Ensembles of random quantum states tunable from volume law to area law

TL;DR

This paper introduces a tunable family of random quantum states called σ-ensembles, which can smoothly transition between volume-law and area-law entanglement, aiding classical simulation and modeling of ground states.

Contribution

The authors develop σ-ensembles with a single parameter to control entanglement scaling, constructed via eigenvalue distributions and MPS, bridging the gap between Haar-random states and realistic Hamiltonian ground states.

Findings

σ-ensembles can be tuned from volume-law to area-law entanglement.

The approach enables classical simulation of states with area-law entanglement.

These states better represent typical Hamiltonian ground states than Haar-random states.

Abstract

A standard approach to generate random pure quantum states relies on sampling from the Haar measure. However, the entanglement properties of such states present a fundamental challenge for their general applicability. Here, we introduce the $\sigma$-ensembles $\unicode{x2013}$ a family of random quantum states with only a single control parameter. Crucially, these states are designed such that they can be tuned between volume-law and area-law behavior, which has been a major obstacle thus far. We construct representatives of this ensemble by imposing a probability distribution on the eigenvalues of the successive subsystems, and subsequently reconstructing a compatible global state using the matrix product state (MPS) formalism. Due to their area-law entanglement, our approach circumvents the intractability of Haar-random pure states in classical simulations of quantum systems and is more representative of typical Hamiltonian ground states.