January 01, 2018

Linear Programming Bounds for Entanglement-Assisted Quantum Error-Correcting Codes by Split Weight Enumerators

  • Ashikhmin A.
  • Lai C.

Linear programming approaches have been applied to derive upper bounds on the size of classical and quantum codes. In this paper, we derive similar results for general quantum codes with entanglement assistance by considering a type of split weight enumerator. After deriving the MacWilliams identities for these enumerators, we are able to prove algebraic linear programming bounds, such as the Singleton bound, the Hamming bound, and the first linear programming bound. Our Singleton bound and Hamming bound are more general than the previous bounds for entanglement-assisted quantum stabilizer codes. In addition, we show that the first linear programming bound improves the Hamming bound when the relative distance is sufficiently large. On the other hand, we obtain additional constraints on the size of Pauli subgroups for quantum codes, which allow us to improve the linear programming bounds on the minimum distance of quantum codes of small length. In particular, we show that there is no $[[27, 15, 5]]$ or $[[28, 14, 6]]$ stabilizer code. We also discuss the existence of some entanglement-assisted quantum stabilizer codes with maximal entanglement. As a result, the upper and lower bounds on the minimum distance of maximal-entanglement quantum stabilizer codes with length up to 20 are significantly improved.

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Recent Publications

January 01, 2019

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  • Bron M.
  • Chute M.
  • Evans H.
  • Lalmas M.
  • Redi M.
  • Silvestri F.

© 2017 International World Wide Web Conference Committee (IW3C2), published under Creative Commons CC BY 4.0 License. Many of today's websites have recognised the importance of mobile friendly pages to keep users engaged and to provide a satisfying user experience. However, next to the experience provided by the sites themselves, ...

January 01, 2019

Analyzing uber's ride-sharing economy

  • Aiello L.
  • Djuric N.
  • Grbovic M.
  • Kooti F.
  • Lerman K.
  • Radosavljevic V.

© 2017 International World Wide Web Conference Committee (IW3C2), published under Creative Commons CC BY 4.0 License. Uber is a popular ride-sharing application that matches people who need a ride (or riders) with drivers who are willing to provide it using their personal vehicles. Despite its growing popularity, there exist ...

January 01, 2019

The paradigm-shift of social spambots: Evidence, theories, and tools for the arms race

  • Cresci S.
  • Petrocchi M.
  • Pietro R.
  • Spognardi A.
  • Tesconi M.

© 2017 International World Wide Web Conference Committee (IW3C2), published under Creative Commons CC BY 4.0 License. Recent studies in social media spam and automation provide anecdotal argumentation of the rise of a new generation of spambots, so-called social spambots. Here, for the first time, we extensively study this novel ...