Frankfurt 2006 – scientific programme
Parts | Days | Selection | Search | Downloads | Help
Q: Quantenoptik und Photonik
Q 50: Quanteninformation IV
Q 50.4: Talk
Wednesday, March 15, 2006, 14:45–15:00, HI
Unambiguous quantum parity check — •Hermann Kamermann1, Matthias Kleinmann1, Tim Meyer1, Philippe Raynal2, Norbert Lütkenhaus2, and Dagmar Bruß1 — 1Heinrich Heine Universität Düsseldorf, Theoretische Physik III — 2Universität Erlangen-Nürnberg, Institut für Theoretische Physik I
We consider the task to determine without error, whether a string consisting of non-orthogonal quantum states ψ0 and ψ1 (with a priori probabilities η0 and η1) has even or odd parity, i.e. whether it consists of an even or odd number of ψ1’s. As perfect discrimination between non-orthogonal quantum states is impossible, the measurement outcomes, even parity (FE), odd parity (FO) or “I don’t know” (F?) can occur. Bennett et al. [1] solved the task of finding the minimal error probability for the case η0=η1, by relating it to an unambiguous state discrimination problem. We prove that the optimal measurement leads to identical failure rates for a string of 2n−1 and 2n states for η0=η1. We investigate the generalization of this task to arbitrary a priori probabilities and its effects on the failure rates.
[1] C.H. Bennett, T. Mor, and J.A. Smolin. Phys. Rev. A, 54(4), 2675, (1996)