An unbiased measure over the matrix product state manifold

Understand

Matrix product states are useful representations for a large variety of naturally occurring quantum states.

• Studying their typical properties is important for understanding universal behavior, including quantum chaos and thermalization, as well as the limits of classical simulations of quantum devices.
• We show that the usual ensemble of sequentially generated random matrix product states (RMPS) using local Haar random unitaries is not uniform when viewed as a restriction of the full Hilbert space.
• As a result, the entanglement across the chain exhibits an anomalous asymmetry under spatial inversion.