相关论文: Quantum Channels and Representation Theory
Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of…
We study an analogous Bloch sphere representation of higher-level quantum systems using the Heisenberg-Weyl operator basis. We introduce a parametrization method that will allow us to identify a real-valued Bloch vector for an arbitrary…
We derive exact analytical expressions for the quantum capacity of a broad subclasses of generalized dephasing channels of the form $\Lambda(\rho)=(1-x)\rho + x D(\rho)$, where $D(\rho)$ represents a structured decoherence process. These…
Representative wave functions, which encode the topological properties of the spin polarized fractional quantum Hall states in the lowest Landau level, can be expressed in terms of correlation functions in conformal field theories. Until…
Quantum channels describe the most general dynamics of open quantum systems. A quantum channel, as a linear map on vectorized quantum states, can be represented by a single matrix, whose spectrum is called the channel spectrum. Here we…
An arbitrarily dense discretisation of the Bloch sphere of complex Hilbert states is constructed, where points correspond to bit strings of fixed finite length. Number-theoretic properties of trigonometric functions (not part of the…
It is proved that every doubly stochastic quantum channel that is properly averaged with the completely depolarizing channel can be written as a convex combination of unitary channels. As a consequence, we find that the collection of…
Hilbert space representations of the cross product *-algebras of the Hopf *-algebra U_q(su_2) and its module *-algebras O(S^2_{qr}) of Podles spheres are investigated and classified by describing the action of generators. The…
We investigate the possibility of dividing quantum channels into concatenations of other channels, thereby studying the semigroup structure of the set of completely-positive trace-preserving maps. We show the existence of 'indivisible'…
The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of…
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…
Quantum process tomography, the standard procedure to characterize any quantum channel in nature, is affected by a circular argument: in order to characterize the channel, the tomographic preparation and measurement need in turn to be…
Quantum spaces with $\frak{su}(2)$ noncommutativity can be modelled by using a family of $SO(3)$-equivariant differential $^*$-representations. The quantization maps are determined from the combination of the Wigner theorem for $SU(2)$ with…
Lieb and Solovej \cite{liebsolBloch} studied traces of quantum channels, defined by the leading component in the decomposition of the tensor product of two irreducible representations of $SU(2)$, to establish a Wehrl-type inequality for…
One of the major achievements of the recently emerged quantum information theory is the introduction and thorough investigation of the notion of quantum channel which is a basic building block of any data-transmitting or data-processing…
A family of infinite-dimensional irreducible $*$-representations on $\mathcal{H}\simeq L^2(\mathbb{R})\otimes\mathbb{C}^N$ is defined for a quantum-deformed Lorentz algebra $\mathscr{U}_{\bf q}(sl_2)\otimes \mathscr{U}_{\widetilde{\bf…
Hilbert space representations of the cross product *-algebra of the Hopf *-algebra U_q(su_2) and its module *-algebras O(S^2_{qc}) of Podles' spheres are studied. Two classes of representations are described by explicit formulas for the…
We report experimental implementation of various types of qubit channels using an individual trapped ion. We analyzed experimental data and we performed tomographic reconstruction of quantum channels based on these data. Specifically, we…
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…
The research presented in this article concerns the stroboscopic approach to quantum tomography, which is an area of science where quantum Physics and linear algebra overlap. In this article we introduce the algebraic structure of the…