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, 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.

13 pages, 7 figures

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Cited by in corpus (34)

• Random Quantum Circuits
• Scrambling is Necessary but Not Sufficient for Chaos
• Temporal Entanglement in Chaotic Quantum Circuits
• Exact dynamics in dual-unitary quantum circuits with projective measurements
• Growth of entanglement of generic states under dual-unitary dynamics
• From Dual Unitarity to Generic Quantum Operator Spreading
• Hierarchical generalization of dual unitarity
• Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
• Quantum information spreading in generalised dual-unitary circuits
• Ternary unitary quantum lattice models and circuits in $2+1$ dimensions
• Quantum Many-Body Scars in Dual-Unitary Circuits
• Fock-space delocalization and the emergence of the Porter-Thomas distribution from dual-unitary dynamics
• The entanglement membrane in exactly solvable lattice models
• From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics
• Dynamical simulations of many-body quantum chaos on a quantum computer
• Operator dynamics and entanglement in space-time dual Hadamard lattices
• Exactly solvable many-body dynamics from space-time duality
• Quantum and Classical Dynamics with Random Permutation Circuits
• Exact Hidden Markovian Dynamics in Quantum Circuits
• Solvable entanglement dynamics in quantum circuits with generalized space-time duality
• Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements
• Localization and integrability breaking in weakly interacting Floquet circuits
• Fundamental charges for dual-unitary circuits
• Dual unitaries as maximizers of the distance to local product gates
• Construction of perfect tensors using biunimodular vectors
• Exact Correlation Functions for Dual-Unitary Quantum circuits with exceptional points
• Ergodic theory of diagonal orthogonal covariant quantum channels
• Solvable Quantum Circuits in Tree+1 Dimensions
• Geometric constructions of generalized dual-unitary circuits from biunitarity
• Non-Equilibrium Quantum Many-Body Physics with Quantum Circuits
• Vanishing correlations in stochastic and bistochastic controlled circuits
• Logarithmic growth of operator entanglement in a clean non-integrable circuit
• Entanglement structure for finite system under dual-unitary dynamics
• Anomalous transport in U(1)-symmetric quantum circuits