The Decompositions of Werner and Isotropic States

Abstract

The decompositions of separable Werner state, and also isotropic state, are well-known tough issues in quantum information theory, in this work we investigate them in the Bloch vector representation, exploring the symmetric informationally complete positive operator-valued measure (SIC-POVM) in the Hilbert space. We successfully get the decomposition for arbitrary $N\times N$ Werner state in terms of regular simplexes. Meanwhile, the decomposition of isotropic state is found to be related to the decomposition of Werner state via partial transposition. It is interesting to note that in the large $N$ limit, while the Werner states are either separable or non-steerably entangled, most of the isotropic states tend to be steerable.

Few typos are corrected

References in corpus (6)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Symmetric Informationally Complete Measurements of Arbitrary Rank
• Fibonacci-Lucas SIC-POVMs
• Another convex combination of product states for the separable Werner state
• Verifying bound entanglement of dephased Werner states
• A Decomposition of Separable Werner States

Cited by in corpus (1)

• An Effective Way to Determine the Separability of Quantum State