Related papers: The operator sum-difference representation for qua…
In this paper we study diagonal quantum channels and their structure by proving some results and giving most applicable instances of them. Firstly, it is shown that action of every diagonal quantum channel on pure state from computational…
We use Deutsch's algorithm as a stand in for more complex quantum algorithms in order to determine how quantum properties of an environment manifest themselves in results that can be obtained on quantum computers. We model pure dephasing in…
Multivariate quantum signal processing (M-QSP) has recently been shown to be applicable for non-Hermitian Hamiltonian simulation, opening several problems regarding the optimization landscape, angle-finding, and constant-factor analysis. We…
In this paper we present a quantum algorithm that uses noise as a resource. The goal of our quantum algorithm is the calculation of operator averages of an open quantum system evolving in time. Selected low-noise system qubits and noisy…
The mathematical framework of quantum theory, though fundamentally distinct from classical physics, raises the question of whether quantum processes can be efficiently simulated using classical resources. For instance, a sender (Alice)…
For decoherence processes induced by weak interactions with the environment, a general quantum channel with one noise parameter has been formulated. This channel is called low-noise channel and very useful for investigating the parameter…
In the present paper we study nonlinear dynamics of quantum quadratic operators (q.q.o) acting on the algebra of $2\times 2$ matrices $\bm_2(\bc)$. First, we describe q.q.o. with Haar state as well as quadratic operators with the…
In the literature, the study of electron transport in quantum devices is mainly devoted to DC properties. The fluctuations of the electrical current around these DC values, the so-called quantum noise, are much less analyzed. The…
We study many-qubit generalizations of quantum noise channels that can be written as an incoherent sum of translations in phase space. Physical description in terms of the spectral properties of the superoperator and the action in phase…
Noise is usually regarded as the main obstacle to achieving a scalable quantum advantage, but recent evidence in quantum reservoir computing [L. Domingo, F. Borondo, and G. G. Carlo. Taking advantage of noise in quantum reservoir computing,…
We introduce and systematically develop the theory of \emph{quantum doubly stochastic operators}, i.e. positive, trace-preserving maps on non-commutative $L_p$-spaces associated to semifinite von Neumann algebras. After establishing basic…
In this work we propose a simple optical architecture, based on phase-only programmable spatial light modulators, in order to characterize general processes on photonic spatial quantum systems in a $d>2$ Hilbert space. We demonstrate the…
We study the estimation of an unknown quantum channel $\mathcal{E}$ with input dimension $d_1$, output dimension $d_2$ and Kraus rank at most $r$. We establish a connection between the query complexities in two models: (i) access to…
The problem of reconstructing a quantum channel from a sample of classical data is considered. When the total fidelity can be represented as a ratio of two quadratic forms (e.g., in the case of mapping a mixed state to a pure state,…
We introduce a framework that allows for the exact analytic treatment of quantum dynamics subject to coherent noise. The noise is modeled via unitary evolution under a Hamiltonian drawn from a random-matrix ensemble for arbitrary…
We define a class of pseudo-differential operators in a completely new way, which is called the abstract operators and expounded systematically the theory of abstract operators. By combining abstract operators with the Laplace transform, we…
We introduce a method to construct non-Markovian variants of completely positive (CP) dynamical maps, particularly, qubit Pauli channels. We identify non-Markovianity with the breakdown in CP-divisibility of the map, i.e., appearance of a…
We address the question of the existence of quantum channels that are divisible in two quantum channels but not in three or, more generally, channels divisible in $n$ but not in $n+1$ parts. We show that for the qubit those channels…
It is shown that many dissipative phenomena of "old" quantum mechanics which appeared 100 years ago in the form of the statistics of quantum thermal noise and quantum spontaneous jumps, have never been explained by the "new" conservative…
The Difference-of-Gaussian (DoG) is a widely used operator across applications, including image processing (feature and edge detection), quantum machine learning, and finite-difference methods (approximations of the Laplacian-of-Gaussian).…