Continuous phase-space representations for finite-dimensional quantum states and their tomography

Continuous phase spaces have become a powerful tool for describing, analyzing, and tomographically reconstructing quantum states in quantum optics and beyond. A plethora of these phase-space techniques are known, however a thorough understanding of their relations was still lacking for finite-dimensional quantum states. We present a unified approach to continuous phase-space representations which highlights their relations and tomography. The infinite-dimensional case from quantum optics is then recovered in the large-spin limit.Comment: 15 pages, 9 figures, v4: extended tomography analysis, added references and figure

Controlling Several Atoms in a Cavity

We treat control of several two-level atoms interacting with one mode of the electromagnetic field in a cavity. This provides a useful model to study pertinent aspects of quantum control in infinite dimensions via the emergence of infinite-dimensional system algebras. Hence we address problems arising with infinite-dimensional Lie algebras and those of unbounded operators. For the models considered, these problems can be solved by splitting the set of control Hamiltonians into two subsets: The first obeys an abelian symmetry and can be treated in terms of infinite-dimensional Lie algebras and strongly closed subgroups of the unitary group of the system Hilbert space. The second breaks this symmetry, and its discussion introduces new arguments. Yet, full controllability can be achieved in a strong sense: e.g., in a time dependent Jaynes-Cummings model we show that, by tuning coupling constants appropriately, every unitary of the coupled system (atoms and cavity) can be approximated with arbitrarily small error

Time-optimal polarization transfer from an electron spin to a nuclear spin

Polarization transfers from an electron spin to a nuclear spin are essential for various physical tasks, such as dynamic nuclear polarization in nuclear magnetic resonance and quantum state transformations on hybrid electron-nuclear spin systems. We present time-optimal schemes for electron-nuclear polarization transfers which improve on conventional approaches and will have wide applications.Comment: 11 pages, 8 figure

Kronecker coefficients, convexity, and generating functions

We give definitions for Kronecker coefficients and discuss possible applications in algebraic complexity theory and quantum information. We describe methods to compute Kronecker coefficients and convex polytopes corresponding to limits of Kronecker coefficients. We explore how generating functions can help to answer questions on Kronecker coefficients. We present low-dimensional examples