Related papers: The operator sum-difference representation for qua…
There are several important abstract operator systems with the convex cone of positive semidefinite matrices at the first level. Well-known are the operator systems of separable matrices, of positive semidefinite matrices, and of block…
A generalization of the representation underlying the discrete spatial geometry of Loop Quantum Gravity, to accomodate states labelled by smooth spatial geometries, was discovered by Koslowski and further studied by Sahlmann. We show how to…
Quantum error correction (QEC) is essential for reliable quantum information processing. Targeting a particular error channel, both the encoding and the recovery channel can be optimized through a biconvex optimization to give a…
This study delves into the efficacy of the Petz recovery map within the context of two paradigmatic quantum channels: dephasing and amplitude-damping. While prior investigations have predominantly focused on qubits, our research extends…
In this paper we introduce EPOSIC channels, a class of SU(2)-covariant quantum channels. We give their definition, a Kraus representation of them, and compute their Choi matrices. We show that these channels form the set of extreme points…
Electrical engineers and physicists are naturally very interested in noise in circuits, amplifiers and detectors. With the advent of quantum computation and other high frequency electronics operating at low temperatures, we have entered a…
How many black-box queries to a quantum channel are needed to learn its full classical description? This question lies at the heart of quantum channel tomography (also known as quantum process tomography), a fundamental task in the…
The volume operator plays a central role in both the kinematics and dynamics of canonical approaches to quantum gravity which are based on algebras of generalized Wilson loops. We introduce a method for simplifying its spectral analysis,…
We introduce a Hartmann system in the generalized Taub-NUT space with Abelian monopole interaction. This quantum system includes well known Kaluza-Klein monopole and MIC-Zwanziger monopole as special cases. It is shown that the…
Solving differential equations is one of the most promising applications of quantum computing. Recently we proposed an efficient quantum algorithm for solving one-dimensional Poisson equation avoiding the need to perform quantum arithmetic…
We study the quantum channel version of Shannon's zero-error capacity problem. Motivated by recent progress on this question, we propose to consider a certain operator space as the quantum generalisation of the adjacency matrix, in terms of…
We investigate the properties of the zeros of the eigenfunctions on quantum graphs (metric graphs with a Schr\"odinger-type differential operator). Using tools such as scattering approach and eigenvalue interlacing inequalities we derive…
Based on our recently developed quantum transport theory in term of an exact master equation, the corresponding particle-number resolved ($n$-resolved) master equation and the related shot noise spectrum formalism covering the full…
Analytical expressions for spectrum, eigenfunctions and dipole matrix elements of a square double quantum well (DQW) are presented for a general case when the potential in different regions of the DQW has different heights and effective…
The lowest eigenvalue of non-commutative harmonic oscillators $Q$ is studied. It is shown that $Q$ can be decomposed into four self-adjoint operators, and all the eigenvalues of each operator are simple. We show that the lowest eigenvalue…
We derive an intuitive and novel method to represent nodes in a graph with special unitary operators, or quantum operators, which does not require parameter training and is competitive with classical methods on scoring similarity between…
We have developed a non-unitary extension of Grover's search algorithm by changing the hidden geometry of Hilbert space carried by diffusion operator. Our algorithm finds the solution for search problem by performing a unique bigger…
In this note, we present the formalism to start a quantum analysis for the recent billiard representation introduced by Damour, Henneaux and Nicolai in the study of the cosmological singularity. In particular we use the theory of Maass…
We introduce map-dependent quantum characteristic functions constructed from the normalized Choi operator of quantum dynamical maps. We prove a Bochner--Choi positivity theorem establishing that the positive-type condition of the associated…
Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…