Regular Article

Detecting two qubit both-way positive discord states

¹ Department of Mathematics, Government Girls’ General Degree College, Ekbalpore, Kolkata 700023, India
² Department of Mathematics, Heritage Institute of Technology, Anandapur, Kolkata 700107, India
³ Department of Mathematics, South Malda College, Malda, West Bengal, India
⁴ Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata 700009, India

^a e-mail: dsarkar1x@gmail.com, dsappmath@caluniv.ac.in

Received: 23 February 2019
Revised: 20 May 2019
Published online: 27 August 2019

Abstract

Quantum discord plays a pragmatic role in analyzing nonclassical feature of quantum correlations beyond entanglement. It is used in several information processing protocols which lacks sufficient amount of entanglement to be used as a resource. We have provided with an analytical method of detecting quantum discord of an arbitrary two qubit state. We have formulated a set of necessary and sufficient conditions for any two qubit state to be a both-way non-zero quantum discord state. As quantum discord is asymmetric in nature, we have framed the set of if and only if conditions for a two qubit state to be classical-quantum as well for it to be quantum-classical. Interestingly, not only correlation tensor but also local Bloch vector (corresponding to the classical party) plays a role for detecting the state to be a positive discord state.