No abstract

The state of quantum systems, their energetics, and their time evolution is modeled by abstract operators. How can one visualize such operators for coupled spin systems? A general approach is presented which consists of several shapes representing linear combinations of spherical harmonics. It is applicable to an arbitrary number of spins and can be interpreted as a generalization of Wigner functions. The corresponding visualization transforms naturally under non-selective spin rotations as well as spin permutations. Examples and applications are illustrated for the case of three spins 1/2.Comment: 27 pages, 12 figures, 10 tables; v2: extended the discussion of Wigner functions, the motivation, and the comparison to other wor

General dynamic properties like controllability and simulability of spin systems, fermionic and bosonic systems are investigated in terms of symmetry. Symmetries may be due to the interaction topology or due to the structure and representation of the system and control Hamiltonians. In either case, they obviously entail constants of motion. Conversely, the absence of symmetry implies irreducibility and provides a convenient necessary condition for full controllability much easier to assess than the well-established Lie-algebra rank condition. We give a complete lattice of irreducible simple subalgebras of su(2 n ) for up to n = 15 qubits. It complements the symmetry condition by allowing for easy tests solving homogeneous linear equations to filter irreducible unitary representations of other candidate algebras of classical type as well as of exceptional types. -The lattice of irreducible simple subalgebras given also determines mutual simulability of dynamic systems of spin or fermionic or bosonic nature. We illustrate how controlled quadratic fermionic (and bosonic) systems can be simulated by spin systems and in certain cases also vice versa.

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 phasespace 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. * balint.koczor@materials.ox.ac.uk