CHARACTERIZING THE DEPOLARIZING QUANTUM CHANNEL IN TERMS OF RIEMANNIAN GEOMETRY

The capacity of the quantum depolarizing channel

The information carrying capacity of the d-dimensional depolarizing channel is computed. It is shown that this capacity can be achieved by encoding messages as products of pure states belonging to an orthonormal basis of the state space, and using measurements which are products of projections onto this same orthonormal basis. In other words, neither entangled signal states nor entangled measur...

Riemannian Geometry of Quantum Computation

An introduction is given to some recent developments in the differential geometry of quantum computation for which the quantum evolution is described by the special unitary unimodular group SU(2n). Using the Lie algebra su(2n), detailed derivations are given of a useful Riemannian geometry of SU(2n), including the connection, curvature, the geodesic equation for minimal complexity quantum compu...

Riemannian Geometry of Quantum Groups

Riemannian Geometry on Quantum Spaces

An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended ∗email address: [email protected] to complex manifolds. Examples include the quantum sphere, the complex quantum projective spaces and the two-sheeted space.

Aspects of Riemannian Geometry in Quantum Field

In this thesis we study in detail several situations where the areas of Riemannian geometry and quantum field theory come together. This study is carried out in three distinct situations. In the first part we show how to introduce new local gauge invariant variables for V = 1 supersymmetric Yang-Mills theory, explicitly parameterizing the physical Hilbert space of the theory. We show that these...