Maximal entanglement velocity implies dual unitarity

TL;DR

This paper demonstrates that achieving maximal entanglement velocity in quantum circuits requires dual unitarity, and this relationship is robust, providing insights into entanglement dynamics and simplifying analysis of solvable models.

Contribution

It establishes a fundamental link between maximal entanglement growth and dual unitarity, extending the understanding of quantum circuit dynamics.

Findings

Maximal entanglement velocity implies dual unitarity.

Approximate maximal velocity suggests approximate dual unitarity.

Maximal velocity correlates with a specific entanglement pattern.

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, which is upper bounded by the growth of the light cone. 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.