Related papers: Tensor products and relation quantales

For L a finite lattice, let C(L) denote the set of pairs g = (g_0,g_1) such that g_0 is a lower cover of g_1 and order it as follows: g <= d iff g_0 <= d_0, g_1 <= d_1, but not g_1 <= d_0. Let C(L,g) denote the connected component of g in…

We apply the homomorphism complex construction to partially ordered sets, introducing a new topological construction based on the set of maximal chains in a graded poset. Our primary objects of study are distributive lattices, with special…

Entanglement is a well known fundamental resource in quantum information. Here the following question is addressed : which are the deeper roots of entanglement that may help in its better understanding and use ? The answer is that one can…

Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\tau_i:X \to X$ for $1 \le i \le n$. To this we associate two topological conjugacy algebras which emerge as the natural candidates for the universal algebra…

We consider the matrix-valued generalizations of bipartite tensor product quantum correlations and bipartite infinite-dimensional tensor product quantum correlations, respectively. These sets are denoted by $C_q^{(n)}(m,k)$ and…

We introduce a tensor product for symmetric monoidal categories with the following properties. Let SMC denote the 2-category with objects small symmetric monoidal categories, arrows symmetric monoidal functors and 2-cells monoidal natural…

We introduce both the notions of tensor product of convex bodies that contain zero in the interior, and of tensor product of $0$-symmetric convex bodies in Euclidean spaces. We prove that there is a bijection between tensor products of…

One of the longstanding problems in universal algebra is the question of which finite lattices are isomorphic to the congruence lattices of finite algebras. This question can be phrased as which finite lattices can be represented as…

We classify all continuous tensor product systems of Hilbert spaces which are ``infinitely divisible" in the sense that they have an associated logarithmic structure. These results are applied to the theory of E_0 semigroups to deduce that…

An ordered semiring is a commutative semiring equipped with a compatible preorder. Ordered semirings generalise both distributive lattices and commutative rings, and provide a convenient framework to unify certain aspects of lattice theory…

In this semi-expository paper, we first explain key notions from current quantum information theory and criteria for them in a coherent way. These include separability/entanglement, Schmidt numbers of bi-partite states and block-positivity,…

A genuine infinite tensor product of complex vector spaces is a vector space ${\bigotimes}_{i\in I} X_i$ whose linear maps coincide with multilinear maps on an infinite family $\{X_i\}_{i\in I}$ of vector spaces. We give a direct sum…

The main result of this paper is a bi-parameter T(b) theorem for the case that b is a tensor product of two pseudo-accretive functions. In the proof, we also discuss the L^2 boundedness of different types of the b-adapted bi-parameter…

Let g be a simple simply laced Lie algebra. In this paper two families of varieties associated to the Dynkin graph of g are described: ``tensor product'' and ``multiplicity'' varieties. These varieties are closely related to Nakajima's…

A proto-quantum space is a (general) matricially normed space in the sense of Effros and Ruan presented in a `matrix-free' language. We show that these spaces have a special (projective) tensor product possessing the universal property with…

A separable quantum state shared between parties $A$ and $B$ can be symmetrically extended to a quantum state shared between party $A$ and parties $B_1,\ldots ,B_k$ for every $k\in\mathbf{N}$. Quantum states that are not separable, i.e.,…

We define a quasimodule Q over a bounded lattice L in an analogous way as a module over a semiring is defined. The essential difference is that L need not be distributive. Also for quasimodules there can be introduced the concepts of inner…

To define a minimal mathematical framework for isolating some of the characteristic properties of quantum entanglement, we introduce a generalization of the tensor product of graphs. Inspired by the notion of a density matrix, the…

The starting point of this work is that the class of evolution algebras over a fixed field is closed under tensor product. This arises questions about the inheritance of properties from the tensor product to the factors and conversely. For…

We show that the pretensor and tensor products of simplicial sets with marking are compatible with the homotopy theory of saturated $N$-complicial sets (which are a proposed model of $(\infty,N)$-categories), in the form of a Quillen…