Spread quantum information in one-shot quantum state merging

TL;DR

This paper investigates the difference in entanglement costs between one-way and two-way quantum state merging in a one-shot setting, introducing the concept of spread quantum information to measure nonlocal quantum information distribution.

Contribution

It introduces the notion of spread quantum information and demonstrates the fundamental difference in entanglement costs between one-way and two-way communication in one-shot quantum state merging.

Findings

Entanglement costs differ between one-way and two-way scenarios in one-shot state merging.

Spread quantum information measures nonlocal quantum information distribution.

The difference is not apparent in asymptotic cases but is significant in one-shot scenarios.

Abstract

We prove the difference between the minimal entanglement costs in quantum state merging under one-way and two-way communication in a one-shot scenario, whereas they have been known to coincide asymptotically. While the minimal entanglement cost in state merging under one-way communication is conventionally interpreted to characterize partial quantum information conditioned by quantum side information, we introduce a notion of spread quantum information evaluated by the corresponding cost under two-way communication. Spread quantum information quantitatively characterizes how nonlocally one-shot quantum information is spread, and it cannot be interpreted as partial quantum information.