Applications of the generalized Pauli group in quantum information Speaker(s): Thomas Durt
Abstract: It is known that finite fields with d elements exist only when d is a prime or a prime power.
When the dimension d of a finite dimensional Hilbert space is a prime power, we can associate to each basis state of the Hilbert space an element of a finite or Galois field, and construct a finite group of unitary transformations, the generalised Pauli group or discrete HeisenbergWeyl group. Its elements can be expressed, in terms of the elements of a Galois field.
This group presents numerous
applications in Quantum Information Science e.g. tomography, dense coding, teleportation, error correction and so on.
The aim of our talk is to give a general survey of these properties and to present recently obtained results in connection with three problems:
the socalled ''Mean King's problem'' in prime power dimension,
discrete Wigner distributions,
and quantum tomography .
Finally we shall discuss a limitation of the possible dimensions in which the socalled epistemic interpretation can be consistently formulated, in relation with the existence of finite affine planes, Euler's conjecture and the 36 officers problem.
Date: 10/10/2007  4:00 pm
