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.

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• Entanglement entropy
• Nonequilibrium statistical mechanics
• Quantum quench
• Nonequilibrium systems
• Quantum spin models
• Chaos & nonlinear dynamics
• Tensor network methods