Related papers: Bipartite matrix-valued tensor product correlation…
Quantum computation is based on tensor products and entangled states. We discuss an alternative to the quantum framework where tensor products are replaced by geometric products and entangled states by multivectors. The resulting theory is…
In this paper, we study the tensor product of two unitary irreducible representations, as well as the tensor product of a unitary irreducible representation with a finite-dimensional one, and determine the corresponding Clebsch-Gordan…
Multipartite quantum correlation (MQC) not only explains many novel microscopic and macroscopic quantum phenomena, but also holds promise for specific quantum technologies with superiorities. MQCs descriptions and measures have been an open…
We consider integrable category $\mathcal{O}$ representations of Borcherds--Kac--Moody algebras whose Cartan matrix is finite dimensional, and determine the necessary and sufficient conditions for which the tensor product of irreducible…
We study finite-dimensional representations of quantum affine algebras using q-characters. We prove the conjectures from math.QA/9810055 and derive some of their corollaries. In particular, we prove that the tensor product of fundamental…
We study irreducible unitary \reps of $U_q(SO(2,1))$ and $U_q(SO(2,3))$ for $q$ a root of unity, which are finite dimensional. Among others, unitary \reps corresponding to all classical one-particle representations with integral weights are…
We present two sets of computable entanglement measures for multipartite systems where each subsystem can have different degrees of freedom (so-called qudits). One set, called 'separability' measure, reveals which of the subsystems are…
Quantum data processing inequality bounds the set of bipartite states that can be generated by two far apart parties under local operations; Having access to a bipartite state as a resource, two parties cannot locally transform it to…
Quantum entanglement serves as a fundamental resource in quantum information theory. This paper presents a comprehensive framework of separability criteria for detecting bipartite and multipartite entanglements. We construct a novel…
We introduce a complete set of complementary quantities in bipartite, two-dimensional systems. Complementarity then relates the quantitative entanglement measure concurrence which is a bipartite property to the single-particle quantum…
In this paper we consider four basic multidimensional matrix operations (outer product, Kronecker product, contraction, and projection) and two derivative operations (dot and circle products). We start with the interrelations between these…
We examine bipartite and multipartite correlations within the construct of unitary orbits. We show that the set of product states is a very small subset of set of all possible states, while all unitary orbits contain classically correlated…
We study representations of $U_q(su(1,1))$ that can be considered as quantum analogs of tensor products of irreducible *-representations of the Lie algebra $su(1,1)$. We determine the decomposition of these representations into irreducible…
Entanglement is a uniquely quantum resource giving rise to many quantum technologies. It is therefore important to detect and characterize entangled states, but this is known to be a challenging task, especially for multipartite mixed…
Correlation matrices (positive semidefinite matrices with ones on the diagonal) are of fundamental interest in quantum information theory. In this work we introduce and study the set of $r$-decomposable correlation matrices: those that can…
We study the tensor product decomposition of the split real quantum group $U_{q\tilde{q}}(sl(2,R))$ from the perspective of finite dimensional representation theory of compact quantum groups. It is known that the class of positive…
We decompose the tensor product of two irreducible representations of $\mathrm{GL}_2(\mathbb{F}_q)$ for odd $q$ and classify the pairs such that their tensor product is multiplicity free. We also classify the pairs such that their tensor…
There is a commonly recognized paradigm in which a multipartite quantum system described by a density matrix having no product eigenbasis is considered to possess nonclassical correlation. Supporting this paradigm, we define two entropic…
We characterize pairs (Q,d) consisting of a quiver Q and a dimension vector d, such that over a given algebraically closed field k there are infinitely many representations of Q of dimension vector d. We also present an application of this…
We investigate relations between computational power and correlation in resource states for quantum computational tensor network, which is a general framework for measurement-based quantum computation. We find that if the size of resource…