Stuttgart 2012 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 8: Quanteninformation: Konzepte und Methoden 2

Q 8.5: Talk

Monday, March 12, 2012, 15:00–15:15, V38.04

Symmetry-adapted visualization of multi-qubit systems — •Ariane Garon, Steffen J. Glaser, and Robert Zeier — Department Chemie, Technische Universität München, Lichtenbergstrasse 4, 85747 Garching, Germany

The evolution of a multi-qubit system is generally understood by analyzing the time variation of its density matrix which is given in some fixed, but arbitrary basis. As the number of entries of a density matrix grow exponentially with the number of qubits, it is usually difficult to describe the general behavior of a state during evolution. We present a symmetry-adapted method to visualize quantum states and their time evolution by considering a basis for the density matrices known as irreducible spherical tensors. The corresponding basis elements are plotted as spherical harmonics on multiple spheres relating different instances of irreducible representations of a direct product which consists of SU(2) and the symmetric group of qubit permutations. Explicit results and examples are shown for three qubits using plots on 11 spheres instead of plotting 64 matrix coefficients.