When the coupler is the channel: an AND condition on cavity photon-number means

Abstract:Can two cavities have equal mean photon numbers whenever at least one of two binary controls is off, and unequal means only when both controls are on? We give an elementary construction using a two-pump beam-splitter interaction whose strength is proportional to the product of the controls. A phase-coherent single-excitation state yields mean occupations $(1/2,1/2)$ for inputs $00$, $01$, and $10$, and $(1,0)$ for input $11$. This realizes the desired AND condition exactly at the level of population means. It also makes the communication resource explicit: the interaction acts after the inputs are supplied and changes local statistics with the remote input. For any no-signalling distribution with finite means, the corresponding exact-mean score is at most $3/4$ under uniform inputs. We give a robust consistency inequality, a finite-sample counting protocol, and a coherent-state realization showing that this mean response does not require entanglement. The construction provides a concrete example for distinguishing controlled interactions from nonlocal-game resources.

arXiv:2610.09103 [quant-ph]

(or arXiv:2610.09103v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.09103 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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