Quantum Discord of Rank-2 Two-qubit States

Among various definitions of quantum correlations, quantum discord has attracted considerable attention. To find analytical expression of quantum discord is an intractable task. In this paper, we discuss thoroughly the case of two-qubit rank-two states. An analytical expression for the quantum discord is obtained by means of Koashi-Winter relation. A geometric picture is demonstrated by means of quantum steering ellipsoid. We point out that in this case the optimal measurement is indeed the von Neumann measurement, which is usually used in the study of quantum discord. However, for some two-qubit states with the rank larger than two, we find that three-element POVM measurement is more optimal. It means that more careful attention should be paid in the discussion of quantum discord.Among various definitions of quantum correlations, quantum discord has attracted considerable attention. To find analytical expression of quantum discord is an intractable task. In this paper, we discuss thoroughly the case of two-qubit rank-two states. An analytical expression for the quantum discord is obtained by means of Koashi-Winter relation. A geometric picture is demonstrated by means of quantum steering ellipsoid. We point out that in this case the optimal measurement is indeed the von Neumann measurement, which is usually used in the study of quantum discord. However, for some two-qubit states with the rank larger than two, we find that three-element POVM measurement is more optimal. It means that more careful attention should be paid in the discussion of quantum discord.

arXiv:1107.2246Journal of Physics A Mathematical and TheoreticalSep 22, 201162 citations

Orthogonal measurements are almost sufficient for quantum discord of two qubits

Fernando Galve, Gian Luca Giorgi, Roberta Zambrini

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.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.

arXiv:1107.2005Europhysics Letters (EPL)Nov 1, 201161 citations

Symmetric quantum discord for a two-qubit state

王仲宵, 王波波

中国物理B：英文版Jan 1, 20140 citations

Analytical expression of quantum discord for rank-2 two-qubit states

Zhu, X., Fei, S., Li-Jost, X.

Quantum correlations characterized by quantum entanglement and quantum discord play important roles in many quantum information processing. We study the relations among the entanglement of formation, concurrence, tangle, linear entropy-based classical correlation and von Neumann entropy-based classical correlation . We present analytical formulae of linear entropy-based classical correlation for arbitrary $d\otimes 2$ quantum states and von Neumann entropy-based classical correlation for arbitrary $2\otimes 2$ rank-2 quantum states. From the von Neumann entropy-based classical correlation, we derive an explicit formula of quantum discord for arbitrary rank-2 two-qubit quantum states.Quantum correlations characterized by quantum entanglement and quantum discord play important roles in many quantum information processing. We study the relations among the entanglement of formation, concurrence, tangle, linear entropy-based classical correlation and von Neumann entropy-based classical correlation . We present analytical formulae of linear entropy-based classical correlation for arbitrary $$d\otimes 2$$ quantum states and von Neumann entropy-based classical correlation for arbitrary $$2\otimes 2$$ rank-2 quantum states. From the von Neumann entropy-based classical correlation, we derive an explicit formula of quantum discord for arbitrary rank-2 two-qubit quantum states.

Jan 1, 20183 citations

d\otimes 2

quantum states and von Neumann entropy-based classical correlation for arbitrary

2\otimes 2

rank-2 quantum states. From the von Neumann entropy-based classical correlation, we derive an explicit formula of quantum discord for arbitrary rank-2 two-qubit quantum states.