In the 2nd half of the 20th century the American mathematician Haskell Curry and logician William Alvin Howard discovered an analogy between logical proofs and working computer programs. This is known as the Curry-Howard correspondence. Mathematical proofs are working computer programs. https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
Computers are physical entities obeying the laws of physics, so if there exists any object in the PHYSICAL UNIVERSE which behaves contrary to the Law of Non-Contradiction (LNC) we have living proof that the LNC is a false authority.
Therefore all I need to do to render the LNC meaningless is to present a computer program which EVALUATES ( ( A = A ) and (A != A) ) to True without producing an error.
Like this: https://repl.it/repls/UrbanUniquePixels
I have invented an object in space-time which behaves exactly contrary to what the LNC prescribes.
So if contradictions can and do exist physical form, but logic prescribes that they don't then surely you need to go with empiricism on this one and discard the LNC?
Is this sufficient proof that the LNC is a meaningless "law"? A false authority!
EDIT (after some feedback): This is NOT a quantum effect. By implementing it on a classical computer I am manifesting this duality in the classical realm.