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arXiv:1706.06505 · Scientific Reports

Genuine Multipartite Entanglement in the 3-Photon Decay of Positronium

Beatrix C. Hiesmayr, Paweł Moskal

Published Nov 6, 2017• 53 citations
arXivHTMLPDF

Abstract

Abstract The electron-positron annihilation into two photons is a standard technology in medicine to observe e.g. metabolic processes in human bodies. A new tomograph will provide the possibility to observe not only direct e+e− annihilations but also the 3 photons from the decay of ortho-positronium atoms formed in the body. We show in this contribution that the three-photon state with respect to polarisation degrees of freedom depends on the angles between the photons and exhibits various specific entanglement features. In particular genuine multipartite entanglement, a type of entanglement involving all degrees of freedom, is subsistent if the positronium was in a definite spin eigenstate. Remarkably, when all spin eigenstates are mixed equally, entanglement –and even stronger genuine multipartite entanglement– survives. Due to a “symmetrization” process, however, Dicke-type or W-type entanglement remains whereas GHZ-type entanglement vanishes. The survival of particular entanglement properties in the mixing scenario may make it possible to extract quantum information in the form of distinct entanglement features, e.g., from metabolic processes in human bodies.

DOI
10.1038/s41598-017-15356-y

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Quantum Entanglement from Positronium Decay

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IntroductionIn this experiment we will explore whether photons emitted from the decay of positronium, a positron-electron composition, are quantum entangled. When talking about quantum entangled particles it is impossible to fully represent the quantum state of one particle independently of another such that if we know one photon from an entangled pair is horizontally polarized then the other must be vertically polarized. We will use this concept along with knowledge from previous experiments on positron-electron annihilation and Compton scattering to try to determine the truth of this model.ProcedureIn this experiment we used two NaI detectors, photo-multiplier tubes (PMT), pre-amplifiers, and amplifiers. Along with two single channel analyzers, a logic gate, a coincidence detector, a high-voltage supply, and a multi-channel analyzer (MCA) and of course two aluminum targets, a sodium-22 radioactive source, and loads of lead bricks. Our source was encased in the center of our detector configuration such that radiation from the source was focused towards both aluminum targets placed opposite of each other with respect to the source. Both detectors were then stationed so that photons coming from the source were detected after a 90 degree Compton scattering from the target. This ninety degree correlation is necessary for proof of quantum entanglement as we expect no coincidences to occur when both detectors are in the same plane do to quantum pairs anti-correlated polarization causing expected scattering to be related by this ninety degree angle. The picture below shows the basic geometry of this set up.

•Dec 14, 2020•0 citations
Abstract The electron-positron annihilation into two photons is a standard technology in medicine to observe e.g. metabolic processes in human bodies. A new tomograph will provide the possibility to observe not only direct e+e− annihilations but also the 3 photons from the decay of ortho-positronium atoms formed in the body. We show in this contribution that the three-photon state with respect to polarisation degrees of freedom depends on the angles between the photons and exhibits various specific entanglement features. In particular genuine multipartite entanglement, a type of entanglement involving all degrees of freedom, is subsistent if the positronium was in a definite spin eigenstate. Remarkably, when all spin eigenstates are mixed equally, entanglement –and even stronger genuine multipartite entanglement– survives. Due to a “symmetrization” process, however, Dicke-type or W-type entanglement remains whereas GHZ-type entanglement vanishes. The survival of particular entanglement properties in the mixing scenario may make it possible to extract quantum information in the form of distinct entanglement features, e.g., from metabolic processes in human bodies.
Entanglement of three photons from the decay of ortho-positronium is re-analyzed. We use the full three body phase space to write down the entangled states classified according to the spin directions of the ortho-positronium. Even in the case when the spin is perpendicular to the decay plane, we find non-negligible phases entering the entangled state. This has not been noticed before. We advocate a fixed quantization axis of the spin for the sake of generality. A brief discussion of a three dimensional formalism for photons, including correlations, versus a two dimensional one is given.
Annihilation photons are quantum-entangled in polarization, a phenomenon that has not been exploited in medical diagnostics so far. We present the first in vivo imaging of the degree of quantum entanglement of photons originating from positron-electron annihilation within a human subject. This study utilized the Jagiellonian Positron Emission Tomography (J-PET) scanner, constructed from plastic scintillators. In plastics, annihilation photons interact primarily via the Compton effect, which provides simultaneous information regarding the photon interaction position and time, as well as the photon polarization plane. The patient was injected with a DOTA-TATE radiopharmaceutical labeled with the 68^{68}68Ga radionuclide. Using the J-PET scanner, we determined the image of the radiopharmaceutical uptake and, simultaneously, the image of the degree of quantum entanglement. The latter was determined from the relative angle between the polarization planes of the annihilation photons. The values of the degree of quantum entanglement extracted for the liver and the spleen are smaller than those predicted for maximally entangled two-photon states, yet larger than expected for separable photons. This demonstration opens new perspectives for the application of quantum entanglement in clinical diagnostics.
The last two decades have witnessed an increasing effort by the scientific community toward pursuing a better framework for quantum resource covariance, with the focus predominantly posed on quantum entanglement. In this work, we move the discussion one step further by analyzing the behavior of both genuine multipartite entanglement and quantum coherence under Lorentz boosts. Specifically, we conduct a case study for the problem of an electron-positron pair created in a superposed multipartite pure state. Our approach is different from the standard treatments also in that we consider all the components of the four-momentum, thus allowing for an inspection of scenarios wherein entanglement can be encoded among these degrees of freedom as well. Our analysis reveals interesting subtleties in this problem, such as the fact that genuine 4-partite entanglement in the laboratory frame transforms into genuine 8-partite entanglement plus quantum coherence in the perspective of the Lorentz-boosted frame. Moreover, a given combination of these quantum resources is shown to form a Lorentz invariant. Although our findings are not able to determine, via first principles, an information-theoretic Lorentz invariant, they pave the way for fundamental incursions along this line.
Tripartite Entanglement in e+e−→ttˉZe^+ e^- \to t \bar{t} Ze+e−→ttˉZ
Multipartite entanglement is a uniquely quantum form of correlation that captures collective properties of a composite quantum state beyond those encoded in its bipartite subsystems. We investigate this phenomenon in the process e+e−→ttˉZe^+e^-\to t\bar tZe+e−→ttˉZ at a future lepton collider, where the final state spins span the tripartite Hilbert space H=C2⊗C2⊗C3\mathscr{H} = \mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^3H=C2⊗C2⊗C3. Starting from the Standard Model helicity amplitudes, we reconstruct the full 12×1212\times 1212×12 spin density matrix and characterise its entanglement structure through one-to-one negativities, one-to-other negativities, and the genuine multipartite negativity, evaluated at three increasingly inclusive levels of phase space integration. Pairwise entanglement is generally suppressed relative to the collective (one-to-other) and the genuine multipartite entanglement, and all measures decrease as more kinematic information is integrated out. Assuming quantum tomography in the fully leptonic decay channel at s=1\sqrt{s}=1s​=1 TeV, we find that collective entanglement should be accessible at a realistic high-luminosity polarised lepton collider. By contrast, certifying genuine multipartite entanglement is more challenging, with only limited sensitivity projected for a specific polarisation benchmark within the expected ILC luminosity. The study establishes e+e−→ttˉZe^+e^-\to t \bar{t}Ze+e−→ttˉZ as an attractive laboratory for probing multipartite entanglement in high-energy collisions and provides a general mixed state framework that applies to any tripartite spin system.
IntroductionIn this experiment we will explore whether photons emitted from the decay of positronium, a positron-electron composition, are quantum entangled. When talking about quantum entangled particles it is impossible to fully represent the quantum state of one particle independently of another such that if we know one photon from an entangled pair is horizontally polarized then the other must be vertically polarized. We will use this concept along with knowledge from previous experiments on positron-electron annihilation and Compton scattering to try to determine the truth of this model.ProcedureIn this experiment we used two NaI detectors, photo-multiplier tubes (PMT), pre-amplifiers, and amplifiers. Along with two single channel analyzers, a logic gate, a coincidence detector, a high-voltage supply, and a multi-channel analyzer (MCA) and of course two aluminum targets, a sodium-22 radioactive source, and loads of lead bricks. Our source was encased in the center of our detector configuration such that radiation from the source was focused towards both aluminum targets placed opposite of each other with respect to the source. Both detectors were then stationed so that photons coming from the source were detected after a 90 degree Compton scattering from the target. This ninety degree correlation is necessary for proof of quantum entanglement as we expect no coincidences to occur when both detectors are in the same plane do to quantum pairs anti-correlated polarization causing expected scattering to be related by this ninety degree angle. The picture below shows the basic geometry of this set up.