metrology. However, for most unitary evolutions and initial states the system does not evolve to an orthogonal quantum state. Here, we ask what proportion of quantum states evolves to nearly orthogonal systems as a function of the dimensionality of the Hilbert space of the system, and numerically study the evolution of quantum states in low-dimensional Hilbert spaces. We find that, as well as the speed of dynamical evolution, the level of maximum distinguishability depends critically on the Hamiltonian of the system.