A paradox in the quantum-mechanical treatment of destructive measurements on photons
Marcoen J. T. F. Cabbolet, Yves Caudano
TL;DR
The paper tackles the problem that destructive photon measurements cannot, within orthodox QM, justify ascribing a premeasurement property to a photon prepared in a superposition of eigenstates. It analyzes the Standard Property Postulate and Projection Postulate, showing that destroying the photon precludes the post-measurement projection needed to certify a property value, thus challenging experimental support for OQM in photonics. A range of proposed resolutions is examined—from treating the vacuum as the measured state, to alternative projection postulates, to ad hoc two-step postulates, to QND and POVM frameworks—and each is shown to fail to preserve the standard eigenvalue–property link for the destroyed photon. The authors further argue that decoherence does not resolve the paradox, since it does not yield a single, definite outcome for the photon prior to measurement. The result is a strong call to rethink the interpretational basis for destructive measurements in quantum optics and Bell-test experiments, highlighting a foundational gap in connecting measurement outcomes to preexisting properties under OQM.
Abstract
Measurements on photons are frequently cited as confirmations of predictions of quantum mechanics (QM), in particular in the context of Bell's theorem. In this paper we show, however, that we cannot ever claim to have measured a property of a photon if we treat a destructive measurement {of the value of a property of a photon prepared in a superposition of eigenstates} in the framework of orthodox QM.