We present new separability criteria for both bipartite and multipartite quantum states. These criteria include the criteria based on the correlation matrix and its generalized form as special cases. We show by detailed examples that our criteria are more powerful than the positive partial transposition criterion, the realignment criterion and the criteria based on the correlation matrices.
In this paper, we study entropic uncertainty relations on a
finite-dimensional Hilbert space and provide several tighter bounds for
multi-measurements, with some of them also valid for R\'{e}nyi and Tsallis
entropies besides the Shannon entropy. We employ majorization theory and
actions of the symmetric group to obtain an {\it admixture bound} for entropic
uncertainty relations for multi-measurements. Comparisons among all bounds for
multi-measurements are shown in figures in our favor.Comment: 7 page
Entanglement of formation for a class of higher dimensional quantum mixed states is studied in terms of a generalized formula of concurrence for N-dimensional quantum systems. As applications, the entanglement of formation for a class of 16 × 16 density matrices are calculated.Quantum entanglement plays important roles in quantum communication, information processing and quantum computing [1], such as in the investigation of quantum teleportation [2, 3, 4], dense coding [5], decoherence in quantum computers [1] and the evaluation of quantum cryptographic schemes [6]. To quantify entanglement, a well justified and mathematically tractable measure of entanglement is needed. A number of entanglement measures such as the entanglement of formation and distillation [7,8,9], negativity [10,11], and relative entropy [9,12] have been proposed for bipartite states [6,8,[12][13][14][15][16][17]. Nevertheless, most 1
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