Limit theorems for the evolution of quantum pure states

TL;DR

This paper establishes strong law of large numbers and central limit theorem analogs for the evolution of quantum pure states under repeated application of random unitary channels, advancing understanding of quantum state dynamics.

Contribution

It introduces limit theorems for quantum pure states evolving through i.i.d. random unitary channels, a novel theoretical development in quantum information theory.

Findings

Proves strong law of large numbers for quantum state evolution.

Establishes central limit theorem for quantum pure states.

Provides mathematical framework for quantum state dynamics under randomness.

Abstract

Limit theorems of strong law of large numbers and central limit theorem types are obtained for the compositions of independent identically distributed random unitary channels.