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Transformations on bounded observables preserving measure of compatibility. (English) Zbl 1243.81079

Summary: We describe the structure of all bijective nonlinear maps on the space of all bounded self-adjoint operators acting on a complex separable Hilbert space of dimension at least 3 which preserve a measure of commutativity, namely, the norm of the commutator of operators.

MSC:

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81P15 Quantum measurement theory, state operations, state preparations
81P05 General and philosophical questions in quantum theory
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