Based on the mutually unbiased bases, the mutually unbiased measurements and
the general symmetric informationally complete positive-operator-valued
measures, we propose three separability criteria for $d$-dimensional bipartite
quantum systems, which are more powerful than the corresponding ones introduced
in [C. Spengler, M. Huber, S. Brierley, T. Adaktylos, and B.C. Hiesmayr, Phys.
Rev. A \textbf{86}, 022311 (2012); B. Chen, T. Ma, and S.M. Fei, Phys. Rev. A
\textbf{89}, 064302 (2014); B. Chen, T. Li, and S.M. Fei, arXiv:1406.7820v1
[quant-ph] (2014)]. Some states such as Werner states and Bell-diagonal states
are used to further illustrate the efficiency of the presented criteria
It is a challenging task to detect genuine multipartite nolocality (GMNL). In this paper, the problem is considered via computing the maximal quantum value of Svetlichny operators for threequbit systems and a tight upper bound is obtained. The constraints on the quantum states for the tightness of the bound are also presented. The approach enables us to give the necessary and sufficient conditions of violating the Svetlichny inequalities (SI) for several quantum states, including the white and color noised GHZ states. The relation between the genuine multipartite entanglement concurrence and the maximal quantum value of the Svetlichny operators for mixed GHZ class states is also discussed. As the SI is useful for the investigation on GMNL, our resultsgive an effective and operational method to detect the GMNL for three-qubit mixed states.
The resource theoretic measure of quantum coherence is basis dependent, and
the amount of coherence contained in a state is different in different bases.
We obtained analytical solutions for the maximum coherence by optimizing the
reference basis and highlighted the essential role of the mutually unbiased
bases (MUBs) on attaining the maximum coherence. Apart from the relative
entropy of coherence, we showed that the MUBs are optimal for the robustness of
coherence, the coherence weight, and the modified skew information measure of
coherence for any state. Moreover, the MUBs are optimal for all the faithful
coherence measures if the state is pure or is of the single qubit. We also
highlighted an upper bound for the $l_1$ norm of coherence and compared it with
the other bounds as well as the maximum one attainable by optimizing the
reference basis.Comment: 7 pages, 2 figure
It is a computationally hard task to certify genuine multipartite entanglement (GME). We investigate the relation between the norms of the correlation vectors and the detection of GME for tripartite quantum systems. A sufficient condition for GME and an effective lower bound for the GME concurrence are derived. Several examples are considered to show the effectiveness of the criterion and the lower bound of GME concurrence.
We investigate the norms of the Bloch vectors for any quantum state with subsystems less than or equal to four. Tight upper bounds of the norms are obtained, which can be used to derive tight upper bounds for entanglement measure defined by the norms of Bloch vectors. By using these bounds a trade-off relation of the norms of Bloch vectors is discussed. Theses upper bounds are then applied on separability. Necessary conditions are presented for different kinds of separable states in four-partite quantum systems. We further present a complete classification of quantum states for four qudits quantum systems.
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