Classical codes in quantum state space
arXiv:1506.03808 · doi:10.1088/1751-8113/48/49/495303
Abstract
We present a construction of Hermitian operators and quantum states labelled by strings from a finite field. The distance between these operators or states is then simply related (typically, proportional) to the Hamming distance between their corresponding strings. This allows a straightforward application of classical coding theory to find arrangements of operators or states with a given distance distribution. Using the simplex or extended Reed-Solomon code in our construction recovers the discrete Wigner function, which has important applications in quantum information theory.
10 pages, 2 figures
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