Efficient implementation of bipartite nonlocal unitary gates using prior entanglement and classical communication

TL;DR

This paper explores efficient methods for implementing bipartite nonlocal unitaries with less entanglement and classical communication than teleportation, using group representations and novel diagrammatic techniques.

Contribution

It introduces a framework for implementing certain bipartite unitaries more efficiently by leveraging group theory and new diagrammatic tools, reducing resource requirements.

Findings

Constructed large families of unitaries using finite group representations.

Developed a diagrammatic approach for representing entangled states.

Established conditions for minimal information transfer during implementation.

Abstract

Any bipartite nonlocal unitary operation can be carried out by teleporting a quantum state from one party to the other, performing the unitary gate locally, and teleporting a state back again. This paper investigates unitaries which can be carried out using less prior entanglement and classical communication than are needed for teleportation. Large families of such unitaries are constructed using (projective) representations of finite groups. Among the tools employed are: a diagrammatic approach for representing entangled states, a theorem on the necessary absence of information at certain times and locations, and a representation of bipartite unitaries based on a group Fourier transform.