2004/01/08 by Thomas Durt, Durt, Thomas
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical functions and polynomials #Matrix Theory and Algorithms #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0401037
Original paper replaced in June 2005 for the following reason: new material added (connections with Aravind's general solution and discrete Wigner functions were established in the meanwhile)
openalex publication_date 2004/01/08 · arxiv created 2005/06/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When the state of a quantum system belongs to a N-dimensional Hilbert space, with N the power of a prime number, it is possible to associate to the system a finite field (Galois field) with N elements. In this paper, we introduce generalized Bell states that can be intrinsically expressed in terms of the field operations.These Bell states are in one to one correspondence with the N2 elements of the generalised Pauli group or Heisenberg-Weyl group. This group consists of discrete displacement operators and provides a discrete realisation of the Weyl function.Thanks to the properties of generalised Bell states and of quadratic extensions of finite fields, we derive a particular solution for the Mean King's problem. This solution is in turn shown to be in one to one correspondence with a set of N2 self-adjoint operators that provides a discrete realisation of the Wigner quasi-distribution.