Maximal entanglement velocity implies dual unitarity

A global quantum quench can be modeled by a quantum circuit with local unitary gates. In general, entangle-ment grows linearly at a rate given by entanglement velocity. Locality yields a finite light cone, which bounds the velocity. We show that the unitary interactions achieving the maximal rate must remain unitary if we exchange the space and time directions-a property known as dual unitarity. Our results are robust: approximate maximal entanglement velocity also implies approximate dual unitarity. We further show that maximal entanglement velocity is always accompanied by a specific dynamical pattern of entanglement, which yields simpler analyses of several known exactly solvable models.

Automated summary

A global quantum quench can be simulated using a quantum circuit with local unitary gates. The growth rate of entanglement is determined by the entanglement velocity, which is bounded by the finite light cone resulting from locality. The study shows that the unitary interactions achieving the maximal rate must remain unitary when the space and time directions are exchanged, known as dual unitarity. The results also indicate that maximal entanglement velocity is always accompanied by a specific pattern of entanglement, making the analysis of solvable models simpler.