Related papers: Graphs States and the necessity of Euler Decomposi…
We present applications of the representation theory of Lie groups to the analysis of structure and local unitary classification of Werner states, sometimes called the {\em decoherence-free} states, which are states of $n$ quantum bits left…
A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…
We give a coalgebra structure on 1-vertex irreducible graphs which is that of a cocommutative coassociative graded connected coalgebra. We generalize the coproduct to the algebraic representation of graphs so as to express a bare 1-particle…
We investigate a graph-theoretic approach to the problem of distinguishing quantum product states in the fundamental quantum communication framework called local operations and classical communication (LOCC). We identify chordality as the…
An analog of Kreimer's coproduct from renormalization of Feynman integrals in quantum field theory, endows an analog of Kontsevich's graph complex with a dg-coalgebra structure. The graph complex is generated by orientation classes of…
Fathoming out quantum state space is a challenging endeavor due to its exponentially growing dimensionality. At the expense of being bound in its expressiveness, the discrete and finite subspace of graph states is easier to investigate via…
We investigate the properties of different levels of entanglement in graph states which correspond to connected graphs. Combining the operational definition of graph states and the postulates of entanglement measures, we prove that in…
We bring together in one place some of the main results and applications from our recent works in quantum information theory, in which we have brought techniques from operator theory, operator algebras, and graph theory for the first time…
In a recent paper [quant-ph/9910066], Arens and Varadarajan gave a characterization of what they call EPR-states on a bipartite composite quantum system. By definition, such states imply perfect correlation between suitable pairs of…
We attempt to reveal the geometry, emerged from the entanglement structure of any general $N$-party pure quantum many-body state by representing entanglement entropies corresponding to all $2^N $ bipartitions of the state by means of a…
Graph states are a unique resource for quantum information processing, such as measurement-based quantum computation. Here, we theoretically investigate using continuous-variable graph states for single-parameter quantum metrology,…
A set of necessary and sufficient conditions are derived for the equivalence of an arbitrary pure state and a graph state on n qubits under stochastic local operations and classical communication (SLOCC), using the stabilizer formalism.…
The Union Closed Sets Conjecture is one of the most renowned problems in combinatorics. Its appeal lies in the simplicity of its statement contrasted with the potential complexity of its resolution. The conjecture posits that, in any union…
The quantum mechanics is proved to admit no hidden-variable in 1960s, which means the quantum systems are contextual. Revealing the mathematical structure of quantum mechanics is a significant task. We develop the approach of partial…
Graph states are the backbone of measurement-based continuous-variable quantum computation. However, experimental realisations of these states induce Gaussian measurement statistics for the field quadratures, which poses a barrier to obtain…
Graph grammars extend the theory of formal languages in order to model distributed parallelism in theoretical computer science. We show here that to certain classes of context-free and context-sensitive graph grammars one can associate a…
A voltage graph is a finite directed graph whose edges are labeled by elements of a finite group $G$. A classical construction of Gross and Tucker associates to every voltage graph with vertex set $V$ a so-called derived graph with vertex…
We present an alternative approach to unveil a different kind of entanglement in bipartite quantum states whose diagonal zero patterns in suitable matrix representations admit a nice description in terms of triangle-free graphs. Upon…
Cluster states and graph states in general offer a useful model of the stabilizer formalism and a path toward the development of measurement-based quantum computation. Their defining structure - the stabilizer group - encodes all possible…
We establish a second anti-blocker theorem for non-commutative convex corners, show that the anti-blocking operation is continuous on bounded sets of convex corners, and define optimisation parameters for a given convex corner that…