Abstract
We first present a generalization of the Robertson-Heisenberg uncertainty principle. This generalization applies to mixed states and contains a covariance term. For faithful states, we characterize when the uncertainty inequality is an equality. We next present an uncertainty principle version for real-valued observables. Sharp versions and conjugates of real-valued observables are considered. The theory is illustrated with examples of dichotomic observables. We close with a discussion of real-valued coarse graining.
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Gudder, S. Real-Valued Observables and Quantum Uncertainty. Int J Theor Phys 62, 94 (2023). https://doi.org/10.1007/s10773-023-05342-8
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DOI: https://doi.org/10.1007/s10773-023-05342-8