In medical applications-such as positron emission tomography (PET)-511 keV photons that experience Compton scattering are studied. We present a consistent framework based on quantum error-correction ...channels-intensively studied in quantum computing-to fully describe the quantum information-theoretic content of high energetic photons undergoing Compton scattering, characterized by the Klein-Nishina formula in unoriented matter. In this way, we can predict the expected spatial distribution of two or more, pure or mixed, polarization entangled or separable photons. This framework allows us to characterize the accessible and inaccessible information for different parameter ranges. It also answers the question of how to describe successive multi-photon scattering. In addition our formalism provides a complete framework for dealing with single and all multi-partite errors that can occur in the propagation, providing the basis for modeling future dedicated experiments that will then have applications in medicine, such as reducing errors in PET imaging or exploring possibilities for quantum-based diagnostic indicators.
We demonstrate genuine multipartite quantum entanglement of four photons in their orbital angular momentum degrees of freedom, where a high-dimensional discrete Hilbert space is attached to each ...photon. This can encode more quantum information compared to the qubit case, but it is a long-standing problem to entangle more than two such photons. In our experiment we use pulsed spontaneous parametric down-conversion to produce the photon quadruplets, which allows us to detect about one four-photon event per second. By means of quantum state reconstruction and a suitable witness operator we find that the photon quadruplets form a genuine multipartite entangled symmetric Dicke state. This opens a new tool for addressing foundational questions in quantum mechanics, and for exploration of novel high-dimensional multiparty quantum information applications such as secret sharing.
A novel approach to tomographic data processing has been developed and evaluated using the Jagiellonian positron emission tomography scanner as an example. We propose a system in which there is no ...need for powerful, local to the scanner processing facility, capable to reconstruct images on the fly. Instead, we introduce a field programmable gate array system-on-chip platform connected directly to data streams coming from the scanner, which can perform event building, filtering, coincidence search, and region-of-response reconstruction by the programmable logic and visualization by the integrated processors. The platform significantly reduces data volume converting raw data to a list-mode representation, while generating visualization on the fly.
We evaluate and analyze the exact value of a measure for local genuine tripartite entanglement in the one-dimensional cluster-Ising model for spin- particles. This model is attractive since cluster ...states are considered to be relevant sources for applying quantum algorithms and the model is experimentally feasible. Whereas bipartite entanglement is identically vanishing, we find that genuine tripartite entanglement is non zero in the anti-ferromagnetic phase and also in the cluster phase well before the critical point. We prove that the measure of local genuine tripartite entanglement captures all the properties of the symmetry-protected topological quantum phase transition. Remarkably, we find that the amount of genuine tripartite entanglement is independent of whether the ground states satisfy or break the symmetries of the Hamiltonian. We provide also strong evidences that local genuine tripartite entanglement represents the unique non-vanishing genuine multipartite entanglement.
•Parallel reconstruction of each emission is a foundation for real-time PET imaging.•Image domain asymmetric 3-component kernel and time-of-flight used for filtering.•High time resolution and ...low-pass filters are the cornerstones for short scans.•Optimal kernel parameters can be trained for the best bias-variance trade-off.
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We perform a parametric study of the newly developed time-of-flight (TOF) image reconstruction algorithm, proposed for the real-time imaging in total-body Jagiellonian PET (J-PET) scanners. The asymmetric 3D filtering kernel is applied at each most likely position of electron-positron annihilation, estimated from the emissions of back-to-back γ-photons. The optimisation of its parameters is studied using Monte Carlo simulations of a 1-mm spherical source, NEMA IEC and XCAT phantoms inside the ideal J-PET scanner. The combination of high-pass filters which included the TOF filtered back-projection (FBP), resulted in spatial resolution, 1.5 times higher in the axial direction than for the conventional 3D FBP. For realistic 10-minute scans of NEMA IEC and XCAT, which require a trade-off between the noise and spatial resolution, the need for Gaussian TOF kernel components, coupled with median post-filtering, is demonstrated. The best sets of 3D filter parameters were obtained by the Nelder-Mead minimisation of the mean squared error between the resulting and reference images. The approach allows training the reconstruction algorithm for custom scans, using the IEC phantom, when the temporal resolution is below 50 ps. The image quality parameters, estimated for the best outcomes, were systematically better than for the non-TOF FBP.
Abstract
Mutually unbiased bases (MUBs) provide a standard tool in the verification of quantum states, especially when harnessing a complete set for optimal quantum state tomography. In this work, we ...investigate the detection of entanglement via inequivalent sets of MUBs, with a particular focus on unextendible MUBs. These are bases for which an additional unbiased basis cannot be constructed and, consequently, are unsuitable for quantum state verification. Here, we show that unextendible MUBs, as well as other inequivalent sets in higher dimensions, can be more effective in the verification of entanglement. Furthermore, we provide an efficient and systematic method to search for inequivalent MUBs and show that such sets occur regularly within the Heisenberg–Weyl MUBs, as the dimension increases. Our findings are particularly useful for experimentalists since they demonstrate that a clever selection of MUBs allows for entanglement detection with fewer measurements.
We analyze the achievable limits of the quantum information processing of the weak interaction revealed by hyperons with spin. We find that the weak decay process corresponds to an interferometric ...device with a fixed visibility and fixed phase difference for each hyperon. Nature chooses rather low visibilities expressing a preference to parity conserving or violating processes (except for the decay Σ(+)→ pπ(0)). The decay process can be considered as an open quantum channel that carries the information of the hyperon spin to the angular distribution of the momentum of the daughter particles. We find a simple geometrical information theoretic interpretation of this process: two quantization axes are chosen spontaneously with probabilities where α is proportional to the visibility times the real part of the phase shift. Differently stated, the weak interaction process corresponds to spin measurements with an imperfect Stern-Gerlach apparatus. Equipped with this information theoretic insight we show how entanglement can be measured in these systems and why Bell's nonlocality (in contradiction to common misconception in literature) cannot be revealed in hyperon decays. Last but not least we study under which circumstances contextuality can be revealed.
J-PET is a detector optimized for registration of photons from the electron–positron annihilation via plastic scintillators where photons interact predominantly via Compton scattering. Registration ...of both primary and scattered photons enables to determinate the linear polarization of the primary photon on the event by event basis with a certain probability. Here we present quantitative results on the feasibility of such polarization measurements of photons from the decay of positronium with the J-PET and explore the physical limitations for the resolution of the polarization determination of 511 keV photons via Compton scattering. For scattering angles of about 82
∘
(where the best contrast for polarization measurement is theoretically predicted) we find that the single event resolution for the determination of the polarization is about 40
∘
(predominantly due to properties of the Compton effect). However, for samples larger than ten thousand events the J-PET is capable of determining relative average polarization of these photons with the precision of about few degrees. The obtained results open new perspectives for studies of various physics phenomena such as quantum entanglement and tests of discrete symmetries in decays of positronium and extend the energy range of polarization measurements by five orders of magnitude beyond the optical wavelength regime.
Purpose
In living organisms, the positron-electron annihilation (occurring during the PET imaging) proceeds in about 30% via creation of a metastable ortho-positronium atom. In the tissue, due to the ...pick-off and conversion processes, over 98% of ortho-positronia annihilate into two 511 keV photons. In this article, we assess the feasibility for reconstruction of the mean ortho-positronium lifetime image based on annihilations into two photons. The main objectives of this work include the (i) estimation of the sensitivity of the total-body PET scanners for the ortho-positronium mean lifetime imaging using 2
γ
annihilations and (ii) estimation of the spatial and time resolution of the ortho-positronium image as a function of the coincidence resolving time (CRT) of the scanner.
Methods
Simulations are conducted assuming that radiopharmaceutical is labeled with
44
S
c
isotope emitting one positron and one prompt gamma. The image is reconstructed on the basis of triple coincidence events. The ortho-positronium lifetime spectrum is determined for each voxel of the image. Calculations were performed for cases of total-body detectors build of (i) LYSO scintillators as used in the EXPLORER PET and (ii) plastic scintillators as anticipated for the cost-effective total-body J-PET scanner. To assess the spatial and time resolution, the four cases were considered assuming that CRT is equal to 500 ps, 140 ps, 50 ps, and 10 ps.
Results
The estimated total-body PET sensitivity for the registration and selection of image forming triple coincidences (2
γ
+
γ
prompt
) is larger by a factor of 13.5 (for LYSO PET) and by factor of 5.2 (for plastic PET) with respect to the sensitivity for the standard 2
γ
imaging by LYSO PET scanners with AFOV = 20 cm. The spatial resolution of the ortho-positronium image is comparable with the resolution achievable when using TOF-FBP algorithms already for CRT = 50 ps. For the 20-min scan, the resolution better than 20 ps is expected for the mean ortho-positronium lifetime image determination.
Conclusions
Ortho-positronium mean lifetime imaging based on the annihilations into two photons and prompt gamma is shown to be feasible with the advent of the high sensitivity total-body PET systems and time resolution of the order of tens of picoseconds.
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