Locally Inaccessible Information as a Fundamental Ingredient to Quantum Information

TL;DR

This paper explores the role of Local Inaccessible Information (LII) in quantum systems, relating it to key quantum measures like entanglement and conditional entropy, and introduces LII flow to analyze multipartite quantum correlations.

Contribution

It establishes a fundamental connection between LII and quantum measures such as EOF and conditional entropy, and introduces the concept of LII flow for multipartite systems.

Findings

LII relates to entanglement of formation and conditional entropy.

LII flow quantifies quantum correlations in multipartite systems.

Relations clarify phenomena like entanglement sudden death.

Abstract

Quantum discord (QD) measures the fraction of the pairwise mutual information that is locally inaccessible, in a multipartite system. Fundamental aspects related to two important measures in quantum information theory the Entanglement of Formation (EOF) and the conditional entropy, can be understood in terms of the distribution of this form of Local Inaccessible Information (LII). As such, the EOF for an arbitrarily mixed bipartite system AB can be related to the gain or loss of LII due to the extra knowledge that a purifying ancillary system E has on the pair AB. Similarly, a clear meaning of the negativity of the conditional entropy for AB is given. We exemplify by showing that these relations elucidate important and yet not well understood quantum features, such as the bipartite entanglement sudden death and the distinction between EOF and QD for quantifying quantum correlation. For that we introduce the concept of LII flow which quantifies the LII shared in multipartite system when a sequential local measurements are performed.