Related papers: The operator sum-difference representation for qua…
It is by now well established that noise itself can be useful for performing quantum information processing tasks. We present results which show how one can effectively reduce the error rate associated with a noisy quantum channel, by…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…
Degradable quantum channels are among the only channels whose quantum and private classical capacities are known. As such, determining the structure of these channels is a pressing open question in quantum information theory. We give a…
In this paper we give a simple sequence of necessary and sufficient finite dimensional conditions for a positive map between certain subspaces of bounded linear operators on separable Hilbert spaces to be completely positive. These…
Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative…
We introduce the Gaussian quantum operator representation, using the most general multi-mode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose…
Non-Hermitian generalized eigenvalue problems (GEPs) play a significant role in many practical applications, such as mechanical engineering. Based on the generalized Schur decomposition, we propose a variational quantum algorithm for…
This thesis is concerning to the Differential Galois Theory point of view of the Supersymmetric Quantum Mechanics. The main object considered here is the non-relativistic stationary Schr\"odinger equation, specially the integrable cases in…
Methods for electronic structure based on Gaussian and molecular orbital discretizations offer a well established, compact representation that forms much of the foundation of correlated quantum chemistry calculations on both classical and…
We consider tunneling of spinless electrons from a single channel emitter into an empty collector through an interacting resonant level of the quantum dot (QD). When all Coulomb screening of sudden charge variations of the dot during the…
Large-scale variational quantum algorithms are widely recognized as a potential pathway to achieve practical quantum advantages. However, the presence of quantum noise might suppress and undermine these advantages, which blurs the…
We study the number of measurements required for quantum process tomography under prior information, such as a promise that the unknown channel is unitary. We introduce the notion of an interactive observable and we show that any unitary…
This paper deals with the partial solution of the energy eigenvalue problem for generalized symmetric quartic oscillators. Algebraization of the problem is achieved by expressing the Schroedinger operator in terms of the generators of a…
We study the protocol of qudit teleportation using quantum systems subjected to several kinds of noise for arbitrary dimensionality $d$. We consider four classes of noise: dit-flip, $d$-phase-flip, dit-phase-flip and depolarizing, each of…
We propose a new method in the spectral analysis of noisy time-series data for damped oscillators. From the Jacobi three terms recursive relation for the denominators of the Pad\'e Approximations built on the well-known Z-transform of an…
Gamow solutions are used to transform self-adjoint energy operators by means of factorization (supersymmetric) techniques. The transformed non-hermitian operators admit a discrete real spectrum which is occasionally extended by a single…
We prove new enclosures for the spectrum of non-selfadjoint operator matrices associated with second order linear differential equations $\ddot{z}(t) + D \dot{z} (t) + A_0 z(t) = 0$ in a Hilbert space. Our main tool is the quadratic…
Quantum operations are usually defined as completely positive (CP), trace preserving (TP) maps on quantum states, and can be represented by operator-sum or Kraus representations. In this paper, we calculate operator-sum representation and…
Quantum process tomography (QPT) plays a central role in characterizing quantum gates and circuits, diagnosing quantum devices, calibrating hardware, and supporting quantum error correction. However, conventional QPT methods face challenges…
The completely positive maps, a generalization of the nonnegative matrices, are a well-studied class of maps from $n\times n$ matrices to $m\times m$ matrices. The existence of the operator analogues of doubly stochastic scalings of…