2009/03/31 by Christopher Ferrie, Joseph Emerson · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Mathematical Analysis and Transform Methods #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1088/1367-2630/11/6/063040
published as New J. Phys. 11 (2009) 063040 · 46 pages, 1 table, contains a review of finite dimensional quasi-probability functions
openalex publication_date 2009/06/22 · arxiv created 2009/06/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an alternate approach to defining a set of quasi-probability representations, based on a more natural generalization of a classical representation, is equivalent to our earlier approach based on frames, and therefore is also subject to our no-go theorem for a non-negative representation. Furthermore, we clarify the relationship between the contextuality of quantum theory and the necessity of negativity in quasi-probability representations and discuss their relevance as criteria for non-classicality. We also provide a comprehensive overview of known quasi-probability representations and their expression within the frame formalism.