A note on hidden quantum discord in two- and three-qubit systems under local filtering operations

Abstract One of the primary goal of quantum information theory is to understand and quantify the various correlations that exist in quantum systems. Quantum correlation is broader than quantum entanglement, and quantum discord has always attracted more attention. In this paper, we investigate the hidden properties of quantum discord. In particular, for a class of two-qubit states, we prove the existence of hidden quantum discord under local filtering operations and give sufficient conditions for the absence of hidden quantum discord. For a class of three-qubit states, we investigate hidden geometric discord and analyze its dynamic behavior under several conditions. Furthermore, by comparing two- and three-qubit systems, we discover the inconsistency of hidden discord for ρ = 1 2 N ( I + ∑ j = 1 3 c j σ j ⊗ … ⊗ σ j ) ( c 3 = 1 , N = 2 , 3 ) .