6533b824fe1ef96bd12815d4
RESEARCH PRODUCT
Scalable Ellipsoidal Classification for Bipartite Quantum States
David A. Herrera-martísubject
Discrete mathematicsPhysicsQuantum PhysicsBasis (linear algebra)Operator (physics)FOS: Physical sciencesEllipsoidAtomic and Molecular Physics and OpticsSeparable spaceEuclidean distanceSeparable stateDimension (vector space)Quantum mechanicsBipartite graphQuantum Physics (quant-ph)description
The Separability Problem is approached from the perspective of Ellipsoidal Classification. A Density Operator of dimension N can be represented as a vector in a real vector space of dimension $N^{2}- 1$, whose components are the projections of the matrix onto some selected basis. We suggest a method to test separability, based on successive optimization programs. First, we find the Minimum Volume Covering Ellipsoid that encloses a particular set of properly vectorized bipartite separable states, and then we compute the Euclidean distance of an arbitrary vectorized bipartite Density Operator to this ellipsoid. If the vectorized Density Operator falls inside the ellipsoid, it is regarded as separable, otherwise it will be taken as entangled. Our method is scalable and can be implemented straightforwardly in any desired dimension. Moreover, we show that it allows for detection of Bound Entangled States
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-06-30 |