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

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.