1998/03/31 by Ariel Caticha · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #cond-mat.stat-mech #gr-qc #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1016/s0375-9601(98)00289-8
published as Phys.Lett. A244 (1998) 13-17
arxiv created 1998/03/31 · openalex publication_date 1998/07/01 · arxiv updated 2009/11/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
Quantum theory is formulated as the uniquely consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if the amplitude of a quantum process can be computed in two different ways, the two answers must agree. The constraint is expressed in the form of functional equations the solution of which leads to the usual sum and product rules for amplitudes. An immediate consequence is that the Schrodinger equation must be linear: non-linear variants of quantum mechanics violate the requirement of consistency. PACS: 03.65.Bz, 03.65.Ca.