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Quantitative entanglement witnesses

Eisert, J. and Brandão, F. G. S. L. and Audenaert, K. M. R. (2007) Quantitative entanglement witnesses. New Journal of Physics, 9 (3). Art. No. 46. ISSN 1367-2630. doi:10.1088/1367-2630/9/3/046.

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Entanglement witnesses provide tools to detect entanglement in experimental situations without the need of having full tomographic knowledge about the state. If one estimates in an experiment an expectation value smaller than zero, one can directly infer that the state has been entangled, or specifically multi-partite entangled, in the first place. In this paper, we emphasize that all these tests—based on the very same data—give rise to quantitative estimates in terms of entanglement measures: 'If a test is strongly violated, one can also infer that the state was quantitatively very much entangled'. We consider various measures of entanglement, including the negativity, the entanglement of formation, and the robustness of entanglement, in the bipartite and multipartite setting. As examples, we discuss several experiments in the context of quantum state preparation that have recently been performed.

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Brandão, F. G. S. L.0000-0003-3866-9378
Additional Information:© 2007 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Articles submitted prior to November 2012 the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported (CC BY-NC-SA version 3.0) licence. Received 5 October 2006. Published 2 March 2007. We thank O Gühne, M Reimpell and R F Werner for valuable discussions on the subject of the paper and P Hyllus for very helpful comments on the manuscript. This study has been coordinated in submission with their independent study [14]. Note also that the independent study [73] (which was made available slightly later on the preprint server) is similar in its spirit, and strongly and nicely complements the present study in that the role of correlation measurements is emphasized and studied in great detail. The semi-definite program was programmed using the packages SeDuMi and Yalmip. This study has been supported by the DFG (SPP 1116, SPP 1078), the EU (QAP), the EPSRC, the QIP-IRC, Microsoft Research, the Brazilian agency Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), and the EURYI Award Scheme.
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)SPP 1116
Deutsche Forschungsgemeinschaft (DFG)SPP 1078
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Microsoft ResearchUNSPECIFIED
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)UNSPECIFIED
European Young Investigator Awards (EURYI)UNSPECIFIED
Issue or Number:3
Record Number:CaltechAUTHORS:20160607-095644015
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Official Citation:J Eisert et al 2007 New J. Phys. 9 46
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:67715
Deposited By: George Porter
Deposited On:07 Jun 2016 17:39
Last Modified:12 Jul 2022 19:50

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