Fuzzy sets in the theory of measurement of incompatible observables

S. Filippov, Teiko Heinosaari, Leevi Leppäjärvi

We quantify the fuzziness of observables in general probabilistic theories and derive a noise content inequality for incompatible observables. We apply the derived inequality to the standard quantum theory, quantum theory of processes, and polytope state spaces. The noise content for positive operator-valued measures takes a particularly simple form and equals the sum of minimal eigenvalues of all the effects. We illustrate our findings by a number of examples including the introduced notion of reverse observables.

Stanley Gudder

Roberto Beneduci, Tommaso Gentile

Niloofar Abbasvandi, M. J. Soleimani, Shahidan Radiman

The Von Neumann quantum measurement theory and Zurek reformulation are based on an assumption that the quantum system, apparatus and environment obey the quantum mechanics rules. According to the Zurek theory the observers typically interact with their surrounding environments. In this article, we give a more realistic image of the quantum measurement theory; we have proposed a correction to Zurek quantum measurement theory based on the fuzzy logic and fuzzy set theory.

Jarosław Pykacz

Niloofar Abbasvandi, M. J. Soleimani, A. P. Othman

The Von Neumann quantum measurement theory and Zurek reformulation are based on an assumption that the quantum system, apparatus and environment obey the quantum mechanics rules. According to the Zurek theory the observers typically interact with their surrounding environments. In this article, we give a more realistic image of the quantum measurement theory; we have proposed a correction to Zurek quantum measurement theory based on the fuzzy logic and fuzzy set theory.