Title: Separability of Bosonic Systems

Speaker：Dr. Nengkun Yu (Inst. for Quantum Comp., Univ. of Waterloo and Dept. of Math. and Stat., Univ. of Guelph, Canada)

Time: 14th May 2014, 9:30am

Venue: Seminar Room (334), Level 3, Building 5, Institute of Software, CAS

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(x)d system such that for general d, determine its separability NP-hard although verifiable conditions for separability is easily derived in case d=3,4.