PIRSA:15030097

Separability of Bosonic Systems

Yu, N. (2015). Separability of Bosonic Systems. Perimeter Institute. https://pirsa.org/15030097

Yu, Nengkun. Separability of Bosonic Systems. Perimeter Institute, Mar. 04, 2015, https://pirsa.org/15030097 

          @misc{ pirsa_PIRSA:15030097,
            doi = {10.48660/15030097},
            url = {https://pirsa.org/15030097},
            author = {Yu, Nengkun},
            keywords = {Quantum Foundations, Quantum Information},
            language = {en},
            title = {Separability of Bosonic Systems},
            publisher = {Perimeter Institute},
            year = {2015},
            month = {mar},
            note = {PIRSA:15030097 see, \url{https://pirsa.org}}
          }

Yu Nengkun University of Technology Sydney

DOI 10.48660/15030097
Collection
Talk Type Scientific Series
Subject

Abstract

We study the separability of quantum states in bosonic system. Our main tool here is the "separability witnesses", and a connection between "separability witnesses" and a new kind of positivity of matrices--- "Power Positive Matrices" is drawn. Such connection is employed to demonstrate that multi-qubit quantum states with Dicke states being its eigenvectors is separable if and only if two related Hankel matrices are positive semidefinite. By employing this criterion, we are able to show that such state is separable if and only if it's partial transpose is non-negative, which confirms the conjecture in [Wolfe, Yelin, Phys. Rev. Lett. (2014)]. Then, we present a class of bosonic states in d⊗d system such that for general d, determine its separabilityNP-hard although verifiable conditions for separability is easily derived in case d=3,4.