Creating ensembles of dual unitary and maximally entangling quantum evolutions

TL;DR

This paper introduces an iterative protocol to generate ensembles of dual unitary and 2-unitary operators, which are maximally entangling quantum gates, advancing the systematic construction of such operators in quantum information and many-body physics.

Contribution

The authors develop a nonlinear iterative protocol to systematically produce dual unitaries and 2-unitaries, filling a gap in methods for constructing maximally entangling quantum operators.

Findings

Protocol successfully generates ensembles close to dual unitaries.

Modified protocol yields many 2-unitaries in qutrits and ququads.

Characterization of operators via entangling power and entanglement distribution.

Abstract

Maximally entangled bipartite unitary operators or gates find various applications from quantum information to being building blocks of minimal models of many-body quantum chaos, and have been referred to as "dual unitaries". Dual unitary operators that can create the maximum average entanglement when acting on product states have to satisfy additional constraints. These have been called "2-unitaries" and are examples of perfect tensors that can be used to construct absolutely maximally entangled states of four parties. Hitherto, no systematic method exists, in any local dimension, which result in the formation of such special classes of unitary operators. We outline an iterative protocol, a nonlinear map on the space of unitary operators, that creates ensembles whose members are arbitrarily close to being dual unitaries, while for qutrits and ququads we find that a slightly modified protocol yields a plethora of 2-unitaries. We further characterize the dual unitary operators via their entangling power and the 2-unitaries via the distribution of entanglement created from unentangled states.