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Scaling of success probabilities for linear optics gates

Stefan Scheel·Koenraad M. R. Audenaert
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Abstract

By using the abstract linear-optical network derived in [S. Scheel and N. Lütkenhaus, New J. Phys. \textbf{6}, 51 (2004)] we show that for the lowest possible ancilla photon numbers the probability of success of realizing a (single-shot) generalized nonlinear sign shift gate on an ($N+1$)-dimensional signal state scales as $1/N^2$. We limit ourselves to single-shot gates without conditional feed-forward. We derive our results by using determinants of Vandermonde-type over a polynomial basis which is closely related to the well-known Jacobi polynomials.

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Stefan Scheel, Koenraad M. R. Audenaert. 2005-08-03. Scaling of success probabilities for linear optics gates. https://doi.org/10.1088/1367-2630%2F7%2F1%2F149

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