Discrete symmetries tested at 10-4 precision using linear polarization of photons from positronium annihilations.

Discrete symmetries play an important role in particle physics with violation of CP connected to the matter-antimatter imbalance in the Universe. We report the most precise test of P, T and CP invariance in decays of ortho-positronium, performed with methodology involving polarization of photons from these decays. Positronium, the simplest bound state of an electron and positron, is of recent interest with discrepancies reported between measured hyperfine energy structure and theory at the level of 10-4 signaling a need for better understanding of the positronium system at this level. We test discrete symmetries using photon polarizations determined via Compton scattering in the dedicated J-PET tomograph on an event-by-event basis and without the need to control the spin of the positronium with an external magnetic field, in contrast to previous experiments. Our result is consistent with QED expectations at the level of 0.0007 and one standard deviation.

Transformation of PET raw data into images for event classification using convolutional neural networks.

In positron emission tomography (PET) studies, convolutional neural networks (CNNs) may be applied directly to the reconstructed distribution of radioactive tracers injected into the patient's body, as a pattern recognition tool. Nonetheless, unprocessed PET coincidence data exist in tabular format. This paper develops the transformation of tabular data into n-dimensional matrices, as a preparation stage for classification based on CNNs. This method explicitly introduces a nonlinear transformation at the feature engineering stage and then uses principal component analysis to create the images. We apply the proposed methodology to the classification of simulated PET coincidence events originating from NEMA IEC and anthropomorphic XCAT phantom. Comparative studies of neural network architectures, including multilayer perceptron and convolutional networks, were conducted. The developed method increased the initial number of features from 6 to 209 and gave the best precision results (79.8) for all tested neural network architectures; it also showed the smallest decrease when changing the test data to another phantom.

On the structure of mirrored operators obtained from optimal entanglement witnesses.

Entanglement witnesses (EWs) are a versatile tool in the verification of entangled states. The framework of mirrored EW doubles the power of a given EW by introducing its twin-a mirrored EW-whereby two EWs related by mirroring can bound the set of separable states more efficiently. In this work, we investigate the relation between the EWs and its mirrored ones, and present a conjecture which claims that the mirrored operator obtained from an optimal EW is either a positive operator or a decomposable EW, which implies that positive-partial-transpose entangled states, also known as the bound entangled states, cannot be detected. This conjecture is reached by studying numerous known examples of optimal EWs. However, the mirrored EWs obtained from the non-optimal ones can be non-decomposable as well. We also show that mirrored operators obtained from the extremal decomposable witnesses are positive semi-definite. Interestingly, the witnesses that violate the well known conjecture of Structural Physical Approximation, do satisfy our conjecture. The intricate relation between these two conjectures is discussed and it reveals a novel structure of the separability problem.

Bound entanglement is not Lorentz invariant.

Bound entanglement, in contrast to free entanglement, cannot be distilled into maximally entangled states by two local observers applying measurements and utilizing classical communication. In this paper we ask whether a relativistic observer classifies states according to being separable, bound or free entangled in the same manner as an unboosted observer. Surprisingly, this turns out not to be the case. And that even if the system in a given inertial frame of reference is separable with respect to the partition momenta versus spins. In detail, we show that if the spin state is initially bound entangled, some boosted observers observe their spin states to be either bound entangled, separable or free entangled. This also explains why a general measure of the entanglement property is difficult to find.

Comparing bound entanglement of bell diagonal pairs of qutrits and ququarts.

We compare the classification as entangled or separable of Bell diagonal bipartite qudits with positive partial transposition (PPT) and their properties for different dimensions. For dimension [Formula: see text], a form of entanglement exists that is hard to detect and called bound entanglement due to the fact that such entangled states cannot be used for entanglement distillation. Up to this date, no efficient solution is known to differentiate bound entangled from separable states. We address and compare this problem named separability problem for a family of bipartite Bell diagonal qudits with special algebraic and geometric structures and applications in quantum information processing tasks in different dimensions. Extending analytical and numerical methods and results for Bell diagonal qutrits ([Formula: see text]), we successfully classify more than [Formula: see text] of representative Bell diagonal PPT states for [Formula: see text]. Via those representative states we are able to estimate the volumes of separable and bound entangled states among PPT ququarts ([Formula: see text]). We find that at least [Formula: see text] of all PPT states are separable, [Formula: see text] bound entangled and for [Formula: see text] it remains unclear whether they are separable or bound entangled. Comparing the structure of bound entangled states and their detectors, we find considerable differences in the detection capabilities for different dimensions and relate those to differences of the Euclidean geometry for qutrits ([Formula: see text]) and ququarts ([Formula: see text]). Finally, using a detailed visual analysis of the set of separable and bound entangled Bell diagonal states in both dimensions, qualitative observations are made that allow to better distinguish bound entangled from separable states.

Almost complete solution for the NP-hard separability problem of Bell diagonal qutrits.

With a probability of success of 95% we solve the separability problem for Bell diagonal qutrit states with positive partial transposition (PPT). The separability problem, i.e. distinguishing separable and entangled states, generally lacks an efficient solution due to the existence of bound entangled states. In contrast to free entangled states that can be used for entanglement distillation via local operations and classical communication, these states cannot be detected by the Peres-Horodecki criterion or PPT criterion. We analyze a large family of bipartite qutrit states that can be separable, free entangled or bound entangled. Leveraging a geometrical representation of these states in Euclidean space, novel methods are presented that allow the classification of separable and bound entangled Bell diagonal states in an efficient way. Moreover, the classification allows the precise determination of relative volumes of the classes of separable, free and bound entangled states. In detail, out of all Bell diagonal PPT states [Formula: see text] are determined to be separable while [Formula: see text] are bound entangled and only [Formula: see text] remain unclassified. Moreover, our applied criteria are compared for their effectiveness and relation as detectors of bound entanglement, which reveals that not a single criterion is capable to detect all bound entangled states.

Free versus bound entanglement, a NP-hard problem tackled by machine learning.

Entanglement detection in high dimensional systems is a NP-hard problem since it is lacking an efficient way. Given a bipartite quantum state of interest free entanglement can be detected efficiently by the PPT-criterion (Peres-Horodecki criterion), in contrast to detecting bound entanglement, i.e. a curious form of entanglement that can also not be distilled into maximally (free) entangled states. Only a few bound entangled states have been found, typically by constructing dedicated entanglement witnesses, so naturally the question arises how large is the volume of those states. We define a large family of magically symmetric states of bipartite qutrits for which we find [Formula: see text] to be free entangled, [Formula: see text] to be certainly separable and as much as [Formula: see text] to be bound entangled, which shows that this kind of entanglement is not rare. Via various machine learning algorithms we can confirm that the remaining [Formula: see text] of states are more likely to belonging to the set of separable states than bound entangled states. Most important we find via dimension reduction algorithms that there is a strong two-dimensional (linear) sub-structure in the set of bound entangled states. This revealed structure opens a novel path to find and characterize bound entanglement towards solving the long-standing problem of what the existence of bound entanglement is implying.

Positronium imaging with the novel multiphoton PET scanner.

In vivo assessment of cancer and precise location of altered tissues at initial stages of molecular disorders are important diagnostic challenges. Positronium is copiously formed in the free molecular spaces in the patient's body during positron emission tomography (PET). The positronium properties vary according to the size of inter- and intramolecular voids and the concentration of molecules in them such as, e.g., molecular oxygen, O2; therefore, positronium imaging may provide information about disease progression during the initial stages of molecular alterations. Current PET systems do not allow acquisition of positronium images. This study presents a new method that enables positronium imaging by simultaneous registration of annihilation photons and deexcitation photons from pharmaceuticals labeled with radionuclides. The first positronium imaging of a phantom built from cardiac myxoma and adipose tissue is demonstrated. It is anticipated that positronium imaging will substantially enhance the specificity of PET diagnostics.

Witnessing Entanglement In Compton Scattering Processes Via Mutually Unbiased Bases.

We present a quantum information theoretic version of the Klein-Nishina formula. This formulation singles out the quantity, the a priori visibility, that quantifies the ability to deduce the polarisation property of single photons. The Kraus-type structure allows a straightforward generalisation to the multiphoton cases, relevant in the decay of positronium which is utilized e.g. for metabolic PET-imaging (Positron- Emission- Tomograph). Predicted by theory but never experimentally proven, the two- or three-photon states should be entangled. We provide an experimentally feasible method to witness entanglement for these processes via MUBs (Mutually Unbiased Bases), exploiting Bohr's complementarity. Last but not least we present explicit cases exemplifying the interrelation of geometry and entanglement including relations to its potentiality for teleportation schemes or Bell inequality violations or in future for detecting cancer in human beings.

Genuine Multipartite Entanglement in the 3-Photon Decay of Positronium.

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.

Experimental investigation on the geometry of GHZ states.

Greenberger-Horne-Zeilinger (GHZ) states and their mixtures exhibit fascinating properties. A complete basis of GHZ states can be constructed by properly choosing local basis rotations. We demonstrate this experimentally for the Hilbert space [Formula: see text] by entangling two photons in polarization and orbital angular momentum. Mixing GHZ states unmasks different entanglement features based on their particular local geometrical connectedness. In particular, a specific GHZ state in a complete orthonormal basis has a "twin" GHZ state for which equally mixing leads to full separability in opposition to any other basis-state. Exploiting these local geometrical relations provides a toolbox for generating specific types of multipartite entanglement, each providing different benefits in outperforming classical devices. Our experiment investigates these GHZ's properties exploiting the HMGH framework which allows us to study the geometry for the different depths of entanglement in our system and showing a good stability and fidelity thus admitting a scaling in degrees of freedom and advanced operational manipulations.

A quantum-information theoretic analysis of three-flavor neutrino oscillations: Quantum entanglement, nonlocal and nonclassical features of neutrinos.

Correlations exhibited by neutrino oscillations are studied via quantum-information theoretic quantities. We show that the strongest type of entanglement, genuine multipartite entanglement, is persistent in the flavor changing states. We prove the existence of Bell-type nonlocal features, in both its absolute and genuine avatars. Finally, we show that a measure of nonclassicality, dissension, which is a generalization of quantum discord to the tripartite case, is nonzero for almost the entire range of time in the evolution of an initial electron-neutrino. Via these quantum-information theoretic quantities, capturing different aspects of quantum correlations, we elucidate the differences between the flavor types, shedding light on the quantum-information theoretic aspects of the weak force.

Detection of high-dimensional genuine multipartite entanglement of mixed states.

We derive a general framework to identify genuinely multipartite entangled mixed quantum states in arbitrary-dimensional systems and show in exemplary cases that the constructed criteria are stronger than those previously known. Our criteria are simple functions of the given quantum state and detect genuine multipartite entanglement that had not been identified so far. They are experimentally accessible without quantum state tomography and are easily computable as no optimization or eigenvalue evaluation is needed.