Orthogonal measurements are almost sufficient for quantum discord of two qubits
IFISC (UIB-CSIC), Instituto de Física Interdisciplinar y Sistemas Complejos, UIB Campus E-07122 Palma de Mallorca, Spain, EU
Accepted: 23 September 2011
The common use in the literature of orthogonal measurements in obtaining quantum discord for two-qubit states is discussed and compared with more general measurements. We prove the optimality of orthogonal measurements for rank-2 states. While for rank-3 and -4 mixed states they are not optimal, we present strong numerical evidence showing that they give the correct quantum discord up to minimal corrections. Based on the connection, through purification with an ancilla, between discord and entanglement of formation (EoF), we give a tight upper bound for the EoF of a 2⊗N mixed state of rank 2, given by an optimal decomposition of 2 elements. We also provide an alternative way to compute the quantum discord for two qubits based on the Bloch vectors of the state.
PACS: 03.67.Mn – Entanglement measures, witnesses, and other characterizations / 03.65.Ta – Foundations of quantum mechanics; measurement theory / 03.65.Ud – Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)
© EPLA, 2011