Entanglement of assistance

David P. Divincenzo; Christopher A. Fuchs; Hideo Mabuchi; John A. Smolin; Ashish Thapliyal; Armin Uhlmann

doi:10.1007/3-540-49208-9_21

Entanglement of assistance

David P. Divincenzo
, Christopher A. Fuchs
, Hideo Mabuchi
, John A. Smolin
, Ashish Thapliyal
, Armin Uhlmann

Physics

IBM
California Institute of Technology
University of California at Santa Barbara
Leipzig University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

The newfound importance of “entanglement as a resource” in quantum computation and quantum communication behooves us to quantify it in as many distinct ways as possible. Here we explore a new quantification of entanglement of a general (mixed) quantum state for a bipartite system, which we name entanglement of assistance. We show it to be the maximum of the average entanglement over all ensembles con- sistent with the density matrix describing the bipartite state. With the help of lower and upper bounds we calculate entanglement of assistance for a few cases and use these results to show the surprising property of superadditivity. We believe that this may throw some light on the question of additivity of entanglement of formation.

Original language	English
Title of host publication	Quantum Computing and Quantum Communications - 1st NASA International Conference, QCQC 1998, Selected Papers
Editors	Colin P. Williams
Publisher	Springer Verlag
Pages	247-257
Number of pages	11
ISBN (Print)	354065514X, 9783540655145
DOIs	https://doi.org/10.1007/3-540-49208-9_21
State	Published - 1999
Event	1st NASA International Conference on Quantum Computing and Quantum Communications, QCQC 1998 - Palm Springs, United States Duration: Feb 17 1998 → Feb 20 1998

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1509
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	1st NASA International Conference on Quantum Computing and Quantum Communications, QCQC 1998
Country/Territory	United States
City	Palm Springs
Period	2/17/98 → 2/20/98

ASJC Scopus Subject Areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/3-540-49208-9_21

Cite this

Divincenzo, D. P., Fuchs, C. A., Mabuchi, H., Smolin, J. A., Thapliyal, A., & Uhlmann, A. (1999). Entanglement of assistance. In C. P. Williams (Ed.), Quantum Computing and Quantum Communications - 1st NASA International Conference, QCQC 1998, Selected Papers (pp. 247-257). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1509). Springer Verlag. https://doi.org/10.1007/3-540-49208-9_21

Entanglement of assistance. / Divincenzo, David P.; Fuchs, Christopher A.; Mabuchi, Hideo et al.
Quantum Computing and Quantum Communications - 1st NASA International Conference, QCQC 1998, Selected Papers. ed. / Colin P. Williams. Springer Verlag, 1999. p. 247-257 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1509).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Divincenzo, DP, Fuchs, CA, Mabuchi, H, Smolin, JA, Thapliyal, A & Uhlmann, A 1999, Entanglement of assistance. in CP Williams (ed.), Quantum Computing and Quantum Communications - 1st NASA International Conference, QCQC 1998, Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1509, Springer Verlag, pp. 247-257, 1st NASA International Conference on Quantum Computing and Quantum Communications, QCQC 1998, Palm Springs, United States, 2/17/98. https://doi.org/10.1007/3-540-49208-9_21

Divincenzo DP, Fuchs CA, Mabuchi H, Smolin JA, Thapliyal A, Uhlmann A. Entanglement of assistance. In Williams CP, editor, Quantum Computing and Quantum Communications - 1st NASA International Conference, QCQC 1998, Selected Papers. Springer Verlag. 1999. p. 247-257. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-49208-9_21

Divincenzo, David P. ; Fuchs, Christopher A. ; Mabuchi, Hideo et al. / Entanglement of assistance. Quantum Computing and Quantum Communications - 1st NASA International Conference, QCQC 1998, Selected Papers. editor / Colin P. Williams. Springer Verlag, 1999. pp. 247-257 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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AB - The newfound importance of “entanglement as a resource” in quantum computation and quantum communication behooves us to quantify it in as many distinct ways as possible. Here we explore a new quantification of entanglement of a general (mixed) quantum state for a bipartite system, which we name entanglement of assistance. We show it to be the maximum of the average entanglement over all ensembles con- sistent with the density matrix describing the bipartite state. With the help of lower and upper bounds we calculate entanglement of assistance for a few cases and use these results to show the surprising property of superadditivity. We believe that this may throw some light on the question of additivity of entanglement of formation.

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Entanglement of assistance

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