Picturing Qubits in Phase Space

2003/06/19 by William K. Wootters, Wootters, William K.
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0306135

26 pages; contribution to the Charles H. Bennett 60th Birthday Symposium; references added in v2, v3, and v4

openalex publication_date 2003/06/19 · arxiv created 2003/08/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Focusing particularly on one-qubit and two-qubit systems, I explain how the quantum state of a system of n qubits can be expressed as a real function--a generalized Wigner function--on a discrete 2ⁿ x 2ⁿ phase space. The phase space is based on the finite field having 2ⁿ elements, and its geometric structure leads naturally to the construction of a complete set of 2ⁿ+1 mutually conjugate bases.

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