Quantum state merging with bound entanglement

TL;DR

This paper investigates quantum state merging involving PPT entangled states, establishing conditions for perfect merging and showing limitations when no additional singlets are available, with implications for quantum information processing.

Contribution

It introduces conditions for perfect merging with PPT entangled states and demonstrates the limitations of free PPT entangled states in merging pure states.

Findings

Certain separable states cannot be perfectly merged without additional singlets.

Free PPT entangled states do not enhance merging of pure states.

Conditional entropy determines the rate of additional singlets needed.

Abstract

Quantum state merging is one of the most important protocols in quantum information theory. In this task two parties aim to merge their parts of a pure tripartite state by making use of additional singlets while preserving correlations with a third party. We study a variation of this scenario where the shared state is not necessarily pure, and the merging parties have free access to local operations, classical communication, and PPT entangled states. We provide general conditions for a state to admit perfect merging, and present a family of fully separable states which cannot be perfectly merged if the merging parties have no access to additional singlets. We also show that free PPT entangled states do not give any advantage for merging of pure states, and the conditional entropy plays the same role as in standard quantum state merging quantifying the rate of additional singlets needed to perfectly merge the state.