title: Exponential Sensitivity and its Cost in Quantum Physics.
abstract: State selective protocols, like entanglement purification, lead to an essentially non-linear quantum evolution, unusual in naturally occurring quantum processes. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications. Here we demonstrate that chaotic behaviour is a rather generic feature in state selective protocols: exponential sensitivity can exist for all initial states in an experimentally realisable optical scheme. Moreover, any complex rational polynomial map, including the example of the Mandelbrot set, can be directly realised. In state selective protocols, one needs an ensemble of initial states, the size of which decreases with each iteration. We prove that exponential sensitivity to initial states in any quantum system has to be related to downsizing the initial ensemble also exponentially. Our results show that magnifying initial differences of quantum states (a Schrödinger microscope) is possible; however, there is a strict bound on the number of copies needed.
authors: Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, Budapest, H-1121, Hungary.|Department of Theoretical Physics, Budapest University of Technology and Economics, Budapest, H-1111, Hungary.
authors: András
authors: A
authors: Gilyén
authors: Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, Budapest, H-1121, Hungary.
authors: Tamás
authors: T
authors: Kiss
authors: Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, 115 19 Praha 1, Czech Republic.
authors: Igor
authors: I
authors: Jex