Abstract
Given a quantum logic (L,L), a measure of noncommutativity for the elements ofL was introduced by Román and Rumbos. For the special case whenL is the lattice of closed subspaces of a Hilbert space, the noncommutativity between two atoms ofL was related to the transition probability between their corresponding pure states. Here we generalize this result to the case where one of the elements ofL is not necessarily an atom.
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References
Beltrametti, E. G., and Cassinelli, G. (1981).The Logic of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts.
Jauch, J. M. (1973).Foundations of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts.
Maczynski, M. (1981). Commutativity and generalized transition probability in quantum logic,Current Issues in Quantum Logic, E. G. Beltrametti and Bas C. van Fraassen, eds., Plenum Press, New York.
Román, L., and Rumbos, B. (1991).Foundations of Physics,21, 727–734.
Rumbos, B. (1993).International Journal of Theoretical Physics,32, 927–932.
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Rumbos, B. Noncommutativity of quantum observables. Int J Theor Phys 32, 1323–1328 (1993). https://doi.org/10.1007/BF00675197
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DOI: https://doi.org/10.1007/BF00675197