Probing entanglement in Compton interactions

Abstract

This theoretical research aims to examine areas of the Compton cross section of entangled annihilation photons for the purpose of testing for possible break down of theory, which could have consequences for predicted optimal capabilities of Compton PET systems. We provide maps of the cross section for entangled annihilation photons for experimental verification. We introduce a strategy to derive cross sections in a relatively straight forward manner for the Compton scattering of a hypothetical separable, mixed and entangled states. To understand the effect that entanglement has on the cross section for annihilation photons, we derive the cross section so that it is expressed in terms of the cross section of a hypothetical separable state and of a hypothetical forbidden maximally entangled state. We find lobe-like structures in the cross section which are regions where entanglement has the greatest effect. We also find that mixed states do not reproduce the cross section for annihilation photons, contrary to a recent investigation which reported otherwise. We review the motivation and method of the most precise Compton scattering experiment for annihilation photons, in order to resolve conflicting reports regarding the extent to which the cross section itself has been experimentally verified.

Photon quantum entanglement in the MeV regime and its application in PET imaging

“…g Earlier works simulating (non-entangled) polarisation effects in PET using standard Geant4 classes 33,34 could be measured ∆φ distribution, a further simulation for unpolarised annihilation γ was also carried out (green line). The intrinsic R for such events is equal to unity, in agreement with analytical calculations for mixed states in Bohm and Aharonov 2 and Caradonna et al 14 . h The ∆φ distribution for unpolarised events in the detector acceptance (green line) is rather uniform albeit with a small acceptance related enhancement near to the centre of the distribution, which is also evidenced in photons for which their first interaction is the (linear polarisation analysing) Compton scatter reaction in the CZT detectors.…”

“…h We note that a very recent work 15 contradicted the original theory of Bohm and Aharonov 2 and the interpretation of all previous experimental works 2,10,12,[17][18][19][20][21][22][23][24] , by inferring a contribution to R from a hypothetical mixed state in Pa (in which the γ need not originate from the same annihilation event). The conclusion has already been refuted by Caradonna et al 14 who re-derived R = 1 for mixed states in a matrix formalism in agreement with Bohm and Aharonov 2 . We note the unpolarised simulation presented here also supports that such events are consistent with R = 1.…”

“…Bohm and Aharonov 2 were the first to recognize that the (∆φ) correlations between the DCSc annihilation photons was an example of the kind of entanglement discussed by Einstein, Podolsky and Rosen 16 . They also derived 2 the upper limit for a (hypothetical) orthogonally polarised, but non-entangled (separable) state as R = 1.63, establishing that measured values above this limit are a witnesses of the entanglement 2,14,15 . Experimental measurements of this amplitude [17][18][19][20][21][22][23][24] focused on restricted kinematics of θ 1 , θ 2 around maximum visibility, and yielded R values well beyond the upper limit for a non-entangled state.…”

“…In these early works, consistent results were obtained when employing time dependent perturbation theory or a Klein-Nishina 13 based approach, as outlined in the PhD thesis of Ward 11 . Subsequently the same form has been derived in DCSc calculations in a matrix formalism 14 and employing Kraus operators 15 .…”

Amplification of polarization correlations in Compton scattering of hard x-ray Bell states

“…To date, only the 511 keV cross-polarized Bell state has been available for Compton scattering experiments. Although much research has been conducted using this system, the most accurate measurement of a quantity known as the 'azimuthal ratio' yielded maximum ratio values that are 87% or less than the predicted value [3,8,10]. Development of novel X-ray sources [11,12] which can be used to generate any one of the 4 Bell states in the hard X-ray energy region [13] is appealing, because azimuthal ratios can now, in principle, be measured using controllable incident beams rather than relying solely on positron emitting sources [2,3,10].…”