Improved bounds on quantum uncommon information

TL;DR

This paper derives improved bounds on quantum uncommon information by developing a subspace exchange strategy and a referee-assisted method, enhancing understanding of quantum state exchange requirements in bipartite and multipartite systems.

Contribution

It introduces a novel subspace exchange technique and a referee-assisted approach to better estimate quantum uncommon information, which was previously lacking analytical bounds.

Findings

Derived tighter bounds on quantum uncommon information.

Developed a subspace exchange strategy for quantum state exchange.

Showed the versatility of the subspace technique in multipartite scenarios.

Abstract

In classical information theory, channel capacity quantifies the maximum number of messages that can be reliably transmitted using shared information. An equivalent concept, termed uncommon information, represents the number of messages required to be exchanged to completely share all information in common. However, this equivalence does not extend to quantum information theory. Specifically, quantum uncommon information is operationally defined as the minimal amount of entanglement required for the quantum communication task of quantum state exchange, where two parties exchange quantum states to share all quantum messages in common. Currently, an analytical closed-form expression for the quantum uncommon information remains undetermined. In this work, by investigating underlying characterization of the quantum uncommon information, we derive improved bounds on it. To obtain these bounds, we develop a subspace exchange strategy that leverages a common subspace of two parties to identify the unnecessary qubits for exchange. We also consider a referee-assisted exchange, wherein a referee aids two parties in efficiently performing the quantum state exchange. Our bounds provide more precise estimations for the quantum uncommon information. Furthermore, we demonstrate that the subspace technique is a versatile tool for characterizing uncommon information not only in the bipartite scenario but also in various multi-partite ones.