Classical codes in quantum state space. (17th November 2015)

• Record Type: Journal Article
• Authors: Howard, Mark
• Is Part Of: Journal of physics. Volume 48:Number 49(2015)
• Publication Date: 2015-11-17
• Subjects: mutually unbiased bases -- code -- simplex -- polyope -- stabilizer -- discrete Wigner function; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/48/49/495303
• Languages: English
• ISSNs: 1751-8113

Abstract

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.