Optimal encoding and decoding of a spin direction
Abstract
For a system of N spins there are quantum states that can encode a direction in an intrinsic way. Information on this direction can later be decoded by means of a quantum measurement. We present here the optimal encoding and decoding procedure using the fidelity as a figure of merit. We compute the maximal fidelity and prove that it is directly related to the largest zeros of the Legendre and Jacobi polynomials. We show that this maximal fidelity approaches unity quadratically in 1/N. We also discuss this result in terms of the dimension of the encoding Hilbert space.
 Publication:

Physical Review A
 Pub Date:
 May 2001
 DOI:
 10.1103/PhysRevA.63.052309
 arXiv:
 arXiv:quantph/0012006
 Bibcode:
 2001PhRvA..63e2309B
 Keywords:

 03.67.a;
 03.65.Ta;
 Quantum information;
 Foundations of quantum mechanics;
 measurement theory;
 Quantum Physics
 EPrint:
 14 pages