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The "half-quantum" vortices ($\sigma$) and quasiparticles ($\psi$) in atwo-dimensional $p_x+ip_y$ superconductor obey the Ising-like fusion rules$\psi\times \psi=1$, $\sigma\times \psi=\sigma$, and $\sigma\times \sigma=1+\psi$. We explain how the physical fusion of vortex-antivortex pairs allowsus to use these rules to read out the information encoded in the topologicallyprotected space of degenerate ground states. We comment on the potentialapplicability of this fact to quantum computation.  Modified 11/30/05 to reflect manuscript as accepted for publication. Includescorrected last section.Comment: 23 pages, REVTEX

physical review. b, condensed matter and materials physics

Fusion rules and vortices in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mi>i</mml:mi><mml:msub><mml:mi>p</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math>superconductors

Fusion rules and vortices inpx+ipysuperconductors