Largest separable balls around the maximally mixed bipartite quantum state

Details Largest separable balls around the maximally mixed bipartite quantum state Largest separable balls around the maximally mixed bipartite quantum state

2002-04-26

arxiv.org/abs/quant-ph/0204159v2

Physical Review A, Vol. 66, Article no. 062311 (Dec. 2002)

Physics

Quantum Physics

7 pages, LaTeX. Motivation and verbal description of results and their implications expanded and improved; one more proof incl

Scientific paper

10.1103/PhysRevA.66.062311

For finite-dimensional bipartite quantum systems, we find the exact size of the largest balls, in spectral $l_p$ norms for $1 \le p \le \infty$, of separable (unentangled) matrices around the identity matrix. This implies a simple and intutively meaningful geometrical sufficient condition for separability of bipartite density matrices: that their purity $\tr \rho^2$ not be too large. Theoretical and experimental applications of these results include algorithmic problems such as computing whether or not a state is entangled, and practical ones such as obtaining information about the existence or nature of entanglement in states reached by NMR quantum computation implementations or other experimental situations.

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