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

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.