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Quantum coherence has recently emerged as a key candidate for use as a resource in various quantum information processing tasks. One of the main problems in any quantum resource theory is the characterization of the conversions between resources by means of the free operations of the theory. In this work, we ask if coherence, already present in a reference system, can be broadcast to the auxiliary system via incoherent operations. We prove that it is impossible for a weaker form of broadcasting via incoherent operations. This shows that broadcasting of coherence is forbidden via incoherent operations in every finite-dimensional system. We also prove that a generalized form of broadcasting via incoherent quantum operations can occur if and only if the state of system is coherent. In this case, we are able to give a method for constructing an incoherent quantum operation to broadcast coherence. [ABSTRACT FROM AUTHOR]

To obtain a classification of correlations of tripartite mixed states, various correlated states are introduced by using measurement-induced disturbance, including CCC, QC, GQC, CCX, CXC, XCC, CXX, XCX and XXC-states. Standard forms of them are established and equivalent characterizations of them are obtained in terms of normality and commutativity of the associated component operators. [ABSTRACT FROM AUTHOR]

We derive that sufficient and necessary conditions for existence of a quantum channel ϕ and a generalized unitary operation ɛ sending A to B (1 ⩾ i ⩾ k) for two given families { A}, { B} of matrices, respectively. As an application, a sufficient and necessary condition for existence of a unitary duality quantum computer with given input-output states is obtained. [ABSTRACT FROM AUTHOR]

Quantum coherence is an important physical resource in quantum information science, and also as one of the most fundamental and striking features in quantum physics. To quantify coherence, two proper measures were introduced in the literature, the one is the relative entropy of coherence C r (ρ) = S (ρ diag) − S (ρ) and the other is the ℓ 1 -norm of coherence C ℓ 1 (ρ) = ∑ i ≠ j | ρ i j | . In this paper, we obtain a symmetry-like relation of relative entropy measure C r (ρ A 1 A 2 ⋯ A n ) of coherence for an n-partite quantum states ρ A 1 A 2 ⋯ A n , which gives lower and upper bounds for C r (ρ) . As application of our inequalities, we conclude that when each reduced states ρ A i is pure, ρ A 1 ⋯ A n is incoherent if and only if the reduced states ρ A i and tr A i ρ A 1 ⋯ A n (i = 1 , 2 , ... , n) are all incoherent. Meanwhile, we discuss the conjecture that C r (ρ) ≤ C ℓ 1 (ρ) for any state ρ , which was proved to be valid for any mixed qubit state and any pure state, and open for a general state. We observe that every mixture η of a state ρ satisfying the conjecture with any incoherent state σ also satisfies the conjecture. We also observe that when the von Neumann entropy is defined by the natural logarithm ln instead of log 2 , the reduced relative entropy measure of coherence C ¯ r (ρ) = − ρ diag ln ρ diag + ρ ln ρ satisfies the inequality C ¯ r (ρ) ≤ C ℓ 1 (ρ) for any state ρ. [ABSTRACT FROM AUTHOR]