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Graph-theoretic approach to quantum correlations.
This work shows that, for any graph, there is always a correlation experiment such that the set of quantum probabilities is exactly the Grötschel-Lovász-Schrijver theta body, and provides a method for singling out experiments with quantum correlations on demand.
The Laplacian of a Graph as a Density Matrix: A Basic Combinatorial Approach to Separability of Mixed States
Abstract.We study entanglement properties of mixed density matrices obtained from combinatorial Laplacians. This is done by introducing the notion of the density matrix of a graph. We characterize
On the Quantum Chromatic Number of a Graph
We investigate the notion of quantum chromatic number of a graph, which is the minimal number of colours necessary in a protocol in which two separated provers can convince a referee that they have a
(Non-)Contextuality of Physical Theories as an Axiom
We show that the noncontextual inequality proposed by Klyachko et al. [Phys. Rev. Lett. 101, 020403 (2008)] belongs to a broader family of inequalities, one associated to each compatibility structure
A Matrix Representation of Graphs and its Spectrum as a Graph Invariant
This work uses the line digraph construction to associate an orthogonal matrix with each graph and shows by computation that the isomorphism classes of many known families of strongly regular graphs are characterized by the spectrum of this matrix.
Hierarchical quantum classifiers
It is shown how quantum algorithms based on two tensor network structures can be used to classify both classical and quantum data and may enable classification of two-dimensional images and entangled quantum data more efficiently than is possible with classical methods.
Parameters of Integral Circulant Graphs and Periodic Quantum Dynamics
The means for simultaneous scouring of metal surfaces contains a waste product in manufacture of fodder yeast, citric acid, ammonium citrate, aqueous solution of sodium gluconate, sulphonated ricinic
Zero-Error Communication via Quantum Channels, Noncommutative Graphs, and a Quantum Lovász Number
A quantum version of Lovász' famous ϑ function on general operator systems is defined, as the norm-completion of a “naive” generalization of ϑ, in terms of which the zero-error capacity of a quantum channel, as well as the quantum and entanglement-assisted zero- error capacities can be formulated.
The von Neumann Entropy of Networks
When the set of vertices is asymptotically large, it is proved that regular graphs and the complete graph have equal entropy and specifically it turns out to be maximum.
Number-theoretic nature of communication in quantum spin systems.
This work determines the exact number of qubits in unmodulated chains (with an XY Hamiltonian) that permit transfer with a fidelity arbitrarily close to 1, a phenomenon called pretty good state transfer and highlights the potential of quantum spin system dynamics for reinterpreting questions about the arithmetic structure of integers and primality.