Busch, P.; Hellwig, K.-E.; Stulpe, W. On classical representations of finite-dimensional quantum mechanics. (English) Zbl 0813.60004 Int. J. Theor. Phys. 32, No. 3, 399-405 (1993). Summary: In the case of a finite-dimensional Hilbert space, it is shown that quantum mechanics can be embedded into discrete classical probability theory. In particular, states can be represented as stochastic vectors and observables as random variables such that all probabilities and expectation values are given in classical terms. Cited in 6 Documents MSC: 60A99 Foundations of probability theory 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) Keywords:relation between quantum mechanics and classical statistical theories; phase-space representations of quantum mechanics; quantum mechanics PDF BibTeX XML Cite \textit{P. Busch} et al., Int. J. Theor. Phys. 32, No. 3, 399--405 (1993; Zbl 0813.60004) Full Text: DOI References: [1] Ali, S. T., and Prugove?ki, E. (1977a).Journal of Mathematical Physics 19, 219-228. · Zbl 0364.46055 · doi:10.1063/1.523259 [2] Ali, S. T., and Prugove?ki, E. (1977b).Physica,89A, 501-521. [3] Bugajski, S., Busch, P., Cassinelli, G., Lahti, P. J., and Quadt, R. (1992). Convex structures and classical embeddings of quantum mechanical state spaces, preprint. [4] Busch, P., and Ruch, E. (1992).International Journal of Quantum Chemistry,41, 163-185. · doi:10.1002/qua.560410115 [5] Hellwig, K.-E., and Singer, M. (1990). Distinction of classical convex structures in the general framework of statistical models, inProceedings of the 2nd Winter School on Measure Theory (Liptowski Jan), A. Dvure?enski and S. Pulmannová, eds., Korund Konzorcium, Nové Zámky, pp. 79-84. · Zbl 0774.46042 [6] Hellwig, K.-E., and Singer, M. (1991). ?Classical? in terms of statistical models, inProceedings of the 18th International Colloquium on Group Theoretical Methods in Physics (Moscow), V. V. Dodonov and V. I. Man’ko, eds., Springer-Verlag, Berlin, pp. 438-441. [7] Singer, M., and Stulpe, W. (1992).Journal of Mathematical Physics,23, 131-142. · doi:10.1063/1.529975 [8] Stulpe, W. (1992). On the representation of quantum mechanics on phase space, inProceedings in Quantum Logics, Gdansk ’90, J. Pykacz, ed., Nova Science Publishers, New York. · Zbl 0803.46088 [9] Stulpe, W. (1993). On discrete and continuous classical representations of quantum mechanics, in preparation. · Zbl 0813.60004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.