Measure of nonclassical correlation in coherence-vector representation

Abstract

We consider the coherence-vector representation of a bipartite state and obtain a necessary and sufficient condition for a zero-discord state. Based on this, a measure of quantum, classical, and total amount of correlations in bipartite states is proposed in this representation. Analytical expressions for this measure are available for any bipartite states. Our measure of nonclassical correlation coincides with the geometric measure of quantum discord for some particular states. I. INTRODUCTIONCharacterizing and quantifying the correlations in bipartite states is a basic and significant problem in quantum physics. The study of quantum correlations has traditionally focused on entanglement [1], which plays an important role in quantum computation and quantum communication [2]. However, quantum entanglement is not the only kind of correlation and is not necessary for deterministic quantum computation with one pure qubit (DQC1) [3,4]. These led to the studies on other kinds of nonclassical correlations over the past decade. One of the measures for nonclassical correlations, the quantum discord, initially introduced by Ollivier and Zurek [5] and by Henderson and Vedral [6], has attracted much attention recently [7][8][9][10][11][12][13][14].Given a bipartite state ρ AB on a composite Hilbert space H AB = H A ⊗ H B , the total amount of correlations is quantified by the quantum mutual information I (ρ AB ) = S(ρ A ) + S(ρ B ) − S(ρ AB ), with S(ρ) = −Trρ log 2 ρ the von Neumann entropy and ρ A(B) = Tr B(A) ρ AB the reduced density matrices for subsystem A(B). The quantum discord is defined as Q(ρ AB ) = I (ρ AB ) − J A (ρ AB ), the discrepancy between the quantum mutual information I (ρ AB ) and its classical version J A (ρ AB ) = S(ρ B ) − min { A

Structures of Three Types of Local Quantum Channels Based on Quantum Correlations

“…Representation above of a CC state shows that every CC state is separable and therefore every entangled state must be a QC state. Thus, quantum correlations are more general than entanglement and then become important resources for a number of quantum information applications without entanglement and then have drawn much attentions [2][3][4][5][6][7][8][9][10][11]. Quantum correlation is an intrinsic aspect of quantum theory that enables the manifestation of several interesting phenomena beyond the realms of the classical world.…”

Existence and construction of a quantum channel with given inputs and outputs

“…If such a Π exists, we call the state ρ is classical correlated [17][18][19][20][21][22]. Gisin [23] presented a theorem in 1991 that states that any pure entangled two-qubit state violates the CHSH inequality.…”

Examining quantum correlations in the XY spin chain by local quantum uncertainty

“…However, the entanglement is not the only type of quantum correlations, and there exist quantum tasks that display the quantum advantage without entanglement [9][10][11]. Therefore, numerous quantifiers have been proposed to reveal the quantum correlations that cannot be captured by entanglement [12][13][14][15][16][17][18][19][20][21][22]. Among them, quantum discord [12], defined as the mismatch between two quantum analogues of classically equivalent expression of the mutual information, provides a larger region of quantum states with non-classical correlations.…”