Quantum Iterated Function Systems
arXiv:quant-ph/0210029 · doi:10.1103/PhysRevE.68.046110
Abstract
Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum iterated functions system (QIFS), where functions act randomly with prescribed probabilities in the Hilbert space. In a more general setting a QIFS consists of completely positive maps acting in the space of density operators. We present exemplary classical IFSs, the invariant measure of which exhibits fractal structure, and study properties of the corresponding QIFSs and their invariant states.
12 pages, 1 figure included
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- A Thermodynamic Formalism for density matrices in Quantum Information
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- Transition from order to chaos in reduced quantum dynamics
- Quantum fractals on n-spheres. Clifford Algebra approach
- A dynamical point of view of Quantum Information: entropy, pressure and Wigner measures
- A quantization procedure based on completely positive maps and Markov operators
- Autonomous choices among deterministic evolution-laws as source of uncertainty
- On Quantum Iterated Function Systems
- Piecewise Deterministic Quantum Dynamics and Quantum Fractals on the Poincare Disk
- Simultaneous Measurement of Non-commuting Observables and Quantum Fractals on Complex Projective Spaces