The process of entanglement swapping showed that suitable measurements can generate nonlocal correlations even from particles that never interacted directly. This fact was generalized to the concept of bilocality for a quantum network, where there are three observers sharing two independent sources. Since then, the nonlocality nature was explored in various quantum networks. In this work, we consider the nonlocality of $(2^n-1)$-partite tree-tensor networks, which are widely used in quantum communications. We derive the Bell-type inequalities which are respectively satisfied by all $(2^n-2)$-local correlations and all local correlations, and demonstrate the maximal quantum violations of these inequalities and the robustness to noise in these tree networks.

Coherence manipulation is fundamental in the study of the resource theory of quantum coherence. It is aimed at identifying when it is possible to convert a given coherent state to another using only incoherent operations. In this paper, it is shown that a finite number of measure conditions are not sufficient to characterize coherence manipulation on general mixed states. Further, a finite number of measure conditions to classify coherence manipulation on subspace-independent states are found. For the input pure state, we also furnish a structural characterization of coherence manipulation in terms of a finite number of measure conditions.

In this paper, we present a characterization of optimal entanglement witnesses in terms of positive maps and then provide a general method of checking optimality of entanglement witnesses. Applying it, we obtain indecomposable optimal witnesses that have no spanning property. These also provide examples that support a recent conjecture saying that the so-called structural physical approximations to optimal positive maps (optimal entanglement witnesses) give entanglement breaking maps (separable states).

It is shown that every entangled state in an infinite-dimensional composite system has a simple entanglement witness of the form $\alpha${}I+T with $\alpha${} a non-negative number and T a finite rank self-adjoint operator. We also provide two methods of constructing an entanglement witness and apply them to obtain some entangled states that cannot be detected by the positive partial transpose criterion and the realignment criterion.

Let 𝒜 be a unital prime ring containing a nontrivial idempotent P. Assume that Φ: 𝒜 → 𝒜 is a nonlinear surjective map. It is shown that Φ preserves strong commutativity if and only if Φ has the form Φ(A) = αA + f(A) for all A ∈ 𝒜, where α ∈ {1, −1} and f is a map from 𝒜 into 𝒵(𝒜). As an application, a characterization of nonlinear surjective strong commutativity preserving maps on factor von Neumann algebras is obtained.