Related papers: On errors generated by unitary dynamics of biparti…
We compute the independence number, zero-error capacity, and the values of the Lov\'asz function and the quantum Lov\'asz function for the quantum graph associated to the partial trace quantum channel…
We study bipartite unitary operators which stay invariant under the local actions of diagonal unitary and orthogonal groups. We investigate structural properties of these operators, arguing that the diagonal symmetry makes them suitable for…
In the model suggested by Smilansky one studies an operator describing the interaction between a quantum graph and a system of K one-dimensional oscillators attached at different points of the graph. This paper is a continuation of our…
We present protocols to generate arbitrary photonic graph states from quantum emitters that are in principle deterministic. We focus primarily on two-dimensional cluster states of arbitrary size due to their importance for measurement-based…
We consider a reducible unitary representation of Heisenberg-Weyl group in a tensor product of two Hilbert spaces. A non-commutative operator graph generated by this representation is introduced. It is shown that spectral projections of…
The symmetries of a finite graph are described by its automorphism group; in the setting of Woronowicz's quantum groups, a notion of a quantum automorphism group has been defined by Banica capturing the quantum symmetries of the graph. In…
A general tool for description of open quantum systems is given by the formalism of quantum operations. Most important of them are trace-preserving maps also known as quantum channels. We discuss those conditions on quantum channels under…
We propose in this note the study of quantum channels from association schemes. This is done by interpreting the $(0,1)$-matrices of a scheme as the Kraus operators of a channel. Working in the framework of one-shot zero-error information…
We consider the Schroedinger operator on graphs and study the spectral statistics of a unitary operator which represents the quantum evolution, or a quantum map on the graph. This operator is the quantum analogue of the classical evolution…
We derive an intuitive and novel method to represent nodes in a graph with special unitary operators, or quantum operators, which does not require parameter training and is competitive with classical methods on scoring similarity between…
We develop two approaches to Quantum (or Non-commutative) Graphs based on arbitrary von Neumann algebras $M\subseteq\mathcal B(H)$: one looking at operator bimodules of Hilbert--Schmidt (instead of bounded) operators, and the second looking…
Motivated by string diagrammatic approach to undirected tracial quantum graphs by Musto, Reutter, Verdon (2018), in the former part of this paper we diagrammatically formulate directed nontracial quantum graphs by Brannan, Chirvasitu,…
In this paper, we propose a new way to represent graphs in quantum space. In that approach, we replace the rows of the adjacency matrix of the graph by state vectors in the occupation number representation. Unlike the traditional definition…
We propose a scheme to distribute graph states over quantum networks in the presence of noise in the channels and in the operations. The protocol can be implemented efficiently for large graph sates of arbitrary (complex) topology. We…
Quantum counting is a key quantum algorithm that aims to determine the number of marked elements in a database. This algorithm is based on the quantum phase estimation algorithm and uses the evolution operator of Grover's algorithm because…
We define several new types of quantum chromatic numbers of a graph and characterise them in terms of operator system tensor products. We establish inequalities between these chromatic numbers and other parameters of graphs studied in the…
We derive a set of coupled non-linear algebraic equations for the asymptotics of the Poisson kernel distribution describing the statistical properties of a two-terminal double-barrier chaotic billiard (or ballistic quantum dot). The…
We introduce a Sinkhorn-type algorithm for producing quantum permutation matrices encoding symmetries of graphs. Our algorithm generates square matrices whose entries are orthogonal projections onto one-dimensional subspaces satisfying a…
Measurement incompatibility is one of the cornerstones of quantum theory. This phenomenon appears in many forms, of which the concept of non-joint measurability has received considerable attention in the recent years. In order to…
We investigate unitary operators acting on a tensor product space, with the property that the quantum channels they generate, via the Stinespring dilation theorem, are of a particular type, independently of the state of the ancilla system…