Related papers: On pure quasi quantum quadratic operators of M_2(C…
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 present paper we study description of Kadison-Schwarz type quantum quadratic operators acting from $\bm_2(\mathbb{C})$ into $\bm_2(\mathbb{C})\o\bm_2(\mathbb{C})$. Note that such kind of operator is a generalization of quantum…
We associate to every quantum channel $T$ acting on a Hilbert space $\mathcal{H}$ a pair of Hamiltonian operators over the symmetric subspace of $\mathcal{H}^{\otimes 2}$. The expectation values of these Hamiltonians over symmetric product…
Matrix quasi exactly solvable operators are considered and new conditions are determined to test whether a matrix differential operator possesses one or several finite dimensional invariant vector spaces. New examples of $2\times 2$-matrix…
We show that the approximate quasiorthogonality of two operator algebras is equivalent to the algebras being approximately private relative to their conditional expectation quantum channels. Our analysis is based on a characterization of…
This work presents a differentiable geometric parameterization of quantum channels in Kraus representation, which can be efficiently probed to find an unknown quantum channel. We explore its feasibility in finding the quasi inverse…
Quantum operations, or quantum channels cannot be inverted in general. An arbitrary state passing through a quantum channel looses its fidelity with the input. Given a quantum channel ${\cal E}$, we introduce the concept of its…
We study completely positive and trace-preserving equivariant maps between operators on irreducible representations of $\mathrm{SU}(2)$. We find asymptotic approximations of channels in the limit of large output representation and we…
We investigate the coherence of quantum channels using the Choi-Jamio\l{}kowski isomorphism. The relation between the coherence and the purity of the channel respects a duality relation. It characterizes the allowed values of coherence when…
A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze…
Conic quasi-linear maps are nonlinear operators from $C_0(X)$ to a normed linear space $E$ which preserve nonnegative linear combinations on positive cones generated by single functions; quasi-linear maps are linear on singly generated…
We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier…
Metaplectic operators form a relevant class of operators appearing in different applications, in the present work we study their Schwartz kernels. Namely, diagonality of a kernel is defined by imposing rapid off-diagonal decay conditions,…
In this work we examine quantum states which have non-negative amplitudes (in a fixed basis) and the channels which preserve them. These states include the ground states of stoquastic Hamiltonians and they are of interest since they avoid…
We introduce a class of quantum channels with correlations acting on pairs of qubits, where the correlation takes the form of a shift operator onto a maximally entangled state. We optimise the output purity and show that below a certain…
We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely…
We review the basic properties of effective actions of families of theories (i.e., the actions depending on additional non-perturbative moduli along with perturbative couplings), and their description in terms of operators (called…
This is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory. After a brief introduction, we discuss quantum algorithms. We outline basic properties of quantum…
Similarly to quantum states, quantum operations can also be transformed by means of quantum superchannels, also known as process matrices. Quantum superchannels with multiple slots are deterministic transformations whichtake independent…
In this paper we characterize $m$-isometric and quasi-$m$-isometric weighted conditional type (WCT) operators on the Hilbert space $L^2(\mu)$. Also, we prove that the subclasses of $m$-isometric and quasi-$m$-isometric of normal WCT…