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<div>Next week's MIT QIP seminar will take place on Monday September
22nd at 16:00 hours in room 4-270, and features:</div>
<div><br></div>
<hr>
<div align="center"><font size="+2"><b>The Minimum Distance Problem
for Two-Way Entanglement Purification</b></font></div>
<div align="center"><br></div>
<div align="center"><font size="+1"><i>by</i><b> Daniel Gottesman</b>
(<i>Perimeter Institute, CANDADA</i>)</font></div>
<div align="center"><br></div>
<div align="center"><u>ABSTRACT</u></div>
<div><br></div>
<blockquote>Entanglement purification protocols (EPPs) with one-way
classical communications are equivalent to quantum error-correcting
codes. The problem of designing such codes has been studied both
for maximum likelihood decoding for large block sizes and
asymptotically high fidelity, and in the minimum distance variant,
usually for fixed small block sizes, in which the number of allowed
errors is strictly bounded. EPPs using two-way classical
communications are known to be substantially more powerful than
one-way EPPs for the maximum likelihood decoding problem, at least as
far as allowable error rate.</blockquote>
<blockquote><br></blockquote>
<blockquote>We study the analog of the minimum distance problem for
two-way EPPs, in which Alice and Bob wish to extract at least k EPR
pairs from an initial set of<i> n</i> pairs, given that errors have
occurred on no more than<i> t</i> of the original pairs. We show
that two-way EPPs can be better than any quantum error-correcting code
in this scenario, and give examples of two-way EPPs that exceed both
the quantum Hamming bound and the quantum Singleton bound. We
also show that two-way EPPs in this minimum distance scenario can
asymptotically achieve the quantum Hamming bound with a fixed fraction
of errors, whereas the best known lower bound on the existence of
quantum codes is the quantum Gilbert-Varshamov bound, allowing only
half the error rate for the same data rate.</blockquote>
<blockquote><br></blockquote>
<blockquote>This is joint work with Andris Ambainis.</blockquote>
<blockquote><br></blockquote>
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