Symmetric States on the Octonionic Bloch Ball

Paul Bourdon, H. T. Williams

V. A. Verbus, L. Martina, A. P. Protogenov

M. A. Jafarizadeh, Y. Mazhari, M. Aali

Using the convex optimization method and Helstrom family of ensembles introduced in Ref. [1], we have discussed optimal ambiguous discrimination in qubit systems. We have analyzed the problem of the optimal discrimination of N known quantum states and have obtained maximum success probability and optimal measurement for N known quantum states with equiprobable prior probabilities and equidistant from center of the Bloch ball, not all of which are on the one half of the Bloch ball and all of the conjugate states are pure. An exact solution has also been given for arbitrary three known quantum states. The given examples which use our method include: 1. Diagonal N mixed states; 2. N equiprobable states and equidistant from center of the Bloch ball which their corresponding Bloch vectors are inclined at the equal angle from z axis; 3. Three mirror-symmetric states; 4. States that have been prepared with equal prior probabilities on vertices of a Platonic solid. Keywords: minimum-error discrimination, success probability, measurement, POVM elements, Helstrom family of ensembles, convex optimization, conjugate states PACS Nos: 03.67.Hk, 03.65.Ta

Shuang Cong

The Bloch vector, or vector of coherence, provides a geometric description of the state and density matrix of two-state quantum system. Mathematically, the Bloch vector may be viewed as the adjoint representation of an su(2) object in an so(3) basis. The pure and mixed states details concerning the geometry of the Bloch ball for a qubit are investigated. The system controls with two and three magnetic fields to closed and open system are analyzed in the Bloch ball.

M. Fannes, D. Testard, André F. Verbeure

Norbert Schuch, J. I. Cirac, Michael M. Wolf