Artykuły w formacie PDF dostępne są dla subskrybentów, którzy zapłacili za dostęp online, po podpisaniu licencji Licencja użytkownika instytucjonalnego. Czasopisma do 2009 są ogólnodostępne (bezpłatnie).

Generating ray class fields of real quadratic fields via complex equiangular lines

Tom 192 / 2020

Marcus Appleby, Steven Flammia, Gary McConnell, Jon Yard Acta Arithmetica 192 (2020), 211-233 MSC: Primary 11R37; Secondary 42C15. DOI: 10.4064/aa180508-21-6 Opublikowany online: 13 November 2019

Streszczenie

For certain real quadratic fields $K$ with sufficiently small discriminant we produce explicit unit generators for specific ray class fields of $K$ using a numerical method that arose in the study of complete sets of equiangular lines in $\mathbb{C}^d $ (known in quantum information as symmetric informationally complete measurements, or SICs). The construction in low dimensions suggests a general recipe for producing unit generators in infinite towers of ray class fields above arbitrary real quadratic $K$, and we summarize this in a conjecture. There are indications in G. S. Kopp’s work that the logarithms of these canonical units are related to the values of L-functions associated to the extensions, following the programme laid out in the Stark Conjectures.

Autorzy

  • Marcus ApplebyCentre for Engineered Quantum Systems
    School of Physics
    University of Sydney
    Physics Road
    Camperdown, NSW 2006, Australia
    e-mail
  • Steven FlammiaCentre for Engineered Quantum Systems
    School of Physics
    University of Sydney
    Physics Road
    Camperdown, NSW 2006, Australia
    e-mail
  • Gary McConnellControlled Quantum Dynamics Theory Group
    Imperial College
    Prince Consort Road
    London, SW7 2BW, United Kingdom
    e-mail
  • Jon YardInstitute for Quantum Computing
    Department of Combinatorics & Optimization
    University of Waterloo
    200 University Avenue West
    Waterloo, ON, N2L 3G1, Canada
    and
    Perimeter Institute for Theoretical Physics
    Waterloo, ON, Canada
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek