There exist nonorthogonal quantum measurements that are perfectly repeatable.
We show that, contrary to the widespread belief, in quantum mechanics repeatable measurements are not necessarily described by orthogonal projectors--the customary paradigm of observable. Nonorthogonal repeatability, however, occurs only for infinite dimensions. We also show that, when a nonorthogonal repeatable measurement is performed, the measured system retains some "memory" of the number of times that the measurement has been performed.
QUIT Group, Unità INFM and Dipartimento di Fisica A. Volta, Università di Pavia, via A. Bassi 6, I-27100 Pavia, Italy.
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Buscemi
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D'Ariano
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Perinotti