There's no such notion as ``quantum logic''.

Stam Nicolis

Please take a look of the following list of references:

1. https://www.researchgate.net/search.Search.html?type=publication&query=quantum%20logic

2. https://en.wikipedia.org/wiki/Quantum_logic

3. http://us.metamath.org/qlegif/mmql.html

4. https://www.iep.utm.edu/qu-logic/

There are, certainly, many more.

It's still wrong to claim that there's some ``quantum logic'' that's different from ``classical logic''. Such a statement doesn't make sense. (Though, unfortunately, that doesn't stop people from writing grammatically and syntactically correct, but meaningless, sentences on the subject.)

While there were many-even famous-people that were, apparently, confused by the space of states of a quantum system, there's no excuse for perpetuating their confusion.

That a quantum system allows for all possible linear superpositions of states doesn't imply that the rules of logic need to be changed. One way to understand this is that probabilities are assigned the usual way-just to more states than in the classical limit.

What is true is that operations such as AND and OR can't be realized by unitary operators. However the unitary operators that are necessary and sufficient to act in a consistent way on the states of a quantum system in a corresponding way are known.

(That's one way to understand that the examples in the Wikipedia article are, in fact, wrong-the AND and OR operations aren't meaningful.)

They don't constitute any ``quantum'' logic, however. They describe, rather, a particular way of taking into account the ``dissipative'' character of classical logic in a way that follows the usual rules of mathematics.