2014/04/25 by Holger F. Hofmann · 15 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Eigenvalues and eigenvectors #Formalism (music) #Joint probability distribution #Mathematics #Observable #Operator (biology) #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum state #Statistical physics #Statistics #quant-ph
paper · pdf · doi:10.1007/s40509-014-0010-x
published in Quantum Studies Mathematics and Foundations 1(1-2), 39-45 (Birkhäuser) · 5 pages, no figures
arxiv created 2014/04/25 · openalex publication_date 2014/07/04 · arxiv updated 2014/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In the operator formalism of quantum mechanics, the density operator describes the complete statistics of a quantum state in terms of d2 independent elements, where d is the number of possible outcomes for a precise measurement of an observable. In principle, it is therefore possible to express the density operator by a joint probability of two observables that cannot actually be measured jointly because they do not have any common eigenstates. However, such joint probabilities do not refer to an actual measurement outcome, so their definition cannot be based on a set of possible events. Here, I consider the criteria that could specify a unique mathematical form of joint probabilities in the quantum formalism. It is shown that a reasonable set of conditions results in the definition of joint probabilities by ordered products of the corresponding projection operators. It is pointed out that this joint probability corresponds to the quasi probabilities that have recently been observed experimentally in weak measurements.