Phase-random states: ensembles of states with fixed amplitudes and uniformly distributed phases in a fixed basis

TL;DR

This paper introduces phase-random states with fixed amplitudes and random phases, showing their typical properties, entanglement growth, and implications for simulating quantum dynamics.

Contribution

It defines phase-random states and analyzes their properties, revealing their relevance to typical subsystem states and the complexity of simulating quantum evolutions.

Findings

Canonical states appear in subsystems of phase-random states

Time evolution under certain Hamiltonians generates high entanglement

Two-qubit diagonal unitaries can produce similar entanglement ensembles

Abstract

Motivated by studies of typical properties of quantum states in statistical mechanics, we introduce phase-random states, an ensemble of pure states with fixed amplitudes and uniformly distributed phases in a fixed basis. We first show that canonical states typically appear in subsystems of phase-random states. We then investigate the simulatability of phase-random states, which is directly related to that of time evolution in closed systems, by studying their entanglement properties. We find that starting from a separable state, time evolutions under Hamiltonians composed of only separable eigenstates generate extremely high entanglement and are difficult to simulate with matrix product states. We also show that random quantum circuits consisting of only two-qubit diagonal unitaries can generate an ensemble with the same average entanglement as phase-random states.