2008/04/30 by Karol Życzkowski, Karol Zyczkowski · 2 citations
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Statistical Mechanics and Entropy #quant-ph
paper · pdf · doi:10.1088/1751-8113/41/35/355302
published as J. Phys. A 41, 355302-23 (2008). · 30 pages in latex with 6 figures included; ver.2: several improvements, new references added
arxiv created 2008/06/30 · openalex publication_date 2008/07/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N -point probability distributions can be embedded inside a higher-dimensional convex body of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embedding proposed corresponds to an assumption that the physical system described in the N -dimensional Hilbert space is coupled with an auxiliary subsystem of the same dimensionality. The extended theory works for simple quantum systems and is shown to be a non-trivial generalization of the standard quantum theory for which K = N 2 . Imposing certain restrictions on initial conditions and dynamics allowed in the quartic theory one obtains quadratic theory as a special case. By imposing even stronger constraints one arrives at the classical theory, for which K = N .