Related papers: Generic properties for random repeated quantum ite…
Efficient methods for generating pseudo-randomly distributed unitary operators are needed for the practical application of Haar distributed random operators in quantum communication and noise estimation protocols. We develop a theoretical…
Let B_1,B_2, ... be independent one-dimensional Brownian motions defined over the whole real line such that B_i(0)=0. We consider the nth iterated Brownian motion W_n(t)= B_n(B_{n-1}(...(B_2(B_1(t)))...)). Although the sequences of…
In this document, some structured operator approximation theoretical methods for system identification of nearly eventually periodic systems, are presented. Let $\mathbb{C}^{n\times m}$ denote the algebra of $n\times m$ complex matrices.…
We present the exact diagonalization of the Schrodinger operator corresponding to a periodic potential with N deltas of different couplings, for arbitrary N. This basic structure can repeat itself an infinite number of times. Calculations…
We examine metrological scenarios where the parameter of interest is encoded onto a quantum state through the action of a noisy quantum gate and investigate the ultimate bound to precision by analyzing the behaviour of the Quantum Fisher…
Let $Q$ be a nonempty closed and convex subset of a real Hilbert space $% \mathcal{H}$. $T:Q\rightarrow Q$ is a nonexpansive mapping which has a least one fixed point. $f:Q\rightarrow \mathcal{H}$ is a Lipschitzian function, and $%…
Let $\ket{\0}$ and $\ket{\1}$ be two states that are promised to come from known subsets of orthogonal subspaces, but are otherwise unknown. Our paper probes the question of what can be achieved with respect to the basis…
We consider tilings $(\mathcal{Q},\Phi)$ of $\mathbb{R}^d$ where $\mathcal{Q}$ is the $d$-dimensional unit cube and the set of translations $\Phi$ is constrained to lie in a pre-determined lattice $A \mathbb{Z}^d$ in $\mathbb{R}^d$. We…
We consider recurrence to the initial state after repeated actions of a quantum channel. After each iteration a projective measurement is applied to check recurrence. The corresponding return time is known to be an integer for the special…
The characterization of a unitary gate is experimentally accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to reconstruct the underlying operator. The process matrix is typically…
Curious spectral properties of an ensemble of random unitary matrices appearing in the quantization of a map p -> p+alpha, q -> q+f(p+alpha) in [Giraud et al. nlin.CD/0403033] are investigated. When alpha=m/n with integer co-prime m,n and…
Iterates of quantum operations and their convergence are investigated in the context of mean ergodic theory. We discuss in detail the convergence of the iterates and show that the uniform ergodic theorem plays an essential role. Our results…
We study the quantum dynamics generated by the repeated action of a non-unitary evolution operator on a system of qubits. Breaking unitarity can lead to the purification of mixed initial states, which corresponds to the loss of sensitivity…
This paper gives a rigorous proof of a conjectured statistical self-similarity property of the eigenvalues random matrices from the Circular Unitary Ensemble. We consider on the one hand the eigenvalues of an $n \times n$ CUE matrix, and on…
We provide a generalization of the idea of unitary designs to cover finite averaging over much more general operations on quantum states. Namely, we construct finite averaging sets for averaging quantum states over arbitrary reductive Lie…
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
We study the scaling of the convergence of several statistical properties of a recently introduced random unitary circuit ensemble towards their limits given by the circular unitary ensemble (CUE). Our study includes the full distribution…
In conventional quantum mechanics the quantum particle is a special object, whose properties are described by special concepts and quantum principles. The quantization is a special procedure, which is accompanied by introduction of special…
The aim of this paper is to show a connection between an extended theory of statistical experiments on the one hand and the foundation of quantum theory on the other hand. The main aspects of this extension are: One assumes a hyperparameter…
We study how iterated and composed completely positive maps act on operator-valued kernels. Each kernel is realized inside a single Hilbert space where composition corresponds to applying bounded creation operators to feature vectors. This…