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

• URL: http://arxiv.org/abs/2604.15300v1
• Date: Thu, 16 Apr 2026 17:57:19 GMT
• Title: Ensembles of random quantum states tunable from volume law to area law
• Abstract summary: We introduce the $$-ensembles $$x$ a family of random quantum states with only a single control parameter.<n>We reconstruct a compatible global state using the matrix product state (MPS) formalism.<n>Due to their area-law entanglement, our approach circumvents the intractability of Haar-random pure states in classical simulations of quantum systems.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $σ$-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.

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