Universal quantum state merging

TL;DR

This paper investigates the optimal entanglement rate for quantum state merging under uncertainty, establishing bounds and capacities for various quantum communication scenarios with unknown states.

Contribution

It introduces a method to determine the minimal entanglement rate for merging unknown states and provides bounds for classical costs and capacities in uncertain quantum settings.

Findings

Optimal entanglement rate matches that of known states.

Lower bound for classical cost under state uncertainty.

Capacity results for entanglement distillation and quantum channels.

Abstract

We determine the optimal entanglement rate of quantum state merging when assuming that the state is unknown except for its membership in a certain set of states. We find that merging is possible at the lowest rate allowed by the individual states. Additionally, we establish a lower bound for the classical cost of state merging under state uncertainty. To this end we give an elementary proof for the cost in case of a perfectly known state which makes no use of the "resource framework". As applications of our main result, we determine the capacity for one-way entanglement distillation if the source is not perfectly known. Moreover, we give another achievability proof for the entanglement generation capacity over compound quantum channels.