New quantum caps in PG(4,4)

Physics – Quantum Physics

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

22 pages

Scientific paper

Calderbank, Rains, Shor and Sloane (see \cite{Sloane}) showed that error-correction is possible in the context of quantum computations. Quantum stabilizer codes are a class of additive quaternary codes in binary projective spaces, which are self-orthogonal with respect to the symplectic form. A geometric description is given in \cite{Bierbra}, where also the notion of quantum cap is introduced. Quantum caps correspond to the special case of quantum stabilizer codes of distance $d=4$ when the code is linear over GF(4). In the present paper we review the translation from quantum error-correction to symplectic geometry and study quantum codes in PG(4,4) where we construct complete quantum caps with 20, 29, 30, 32, 33, 34, 36 and 38 points and incomplete quantum caps with 10, 12, 13, 20, 23, 24, 25 and 26 points and we prove the non existence of 11-quantum caps. In particular the quantum caps of sizes 36 and 38 yield positive answers to the existence questions of quantum codes $[[36,26,4]]$ and $[[38,28,4]]$ that remained open in the data base \cite{codetable}.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

New quantum caps in PG(4,4) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with New quantum caps in PG(4,4), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and New quantum caps in PG(4,4) will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-455838

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.