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arXiv:quant-ph/0106155 · Optical Fiber Communication Conference

Communicating a direction using spin states

E. Bagán, M. Baig, R. Muñoz-Tapia

Published Jan 1, 2001• 2 citations
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Abstract

The communication of directions using quantum states is a useful laboratory test for some basic facts of quantum information. For a system of spin-1/2 particles there are different quantum states that can encode directions. This information can later be decoded by means of a generalized measurement. In this talk we present the optimal strategies under different assumptions.

DOI
10.1364/icqi.2001.pa41

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The communication of directions using quantum states is a useful laboratory test for some basic facts of quantum information. For a system of spin-1/2 particles there are different quantum states that can encode directions. This information can later be decoded by means of a generalized measurement. In this talk we present the optimal strategies under different assumptions.
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.1/N.1/N. We also discuss this result in terms of the dimension of the encoding Hilbert space.
We consider the use of NNN spin- 12\frac{1}{2}21​ particles for indicating a direction in space. If N>2N>2N>2, their optimal state is entangled. For large NNN, the mean square error decreases as ${N}^{\ensuremath{-}2}$ (rather than ${N}^{\ensuremath{-}1}$ for parallel spins).