Asymmetric local label interference with polarization-entangled photon pairs: block-averaged spatial structure in unconditional detection records

We analyze a concrete local quantum-optical measurement architecture for polarization-entangled photon pairs in which Bob coherently maps polarization onto an additional path degree of freedom that functions as a local quantum label. Within an explicit loss-inclusive POVM model that includes no-detection events, and without coincidence matching, event-by-event pairing, or any side information from Alice, we compare three regimes: direct label readout, symmetric label-interference networks, and an asymmetric 2 + 3-aperture architecture. Direct readout and a broad symmetric class yield setting-independent local POVM outcome probabilities and linear unconditional count rates, in agreement with standard no-signaling expectations for ordinary local statistics. In contrast, for the asymmetric architecture we identify a separately defined normalized, block-averaged spatial morphology constructed from Bob’s unconditional detection records that becomes setting-distinguishable as Alice’s polarization setting is varied. Numerical simulations for contrasted settings show distinct block-averaged spatial structure and spatial-frequency content, and a complementary phase-shift/path-sum analysis independently confirms asymmetric multipath interference as the underlying mechanism. The result is an explicit, implementable distinction within standard quantum mechanics between setting-independent ordinary local statistics and setting-distinguishable structure in a derived block-averaged observable generated by asymmetric local label interference. These results delineate within the explicit measurement model, where quantum-label interference leaves ordinary local statistics unchanged and where it generates setting-distinguishable structure in a derived block-averaged local observable.