caa a22 4500 445886684 CHVBK 20180317145602.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s11128-010-0223-9 doi (NATIONALLICENCE)springer-10.1007/s11128-010-0223-9 An analytic approach to the problem of separability of quantum states based upon the theory of cones [Elektronische Daten] [D. Salgado, J. Sánchez-Gómez, M. Ferrero] Exploiting the cone structure of the set of unnormalized mixed quantum states, we offer an approach to detect separability independently of the dimensions of the subsystems. We show that any mixed quantum state can be decomposed as ρ=(1−λ)C ρ+λE ρ, where C ρ is a separable matrix whose rank equals that of ρ and the rank of E ρ is strictly lower than that of ρ. With the simple choice $${C_{\rho}=M_{1}\otimes M_{2}}$$ we have a necessary condition of separability in terms of λ, which is also sufficient if the rank of E ρ equals 1. We give a first extension of this result to detect genuine entanglement in multipartite states and show a natural connection between the multipartite separability problem and the classification of pure states under stochastic local operations and classical communication. We argue that this approach is not exhausted with the first simple choices included herein. Springer Science+Business Media, LLC, 2010 Entanglement nationallicence Separability nationallicence Cone nationallicence Bipartite nationallicence Multipartite nationallicence Salgado D. D.G. Metodología, Calidad y Tecnologías de la Información y las Comunicaciones, Insto. Nacional de Estadística, 28071, Madrid, Spain aut Sánchez-Gómez J. Dpto. Física Teórica, Universidad Autónoma de Madrid, 28049, Madrid, Spain aut Ferrero M. Dpto. Física, Universidad de Oviedo, 33007, Oviedo, Spain aut Quantum Information Processing Springer US; http://www.springer-ny.com 10/5(2011-10-01), 633-651 1570-0755 10:5<633 2011 10 11128 https://doi.org/10.1007/s11128-010-0223-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11128-010-0223-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Salgado D. D.G. Metodología, Calidad y Tecnologías de la Información y las Comunicaciones, Insto. Nacional de Estadística, 28071, Madrid, Spain aut NATIONALLICENCE 700 1- Sánchez-Gómez J. Dpto. Física Teórica, Universidad Autónoma de Madrid, 28049, Madrid, Spain aut NATIONALLICENCE 700 1- Ferrero M. Dpto. Física, Universidad de Oviedo, 33007, Oviedo, Spain aut NATIONALLICENCE 773 0- Quantum Information Processing Springer US; http://www.springer-ny.com 10/5(2011-10-01), 633-651 1570-0755 10:5<633 2011 10 11128 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer