Locally Inaccessible Information and Entanglement of Formation

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. To appear in New Journal of Physics. See preprint at http://xxx.lanl.gov/abs/1106.0289

Depiction of flow of Local Inaccessible Information departing from measurements in E (blue arrows) and concentrating in E (red arrows). The net result of these two flows is the difference between the EOF and the QD for AB when measurements are made on B.

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