Related papers: Random quantum channels I: graphical calculus and …
The adjacency matrix of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. Although the entries of the adjacency matrix are integers, its eigenvalues are generally irrational and, because of this, the…
A parametrized family of normal states on a von Neumann algebra is called a statistical experiment, which generalizes the corresponding concepts in classical statistics and finite-dimensional quantum systems. We introduce randomization…
In the first part of this thesis, we discuss the algebraic approach to classical and quantum physics and develop information theoretic concepts within this setup. In the second part, we discuss the uncertainty principle in quantum…
Inspired by "quantum graphity" models for spacetime, a statistical model of graphs is proposed to explore possible realizations of emergent manifolds. Graphs with given numbers of vertices and edges are considered, governed by a very…
We consider a pair of causally independent processes, modelled as the tensor product of two channels, acting on a possibly correlated input to produce random outputs X and Y. We show that, assuming the processes produce a sufficient amount…
We present an end-to-end and practical randomness amplification and privatisation protocol based on Bell tests. This allows the building of device-independent random number generators which output (near-)perfectly unbiased and private…
World-wide efforts aim at the realization of advanced quantum simulators and processors. However, despite the development of intricate hardware and pulse control systems, it may still not be generally known which effective quantum dynamics,…
Inspired by the ideas from the field of stochastic approximation, we propose a randomized algorithm to compute the capacity of a finite-state channel with a Markovian input. When the mutual information rate of the channel is concave with…
Random quantum circuits take an input quantum state and randomize it. This is a task with a growing number of identified uses in quantum information processing. We suggest a scheme to implement random circuits in a weighted graph state. The…
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…
Kemeny's constant quantifies the expected time for a random walk to reach a randomly chosen vertex, providing insight into the global behavior of a Markov chain. We present a novel eigenvector-based formula for computing Kemeny's constant.…
We describe analytical and numerical results on the statistical properties of complex eigenvalues and the corresponding non-orthogonal eigenvectors for non-Hermitian random matrices modeling one-channel quantum-chaotic scattering in systems…
Quantum hypothesis testing is a central task in the entire field of quantum information theory. Understanding its ultimate limits will give insight into a wide range of quantum protocols and applications, from sensing to communication.…
We explore the task of optimal quantum channel identification, and in particular the estimation of a general one parameter quantum process. We derive new characterizations of optimality and apply the results to several examples including…
The temporal evolution of a quantum system can be characterized by quantum process tomography, a complex task that consumes a number of physical resources scaling exponentially with the number of subsystems. An alternative approach to the…
Boundary conditions in quantum graph vertices are generally given in terms of a unitary matrix $U$. Observing that if $U$ has at most two eigenvalues, then the scattering matrix $\mathcal{S}(k)$ of the vertex is a linear combination of the…
We derive upper and lower bounds on the convergence behavior of certain classes of one-parameter quantum dynamical semigroups. The classes we consider consist of tensor product channels and of channels with commuting Liouvillians. We…
The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…
The introduction of quantum concepts is increasingly making its way into generative machine learning models. However, while there are various implementations of quantum Generative Adversarial Networks, the integration of quantum elements…
For any graph consisting of $k$ vertices and $m$ edges we construct an ensemble of random pure quantum states which describe a system composed of $2m$ subsystems. Each edge of the graph represents a bi-partite, maximally entangled state.…