Revisiting Pure State Transformations with Zero Communication

TL;DR

This paper investigates the limits of transforming bipartite pure states with zero communication, deriving optimal fidelities and exploring catalytic conversions under local operations, revealing potential for error-tolerant, communication-free protocols.

Contribution

It introduces the first precise characterization of pure state conversion fidelity with zero communication and analyzes catalytic transformations in this setting.

Findings

Derived the optimal fidelity for pure state conversions with zero communication.

Identified conditions under which catalytic conversions are possible without communication.

Showed that certain state transformations can achieve high fidelity with no classical communication.

Abstract

It is known that general convertibility of bipartite entangled states is not possible to arbitrary error without some classical communication. While some trade-offs between communication cost and conversion error have been proven, these bounds can be very loose. In particular, there are many cases in which tolerable error might be achievable using zero-communication protocols. In this work we address these cases by deriving the optimal fidelity of pure state conversions under local unitaries as well as local operations and shared randomness (LOSR). We also uses these results to explore catalytic conversions between pure states using zero communication.