Related papers: Geometry of phase-covariant qubit channels

In the space of quantum channels, we establish the geometry that allows us to make statistical predictions about relative volumes of entanglement breaking channels among all the Gaussian quantum channels. The underlying metric is…

We analyze the geometrical properties of trace-preserving Pauli maps. Using the Choi-Jamio\lkowski isomorphism, we express the Hilbert-Schmidt line and volume elements in terms of the eigenvalues of the Pauli map. We analytically compute…

We analyze convex combinations of non-unital qubit maps that are phase-covariant. In particular, we consider the behavior of maps that combine amplitude damping, inverse amplitude damping, and pure dephasing. We show that mixing non-unital…

We analyze the geometry of positive and completely positive, trace preserving Pauli maps that are fully determined by up to two distinct parameters. This includes five classes of symmetric and non-invertible Pauli channels. Using the…

The physically allowed quantum evolutions on a single qubit can be described in terms of their geometry. From a simple parameterisation of unital single-qubit channels, the canonical form of all such channels can be given. The related…

We analyze quantum communication properties of phase-covariant channels depending on their degree of non-unitality. In particular, we derive analytical formulas for minimal and maximal channel fidelity on pure states and maximal output…

The purpose of this article is to investigate the geometry of the set of locally diagonalizable bipartite quantum states. We have the following new results: the Hilbert-Schmidt volume of all locally diagonalizable states, and a necessary…

A generalization of the Choi-Jamiolkowski isomorphism for completely positive maps between operator algebras is introduced. Particular emphasis is placed on the case of normal unital completely positive maps defined between von Neumann…

We describe a general framework to study covariant symmetric broadcasting maps for mixed qubit states. We explicitly derive the optimal N to M superbroadcasting maps, achieving optimal purification of the single-site output copy, in both…

A canonical form for unital qubit channels under local unitary transforms is obtained. In particular, it is shown that the eigenvalues of the Choi matrix of a unital quantum channel form a complete set of invariants of the canonical form.…

The simplest building blocks for quantum computations are the qubit-qubit quantum channels. In this paper, we analyze the structure of these channels via their Choi representation. The restriction of a quantum channel to the space of…

A non--commutative analogue of the classical differential forms is constructed on the phase--space of an arbitrary quantum system. The non--commutative forms are universal and are related to the quantum mechanical dynamics in the same way…

We obtain an explicit characterization of linear maps, in particular, quantum channels, which are covariant with respect to an irreducible representation ($U$) of a finite group ($G$), whenever $U \otimes U^c$ is simply reducible (with…

A version of noncommutative geometry is proposed which is based on phase-space rather than position space. The momenta encode the information contained in the algebra of forms by a map which is the noncommutative extension of the duality…

We extend the off-diagonal geometric phase [Phys. Rev. Lett. {\bf 85}, 3067 (2000)] to mixed quantal states. The nodal structure of this phase in the qubit (two-level) case is compared with that of the diagonal mixed state geometric phase…

We give an algorithm allowing to construct bases of local unitary invariants of pure k-qubit states from the knowledge of polynomial covariants of the group of invertible local filtering operations. The simplest invariants obtained in this…

In the following paper, we generalize the geometrical framework of qubit decoherence to higher dimensions. The quantum mixed state is represented by the probability distribution, which is the K\"ahler function on the projective Hilbert…

Quantum phase is not a direct observable and is usually determined by interferometric methods. We present a method to map complete electron wave functions, including internal quantum phase information, from measured single-state probability…

The geometry of four-qubit entanglement is investigated. We replace some of the polynomial invariants for four-qubits introduced recently by new ones of direct geometrical meaning. It is shown that these invariants describe four points, six…

We further elaborate on a phase-space picture for a system of $N$ qubits and explore the structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves satisfying certain additional properties and…