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Observational entropy is a generalization of Boltzmann entropy to quantum mechanics. Observational entropy based on coarse-grained measurements has a certain relations with other quantum information measures. We study the relations between observational entropy and Rényi information measures and give some examples to explain the rationality of these relations. [ABSTRACT FROM AUTHOR]

We study the genuine tripartite nonlocality of some qubit states in a triple JCM. In this model, each atom state (A, B or C) was initially prepared with an independent cavity (a, b or c). By using two kinds of GHZ-like states as the atomic initial states, we investigate the genuine tripartite nonlocality as the time evolutions for the non-interaction three-qubit subsystems. We also study the genuine tripartite nonlocality of the subsystems by using the Svetlichny inequality. For the subsystems of three atoms ABC and three cavity modes abc, we show that they are genuinely nonlocal at certain period intervals of time. The states of all the other inequivalent subsystems satisfy the Svetlichny inequality for two types of GHZ-like states. [ABSTRACT FROM AUTHOR]

In this paper, we consider the violation of Bell inequalities for quantum system $$\mathbb {C}^K\otimes \mathbb {C}^K$$ (integer $$K\ge 2$$ ) with group theoretical method. For general M possible measurements, and each measurement with K outcomes, the Bell inequalities based on the choice of two orbits are derived. When the observables are much enough, the quantum bounds are only dependent on M and approximate to the classical bounds. Moreover, the corresponding nonlocal games with two different scenarios are analyzed. [ABSTRACT FROM AUTHOR]

We study the concurrence of arbitrary dimensional multipartite quantum systems. An explicit analytical lower bound of concurrence for four-partite mixed states is obtained in terms of the concurrences of tripartite mixed states. Detailed examples are given to show that our lower bounds improve the existing lower bounds of concurrence. The approach is generalized to five-partite quantum systems. [ABSTRACT FROM AUTHOR]

We study the perfectly local indistinguishability of multipartite product states. Firstly, we follow the method of Zhang et al. (Phys Rev A 93:012314, 2016) to give another more concise set of $$2n-1$$ orthogonal product states in $${\mathbb {C}}^m\otimes {\mathbb {C}}^n$$ $$(4\le m\le n)$$ which can not be distinguished by local operations and classical communication. Then we use the three-dimensional cubes to present some product states which give us an intuitive view on how to construct locally indistinguishable product states in tripartite quantum systems. At last, we give an explicit construction of locally indistinguishable orthogonal product states for general multipartite systems. [ABSTRACT FROM AUTHOR]