منابع مشابه
Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
We report new results and generalizations of our work on unextendible product bases (UPB), uncompletable product bases and bound entanglement. We present a new construction for bound entangled states based on product bases which are only completable in a locally extended Hilbert space. We introduce a very useful representation of a product basis, an orthogonality graph. Using this representatio...
متن کاملUnextendible Product Bases
Let C denote the complex field. A vector v in the tensor product ⊗i=1C is called a pure product vector if it is a vector of the form v1 ⊗ v2 · · · ⊗ vm, with vi ∈ Ci . A set F of pure product vectors is called an unextendible product basis if F consists of orthogonal nonzero vectors, and there is no nonzero pure product vector in ⊗i=1C which is orthogonal to all members of F . The construction ...
متن کاملOrthonormal bases for product measures
Let B be the Borel σ-algebra of R, and let B be the Borel σ-algebra of [−∞,∞] = R ∪ {−∞,∞}: the elements of B are those subsets of R of the form B,B ∪ {−∞}, B ∪ {∞}, B ∪ {−∞,∞}, with B ∈ B. Let (X,A , μ) be a measure space. It is a fact that if fn is a sequence of A → B measurable functions then supn fn and infn fn are A → B measurable, and thus if fn is a sequence of A → B measurable functions...
متن کاملDistinguishability of complete and unextendible product bases
It is not always possible to distinguish multipartite orthogonal states if only local operation and classical communication (LOCC) are allowed. We prove that we cannot distinguish the states of an unextendible product bases (UPB) by LOCC even when infinite resources (infinite-dimensional ancillas, infinite number of operations). Moreover we give a method to check the LOCC distinguishability of ...
متن کاملMinimum cycle bases of product graphs
A construction for a minimal cycle basis for the Cartesian and the strong product of two graphs from the minimal length cycle bases of the factors is presented. Furthermore, we derive asymptotic expressions for the average length of the cycles in the minimal cycle bases of the powers (iterated products) of graphs. In the limit only triangles and squares play a role.
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1982
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1982.99.105