On channels with positive quantum zero-error capacity having vanishing n-shot capacity

On channels with positive quantum zero-error capacity having vanishing n-shot capacity We show that unbounded number of channel uses may be necessary for perfect transmission of quantum information. For any n, we explicitly construct low-dimensional quantum channels (input dimension 4, Choi rank 2 or 4) whose quantum zero-error capacity is positive, but the corresponding n-shot capacity is zero. We give estimates for quantum zero-error capacity of such channels as a function of n and show that these channels can be chosen in any small vicinity (in the $$cb$$ c b -norm) of a classical–quantum channel. Mathematically, this property means appearance of an ideal (noiseless) subchannel only in sufficiently large tensor power of a channel. Our approach (using special continuous deformation of a maximal commutative $$*$$ ∗ -subalgebra of $$M_4$$ M 4 ) also gives low-dimensional examples of the superactivation of 1-shot quantum zero-error capacity. Finally, we consider multi-dimensional construction which increases the estimate for quantum zero-error capacity of channels having vanishing n-shot capacity. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

On channels with positive quantum zero-error capacity having vanishing n-shot capacity

Loading next page...
Springer US
Copyright © 2015 by Springer Science+Business Media New York
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
Publisher site
See Article on Publisher Site


You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial