Abstract
Violations of Bell inequalities have been an incontestable indicator of non-classicality since the seminal paper by John Bell. However, recent claims of Bell inequalities violations with classical light have cast some doubts on their significance as hallmarks of non-classicality. Here, we challenge those claims. The crux of the problem is that such classical experiments simulate quantum probabilities with intensities of classical fields. However, fields intensities measurements are radically different from single-photon detections, which are primitives of any genuine Bell experiment. We show that this fundamental difference between field intensities measurements and single photon detections shifts the classical bound of relevant Bell inequalities to its non-signaling limit, leaving no place for their violations.
Highlights
The quantum-to-classical transition in optical interferometry can be observed either in a single-particle or multi-particle interference.[1]
In the HOM setting it can be attributed to the strength of particle indistinguishability[4] whereas multi-photon Bell inequality violations are tied to the coherence strength between entangled photons or, in the limit of many particles, to the vanishing ability of revealing single particle properties with multi-photon measurements.[5]
What changes is the physical meaning of a mathematical formalism used to describe the experiment—the probability amplitudes of a single photon become amplitudes of a classical electromagnetic wave
Summary
The quantum-to-classical transition in optical interferometry can be observed either in a single-particle or multi-particle interference.[1]. Let us consider the simplest case—a Young double-slit experiment.[6] Here the classical limit is achieved by increasing the average number of photons prepared in a coherent state or a mixture of such states. In this limit, the interference pattern does not change. What changes is the physical meaning of a mathematical formalism used to describe the experiment—the probability amplitudes of a single photon become amplitudes of a classical electromagnetic wave Straightforward as it seems, a relatively recent ‘discovery’ of Bell inequality violations with classical light, dubbed ‘classical entanglement’, makes the whole classical to quantum transition less obvious
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