Exponential Sensitivity and its Cost in Quantum Physics

András Gilyén, Tamás Kiss, Igor Jex

Research output: Contribution to journalArticle

7 Citations (Scopus)

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.

Original languageEnglish
Article number20076
JournalScientific reports
Volume6
DOIs
Publication statusPublished - Feb 10 2016

ASJC Scopus subject areas

  • General

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