Search

Quantum coherence is known as an important resource in many quantum information tasks, which is a basis-dependent property of quantum states. In this paper, we discuss quantum incoherence based simultaneously on k bases using Matrix Theory Method. First, by defining a correlation function m (e , f) of two orthonormal bases e and f, we investigate the relationships between sets I (e) and I (f) of incoherent states with respect to e and f. We prove that I (e) = I (f) if and only if the rank-one projective measurements generated by e and f are identical. We give a necessary and sufficient condition for the intersection I (e) ⋂ I (f) to include a state except the maximally mixed state. Especially, if two bases e and f are mutually unbiased, then the intersection has only the maximally mixed state. Secondly, we introduce the concepts of strong incoherence and weak coherence of a quantum state with respect to a set B of k bases and propose a measure for the weak coherence. In the two-qubit system, we prove that there exists a maximally coherent state with respect to B when k = 2 and it is not the case for k = 3 . [ABSTRACT FROM AUTHOR]

Masking of quantum information means that information is hidden from a subsystem and spread over a composite system. Modi et al. proved in [Phys. Rev. Lett. 120, 230501 (2018)] that this is true for some restricted sets of nonorthogonal quantum states and it is not possible for arbitrary quantum states. In this paper, we discuss the problem of masking quantum information encoded in pure and mixed states, respectively. Based on an established necessary and sufficient condition for a set of pure states to be masked by an operator, we find that there exists a set of four states that can not be masked, which implies that to mask unknown pure states is impossible. We construct a masker S♯ and obtain its maximal maskable set, leading to an affirmative answer to a conjecture proposed in Modi's paper mentioned above. We also prove that an orthogonal (resp. linearly independent) subset of pure states can be masked by an isometry (resp. injection). Generalizing the case of pure states, we introduce the maskability of a set of mixed states and prove that a commuting subset of mixed states can be masked by an isometry S◇ while it is impossible to mask all of mixed states by any operator. We also find the maximal maskable sets of mixed states of the isometries S♯ and S◇, respectively. [ABSTRACT FROM AUTHOR]

Overlap between quantum states or observables is a fundamental quantity in quantum theory. Equioverlapping measurements arise naturally when considering quantum measurements with equal overlap between measurement operators. This is essentially a kind of symmetric configuration for quantum measurements. The conventional von Neumann measurements and symmetric informationally complete positive operator valued measures (SIC-POVMs) are two extreme cases of equioverlapping measurements. These measurements not only have intuitive physical significance, but also have rich and subtle mathematical structures. However, they remain largely unexplored. In this work, we investigate some general features of equioverlapping measurements with focus on qutrit systems (i.e., three dimensional systems), and partially classify equioverlapping measurements in this case. We further pose the challenge of complete classification and construction of equioverlapping measurements. • Some general features of equioverlapping measurements are revealed. • Equioverlapping measurements in qutrit systems are partially classified and explicitly constructed. • The challenge of complete classification and construction of equioverlapping measurements is proposed. [ABSTRACT FROM AUTHOR]

EPR steering is a kind of quantum correlation that is intermediate between entanglement and Bell nonlocality. In this paper, by recalling the definitions of unsteerability and steerability, some properties of them are given, e.g, it is proved that a local quantum channel transforms every unsteerable state into an unsteerable state. Second, a way of quantifying quantum steering, which we called the generalized steering robustness (GSR), is introduced and some interesting properties are established, including: (1) GSR of a state vanishes if and only if the state is unsteerable; (2) a local quantum channel does not increase GSR of any state; (3) GSR is invariant under each local unitary operation; (4) as a function on the state space, GSR is convex and lower-semi continuous. Lastly, by using the majorization between the reduced states of two pure states, GSR of the two pure states are compared, and it is proved that every maximally entangled state has the maximal GSR. [ABSTRACT FROM AUTHOR]

Maximally entangled states, defined as those states that have the maximal entanglement of formation under some entanglement measure, are the ideal resource for many quantum missions. In this paper, we call a convex roof of maximally entangled pure states a quasi maximally entangled state. First, we present the concept of a witness for non-quasi maximally entangled states, which is an observable that can distinguish some non-quasi maximally entangled states from quasi maximally entangled ones. Then we prove that every non-quasi maximally entangled state can be witnessed by a witness and obtain some necessary and sufficient conditions for an observable to be a witness for non-quasi maximally entangled states. Lastly, we give some classes of Hermitian operators, which can become witnesses. Especially, we compute non-quasi maximally entangled states that can be detected by a specific product operator. [ABSTRACT FROM AUTHOR]

In a bipartite quantum system, quantum states are classified as classically correlated (CC) and quantum correlated (QC) states, the later are important resources of quantum information and computation protocols. Since correlations of quantum states may vary under a quantum channel, it is necessary to explore the influence of quantum channels on correlations of quantum states. In this paper, we discuss CC-preserving, QC-breaking and strongly CC-preserving local quantum channels of the form $$\Phi _1\otimes \Phi _2$$ and obtain the structures of these three types of local quantum channels. Moreover, we obtain a necessary and sufficient condition for a quantum state to be transformed into a CC state by a specific local channel $$\Phi _1\otimes \Phi _2$$ in terms of the structure of the input quantum state. Lastly, as applications of the obtained results, we present a classification of local quantum channels $$\Phi _1\otimes \Phi _2$$ and describe the quantum states which are transformed as CC ones by the corresponding local quantum channel. [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]