Maximal entanglement velocity implies dual unitarity

Abstract

A global quantum quench can be modeled by a quantum circuit with local unitary gates. In general, entanglement 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.