Quantum thieves?

Giugno 7th, 2021 | by Marcello Colozzo |

Recently I've lived the following experience: some thieves came into my house while I was sleeping ... More precisely, they entered a bedroom (through an open window), where there was a cat sleeping. I noticed all this because I got up to go to the kitchen to get a glass of water... Opening the door (in the dark) I was almost "blinded" by the light of a flashlight or a smartphone. Suddenly I was pushed violently towards a bookstore... I fell heavily as I felt a throbbing pain in my shoulder. I remained in that position for an endless time.
When I got up the thieves were gone ... At the same time the cat continued to sleep as if nothing had happened. This is most singular, because the cat recognizes the footsteps of a stranger and his smell. In other words, the cat should have run away... So I tried to solve this puzzle in the quantum mechanics paradigm:

where H_G is the Hilbert space associated with the cat. More precisely, |G IN>,|G OUT> are eigenvectors of a hermitian operator G. Also

are eigenvectors of a hermitian operator T, which represents the thieves in the appropriate Hilbert space H_T. Physically |G IN> and |G OUT> are the quantum states corresponding to the "cat inside" and the "cat out" respectively. Likewise, |T IN>,|T OUT> are the quantum states corresponding to the "thieves inside" and the "thieves out". Moreover, the equations eigenvalue for G and T are