Related papers: Double Dilation $\neq$ Double Mixing
We introduce a formulation of quantum theory (QT) as a general probabilistic theory but expressed via quasi-expectation operators (QEOs). This formulation provides a direct interpretation of density matrices as quasi-moment matrices. Using…
We define a product between quantum superoperators which is preserved under the Choi-Jamio{\l}kowski-Kraus-Sudarshan channel-state isomorphism. We then identify the product as the convolution on the space of superoperators, with respect to…
We study the effect of linear duality on action bialgebroids (also known as smash product or scalar extension bialgebroids) and, for those bearing a quantisation nature, the effect of Drinfeld functors underlying the quantum duality…
Modern applications in quantum computation and quantum communication require the precise characterization of quantum states and quantum channels. In practice, this means that one has to determine the quantum capacity of a physical system in…
We show that sampling or interpolation formulas in reproducing kernel Hilbert spaces can be obtained by reproducing kernels whose dual systems form molecules, ensuring that the size profile of a function is fully reflected by the size…
We are studying here the classical operator creating secondary polynomials associated with an orthogonal system for a continuous probability density function on a real interval. We know it is possible with the coupling of Stietjes…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…
Quantum Measure Theory (QMT) is a generalization of quantum theory where physical predictions are computed from a matrix known as \emph{decoherence functional} (DF). Previous works have noted that, in its original formulation, QMT exhibits…
A group of symmetric operators are introduced to carry out the separability criterion for bipartite and multipartite quantum states. Every symmetric operator, represented by a symmetric matrix with only two nonzero elements, and their…
We show how the separability problem is dual to that of decomposing any given matrix into a conic combination of rank-one partial isometries, thus offering a duality approach different to the positive maps characterization problem. Several…
Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation…
The DT-operators are introduced, one for every pair (\mu,c) consisting of a compactly supported Borel probability measure \mu on the complex plane and a constant c>0. These are operators on Hilbert space that are defined as limits in…
We present a general and natural framework to study the dynamics of composition operators on spaces of measurable functions, in which we then reconsider the characterizations for hypercyclic and mixing composition operators obtained by…
(1) Let $A$ be an operator on a space ${\cal H}$ of even finite dimension. Then for some decomposition ${\cal H}={\cal F}\oplus{\cal F}^{\perp}$, the compressions of $A$ onto ${\cal F}$ and ${\cal F}^{\perp}$ are unitarily equivalent. (2)…
Mixed distributions are considered as a results of application of a linear operator, which maps mixing measures to mixed measures. The main result is a proof of continuity of this mixing operator. Corollaries for parametric families of…
Considerable progress has been made in understanding how dissipation drives the state of a single qubit from a quantum-mechanical superposition to a classical mixed state. This paper uses a Bloch-Redfield approach to study how, in a system…
The need to retain the relative phases in quantum mechanics implies an addition law parametrized by a phase of two density operators required for the purification of a density matrix. This is shown with quantum tomography and the Wigner…
We reexamine basic aspects of a nonequilibrium steady state in the Kondo problem for a quantum dot under a bias voltage using a reduced density matrix, which is obtained in the Fock space by integrating out one of the two conduction…
When the $q$-deformed creation and annihilation operators are used in a second quantization procedure, the algebra satisfied by basis vectors (orthogonal complete set) should be also deformed such as a field operator remains invariant under…
A molecular dynamics simulation of the demixing process of a binary complex plasma is analysed and the role of distinct interaction potentials is discussed by using morphological Minkowski tensor analysis of the minority phase domain growth…