Fisher information from stochastic quantum measurements

Year: 2016

Authors: Muller MM., Gherardini S., Smerzi A., Caruso F.

Autors Affiliation: LENS, Via Carrara 1, I-50019 Sesto Fiorentino, Italy; QSTAR, Via Carrara 1, I-50019 Sesto Fiorentino, Italy; Univ Florence, Dept Phys, Via G Sansone 1, I-50019 Sesto Fiorentino, Italy; Univ Florence, Ist Nazl Fis Nucl, Via S Marta 3, I-50139 Florence, Italy; Univ Florence, Dept Informat Engn, Via S Marta 3, I-50139 Florence, Italy; INO CNR, Largo E Fermi 2, I-50125 Florence, Italy.

Abstract: The unavoidable interaction between a quantum system and the external noisy environment can be mimicked by a sequence of stochastic measurements whose outcomes are neglected. Here we investigate how this stochasticity is reflected in the survival probability to find the system in a given Hilbert subspace at the end of the dynamical evolution. In particular, we analytically study the distinguishability of two different stochastic measurement sequences in terms of a Fisher information measure depending on the variation of a function, instead of a finite set of parameters. We find a characterization of Zeno phenomena as the physical result of the random observation of the quantum system, linked to the sensitivity of the survival probability to an arbitrary small perturbation of the measurement stochasticity. Finally, the implications on the Cramer-Rao bound and the Zeno time are discussed, together with a numerical example.

Journal/Review: PHYSICAL REVIEW A

Volume: 94 (4)      Pages from: 042322-1  to: 042322-7

More Information: We acknowledge fruitful discussions with S. Ruffo, S. Gupta, and F. S. Cataliotti. This work was supported by the European Union through the EU FP7 Marie-Curie Programme (Career Integration Grant, Project No. 293449), a national MIUR-FIRB Project (No. RBFR10M3SB), and by the Ente Cassa di Risparmio di Firenze through the Project No. Q-BIOSCAN.
KeyWords: ZENO DYNAMICS; STATISTICAL DISTANCE
DOI: 10.1103/PhysRevA.94.042322

Citations: 17
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