Eur. Phys. J. D (2014) 68: 136
https://doi.org/10.1140/epjd.e2014-40677-6

Regular Article

Quantum discord for generalized bloch sphere states

¹ Department of Theoretical Physics and Astrophysics, Tabriz University, 51664 Tabriz, Iran
² Institute for Studies in Theoretical Physics and Mathematics, 19395-1795 Tehran, Iran
³ Research Institute for Fundamental Sciences, 51664 Tabriz, Iran
⁴ Physics Department, Payame Noor University, Tehran, Iran

^a e-mail: nakarimi@yahoo.com

Received: 30 October 2013
Received in final form: 23 March 2014
Published online: 28 May 2014

Abstract

In this study, for particular states of bipartite quantum system in 2ⁿ × 2^m dimensional Hilbert space state, similar to m or n-qubit density matrices represented in Bloch sphere which we call them generalized Bloch sphere states (GBSS), we give an efficient optimization procedure so that analytic evaluation of quantum discord can be performed. Using this optimization procedure, we find an exact analytical formula for the optimum positive operator valued measure (POVM) that maximizes the measure of the classical correlation for these states. The presented optimization procedure is also used to show that for any concave entropy function the same POVMs are sufficient for quantum discord of mentioned states. Furthermore, we show that such optimization procedure can be used to calculate the geometric measure of quantum discord (GMQD) and then an explicit formula for GMQD is given. Finally, a complete geometric view is presented for quantum discord of GBSS.