[QIP-Sem] MIT QIP Seminar Announcement

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Next week's MIT QIP seminar will take place on Monday September 22nd 
at 16:00 hours in room 4-270, and features:


The Minimum Distance Problem for Two-Way Entanglement Purification

by Daniel Gottesman (Perimeter Institute, CANDADA)

ABSTRACT

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.

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 n pairs, given that errors have occurred on no more 
than t 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.

This is joint work with Andris Ambainis.

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