Frankfurt 2006 – wissenschaftliches Programm

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Q: Quantenoptik und Photonik

Q 50: Quanteninformation IV

Q 50.4: Vortrag

Mittwoch, 15. März 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 (F_E), odd parity (F_O) 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)