Abstract
Quantum discord is a manifestation of quantum correlations due to non-commutativity rather than entanglement. Two measures of quantum discord by the amount of non-commutativity via the trace norm and the Hilbert-Schmidt norm respectively are proposed in this paper. These two measures can be calculated easily for any state with arbitrary dimension. It is shown by several examples that these measures can reflect the amount of the original quantum discord.
Highlights
Quantum discord is initially introduced by Ollivier and Zurek[4] and by Henderson and Vedral[5]
It follows that the non-commutativity of the local operators Bijs implies ρ contains quantum discord
By comparing them with that of D in ref. 51, we find that the trends of DN and DN′ are roughly the same as that of D: DN and DN′ increase when D increases roughly and vice versa. (The geometry of the set of the Bell-diagonal states is a tetrahedron with the four Bell states sit at the four vertices, the extreme points of tetrahedron (i.e., (− 1, 1, 1), (1, − 1, 1), (1, 1, − 1) and (− 1, − 1, − 1)), see Fig. 1 in ref. 51 for detail.)
Summary
Quantum discord is a manifestation of quantum correlations due to non-commutativity rather than entanglement. Two measures of quantum discord by the amount of non-commutativity via the trace norm and the Hilbert-Schmidt norm respectively are proposed in this paper. These two measures can be calculated for any state with arbitrary dimension. Quantum discord has aroused great interest in the past decade[11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30].
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