"Linear maps preserving maximal deviation and the Jordan structure of quantum systems"@en . "21230" . . . "10.1063/1.4771671" . "In the algebraic approach to quantum theory, a quantum observable is given by an element of a Jordan algebra and a state of the system is modelled by a normalized positive functional on the underlying algebra. Maximal deviation of a quantum observable is the largest statistical deviation one can obtain in a particular state of the system. The main result of the paper shows that each linear bijective transformation between JBW algebras preserving maximal deviations is formed by a Jordan isomorphism or a minus Jordan isomorphism perturbed by a linear functional multiple of an identity. It shows that only one numerical statistical characteristic has the power to determine the Jordan algebraic structure completely. As a consequence, we obtain that only very special maps can preserve the diameter of the spectra of elements. Nonlinear maps preserving the pseudometric given by maximal deviation are also described. The results generalize hitherto known theorems on preservers of maximal deviation in the case of self-adjoint parts of von Neumann algebras proved by Moln\u00E1"@en . . "Linear maps preserving maximal deviation and the Jordan structure of quantum systems" . . "RIV/68407700:21230/12:00198977!RIV13-GA0-21230___" . . "10"^^ . "P(GAP201/12/0290)" . "147118" . . "Hamhalter, Jan" . "53" . . . . "Journal of Mathematical Physics" . "RIV/68407700:21230/12:00198977" . . "1"^^ . "000312832800018" . . . "In the algebraic approach to quantum theory, a quantum observable is given by an element of a Jordan algebra and a state of the system is modelled by a normalized positive functional on the underlying algebra. Maximal deviation of a quantum observable is the largest statistical deviation one can obtain in a particular state of the system. The main result of the paper shows that each linear bijective transformation between JBW algebras preserving maximal deviations is formed by a Jordan isomorphism or a minus Jordan isomorphism perturbed by a linear functional multiple of an identity. It shows that only one numerical statistical characteristic has the power to determine the Jordan algebraic structure completely. As a consequence, we obtain that only very special maps can preserve the diameter of the spectra of elements. Nonlinear maps preserving the pseudometric given by maximal deviation are also described. The results generalize hitherto known theorems on preservers of maximal deviation in the case of self-adjoint parts of von Neumann algebras proved by Moln\u00E1" . "0022-2488" . "algebra; numerical analysis; quantum theory; statistical analysis"@en . "Linear maps preserving maximal deviation and the Jordan structure of quantum systems"@en . "1"^^ . "12" . "http://link.aip.org/link/?JMP/53/122208" . . . "[48BD3E6B2F5D]" . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . . "Linear maps preserving maximal deviation and the Jordan structure of quantum systems" . . .