Related papers: The traces of quantum powers commute

Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…

As time passes, once simple quantum states tend to become more complex. For strongly coupled k-local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive and universal pattern. In this paper we…

I argue that the leading quantum corrections, in powers of the energy or inverse powers of the distance, may be computed in quantum gravity through knowledge of only the low energy structure of the theory. As an example, I calculate the…

We describe an approach to the quantization of (2+1)--dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q--commutation relation. Solutions of diagonal and…

A continuous-time quantum walk is investigated on complex networks with the characteristic property of community structure, which is shared by most real-world networks. Motivated by the prospect of viable quantum networks, I focus on the…

In this survey article we give basic introduction to the theory of quantum families of maps. We begin with a general look at non-commutative (or "quantum") topology. Then we formulate all our results in this language. Existence of quantum…

A basic linearity of quantum dynamics, that density matrices are mapped linearly to density matrices, is proved very simply for a system that does not interact with anything else. It is assumed that at each time the physical quantities and…

Quantum walks can reconstruct quantum algorithms for quantum computation, where the precise controls of quantum state transfers between arbitrary distant sites are required. Here, we investigate quantum walks using a periodically…

Consider two agents, Alice and Bob, each of whom takes a quantum input, operates on a shared quantum system $K$, and produces a quantum output. Alice and Bob's operations may commute, in the sense that the joint input-output behaviour is…

We study the transition matrix of a quantum walk on strongly regular graphs. It is proposed by Emms, Hancock, Severini and Wilson in 2006, that the spectrum of $S^+(U^3)$, a matrix based on the amplitudes of walks in the quantum walk,…

Recently, the quaternionic quantum walk was formulated by the first author as a generalization of discrete-time quantum walks. We treat the right eigenvalue problem of quaternionic matrices to analysis the spectra of its transition matrix.…

We explicitly construct an Archimedean order unit space whose state space is affinely isomorphic to the set of quantum commuting correlations. Our construction only requires fundamental techniques from the theory of order unit spaces and…

We study, from a combinatorial viewpoint, the quantized coordinate ring of mxn matrices over an infinite field K (also called quantum matrices) and its torus-invariant prime ideals. The first part of this paper shows that this algebra,…

We present evidence that anomalous transport in the classical standard map results in strong enhancement of fluctuations in the localization length of quasienergy states in the corresponding quantum dynamics. This generic effect occurs even…

Experimental studies of infinite (unrestricted at least in one direction) quantum particle motion using probe nanotechnologies have revealed the necessity of revising previous concepts of their motion. Particularly, quantum particles…

We set the ground for a theory of quantum walks on graphs- the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible.…

Using the analytic assembly map that appears in the Baum-Connes conjecture in noncommutative geometry, we generalise the $\Spin^c$-version of the Guillemin-Sternberg conjecture that `quantisation commutes with reduction' to (discrete series…

A new approach to quantum mechanics based on independence of the Continuum Hypothesis is proposed. In one-dimensional case, it is shown that the properties of the set of intermediate cardinality coincide with quantum phenomenology.

Quantum walks have been shown to be fruitful tools in analysing the dynamic properties of quantum systems. This article proposes to use quantum walks as an approach to Quantum Neural Networks (QNNs). QNNs replace binary McCulloch-Pitts…

A general density-matrix formulation of quantum-transport phenomena in semiconductor nanostructures is presented. More specifically, contrary to the conventional single-particle correlation expansion, we shall investigate separately the…