Next Article in Journal
Rectification and Non-Gaussian Diffusion in Heterogeneous Media
Previous Article in Journal
Feature Extraction of Ship-Radiated Noise Based on Permutation Entropy of the Intrinsic Mode Function with the Highest Energy
Article Menu
Issue 11 (November) cover image

Export Article

Open AccessArticle
Entropy 2016, 18(11), 395; doi:10.3390/e18110395

Unextendible Mutually Unbiased Bases (after Mandayam, Bandyopadhyay, Grassl and Wootters)

Department of Mathematics, Ghent University, Ghent 9000, Belgium
Academic Editor: Jay Lawrence
Received: 7 September 2016 / Revised: 25 October 2016 / Accepted: 31 October 2016 / Published: 11 November 2016
(This article belongs to the Section Quantum Information)
View Full-Text   |   Download PDF [312 KB, uploaded 11 November 2016]   |  

Abstract

We consider questions posed in a recent paper of Mandayam et al. (2014) on the nature of “unextendible mutually unbiased bases.” We describe a conceptual framework to study these questions, using a connection proved by the author in Thas (2009) between the set of nonidentity generalized Pauli operators on the Hilbert space of N d-level quantum systems, d a prime, and the geometry of non-degenerate alternating bilinear forms of rank N over finite fields F d . We then supply alternative and short proofs of results obtained in Mandayam et al. (2014), as well as new general bounds for the problems considered in loc. cit. In this setting, we also solve Conjecture 1 of Mandayam et al. (2014) and speculate on variations of this conjecture. View Full-Text
Keywords: mutually unbiased bases; Pauli operator; symplectic polar space mutually unbiased bases; Pauli operator; symplectic polar space
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Thas, K. Unextendible Mutually Unbiased Bases (after Mandayam, Bandyopadhyay, Grassl and Wootters). Entropy 2016, 18, 395.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top