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Optics and Spectroscopy

On production and detection of entanglement

Marek Żukowski

Published Feb 1, 2010• 0 citations
Publisher

Abstract

Progress in multiphoton interferometry allows us now to observe even six-photon interference of a very high contrast. Also, it is possible to observe interference of two photons originating from truly independent sources. Non-classical effects may violate Bell inequalities, or reveal quantum non-separability. Methods of producing non-classical states of few photons, and the detection of entanglement via Bell inequalities, or via nor-separability criteria will be presented. Implications of violations of Bell inequalities will be discussed, with a special stress on over-interpretations of this fact.

DOI
10.1134/s0030400x10020049

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Progress in multiphoton interferometry allows us now to observe even six-photon interference of a very high contrast. Also, it is possible to observe interference of two photons originating from truly independent sources. Non-classical effects may violate Bell inequalities, or reveal quantum non-separability. Methods of producing non-classical states of few photons, and the detection of entanglement via Bell inequalities, or via nor-separability criteria will be presented. Implications of violations of Bell inequalities will be discussed, with a special stress on over-interpretations of this fact.
Some new experiments leading to observation of multi-photon entanglement will be presented. They utilize multi-pair emissions in a down-conversion crystal. In configurations that avoid interferometric overlaps this leads to a high visibility multi-photon interference. General theoretical results concerning the influence of photon statistics and distinguishability on the interference effects in such experiments is be given. Methods of detection of entanglement in multi-qubit systems, via Bell's theorem and a non-linear generalization of entanglement witnesses, will be presented. Finally it will be shown that multi-photon entanglement can be applied to reduce of communication complexity of some computational tasks.
The original Bell inequalities were derived with four terms of channel-to-channel correlations of paired photons but are violated with sixteen terms of channel-to-channel correlations. The same correlation function can be derived for non-entangled photons as it was for entangled ones. The correlation probability for independent photons and qubits exceeds that of the entangled photons. Entanglement reduces the detection probability of the first measurement to 1/2 but does not affect the second photon’s maximal probability of detection. For one channel-to-one channel correlation, the quantum probability of entangled photons can be factorized, which should enable a local determination of a quantum nonlocal effect. A single photon is scattered by the quantum Rayleigh scattering making it impossible to synchronize the detections of an original pair of photons. All experimental results can be explained by means of the intrinsic field of photons as confirmed by independently published experimental results involving independent photons.
It is theoretically and experimentally shown that photons emitted by statistically independent incoherent classical light sources and measured in the far field in spatially separated modes may display spatial correlations akin to path-entanglement of photons produced by quantum sources. By measuring higher order photon-correlations at different locations, i.e., mmm photons in one mode and one photon in another mode, we experimentally demonstrate for m≥6m \geq 6m≥6 a violation of Bell-type inequalities for spatial degrees of freedom. The spatial correlations among the photons can be understood from state projection where the detection of the first mmm photons projects the sources onto a state which emits the subsequent photon in a strongly correlated manner. From this perspective the entanglement and violation of Bell's inequalities appears as a consequence of nonvanishing cross correlations between noncommuting quadrature phase components of the two spatially separated fields after mmm photons have been recorded. In this way we show that classical systems may produce spatial field correlations violating local realistic theories.
Wang et al. [Science Advances, 1 Aug 2025 Vol 11, Issue 31] recently reported an experiment that they interpret as demonstrating a violation of Bell's inequality using unentangled photons. Such a claim is highly controversial, since it is well established that product states cannot surpass the bounds set by local hidden variable models. In this manuscript, we analyze the essential features of the experiment through simplified, idealized scenarios. Our analysis shows that the apparent violation of Bell's inequality originates from two key elements: postselection and an unconventional normalization procedure. These steps produce quantities that formally mimic Bell-type correlations but lack the operational meaning required in a genuine Bell test. We therefore argue that the reported violation does not demonstrate nonlocality without entanglement, but rather reflects a misinterpretation of otherwise valid and interesting multiphoton interference effects.