All maximally entangling unitary gates

TL;DR

This paper characterizes all bipartite unitary gates that can generate maximal entanglement, explaining their properties and capacities, especially when ancillary systems are used, and clarifying differences in entangling capacities.

Contribution

It provides a complete characterization of all maximally entangling bipartite unitary operators with ancillary systems, revealing key properties and capacity relations.

Findings

Capacities of maximally entangling unitaries can differ

Capacities are equal when system dimensions are equal

Characterization applies to arbitrary finite dimensions

Abstract

We characterize all maximally entangling bipartite unitary operators, acting on systems $A,B$ of arbitrary finite dimensions $d_A\le d_B$, when use of ancillary systems by both parties is allowed. Several useful and interesting consequences of this characterization are discussed, including an understanding of why the entangling and disentangling capacities of a given (maximally entangling) unitary can differ and a proof that these capacities must be equal when $d_A=d_B$.