arXiv subjects

Beatrix C. Hiesmayr

Publications and source records attributed to Beatrix C. Hiesmayr.

At least 37 records · Page 2Linked to original sources

arXiv2023

How many mutually unbiased bases are needed to detect bound entangled states?

From a practical perspective it is advantageous to develop methods that verify entanglement in quantum states with as few measurements as possible. In this paper we investigate the minimal number of mutually unbiased bases (MUBs) needed to detect bound entanglement in bipartite $(d\times d)$-dimensional states, i.e. entangled states that are positive under partial transposition. In particular, we show that a class of entanglement witnesses composed of mutually unbiased bases can detect bound entanglement if the number of measurements is greater than $d/2+1$. This is a substantial improvement over other detection methods, requiring significantly fewer resources than either full quantum state tomography or measuring a complete set of $d+1$ MUBs. Our approach is based on a partial characterisation of the (non-)decomposability of entanglement witnesses. We show that non-decomposability is a universal property of MUBs, which holds regardless of the choice of complementary observables, and we find that both the number of measurements and the structure of the witness play an important role in the detection of bound entanglement.

quant-ph↗

arXiv2023

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 $d \geq 3$, 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 ($d=3$), we successfully classify more than $75\%$ of representative Bell diagonal PPT states for $d=4$. Via those representative states we are able to estimate the volumes of separable and bound entangled states among PPT ququarts ($d=4$). We find that at least $75.7\%$ of all PPT states are separable, $1.7\%$ bound entangled and for $22.6\%$ 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 ($d=3$) and ququarts ($d=4$). 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.

quant-ph↗

arXiv2022

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.

quant-ph↗

arXiv2022

Is bound entanglement 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.

quant-ph↗

arXiv2022

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 $81.0 \%\pm0.1\%$ are determined to be separable while $13.9\pm0.1\%$ are bound entangled and only $5.1\pm0.1\%$ 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.

quant-ph↗

arXiv2022

On the Geometric Phase and Majorana Neutrinos

We analyze the geometric phase for neutrinos and we demonstrate that the geometric invariants associated to transitions between different neutrino flavors, for Majorana neutrinos, can depend on the representation of the mixing matrix and then are sensitive to the nature of neutrinos. The dependence of geometric invariants on the Majorana phase cannot be eliminated by a charged lepton rephasing transformation. By considering kinematic and geometric approach we also demonstrate that the Majorana phase is relevant in the projective Hilbert space. Geometric invariants can in principle be used as tools to distinguish between Dirac and Majorana neutrinos.

hep-ph↗

arXiv2021

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.

physics.med-ph↗

arXiv2021

Free versus Bound Entanglement: Machine learning tackling a NP-hard problem

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 $82\%$ to be free entangled, $2\%$ to be certainly separable and as much as $10\%$ 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 $6\%$ 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 $2$-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.

quant-ph↗

arXiv2020

Entanglement Witness $2.0$: Compressed/Mirrored Entanglement Witnesses

An entanglement witness is an observable detecting entanglement for a subset of states. We present a framework that makes an entanglement witness twice as powerful due to the general existence of a second (lower) bound, in addition to the (upper) bound of the very definition. This second bound, if non-trivial, is violated by another subset of entangled states. Differently stated, we prove via the structural physical approximation that two witnesses can be compressed into a single one. Consequently, our framework shows that any entanglement witness can be upgraded to a witness $2.0$. The generality and its power are demonstrate by applications to bipartite and multipartite qubit/qudit systems.

quant-ph↗

arXiv2019

A quantum information theoretic quantity sensitive to the neutrino mass-hierarchy

In this work, we derive a quantum information theoretic quantity similar to the Leggett-Garg inequality, which can be defined in terms of neutrino transition probabilities. For the case of $ν_μ\to ν_e/\barν_μ\to\barν_e$ transitions, this quantity is sensitive to CP violating effects as well as the neutrino mass-hierarchy, namely which neutrino mass eigenstate is heavier than the other ones. The violation of the inequality for this quantity shows an interesting dependence on mass-hierarchy. For normal (inverted) mass-hierarchy, it is significant for $ν_μ\to ν_e$ ($\barν_μ\to \barν_e$) transitions. This is applied to the two ongoing accelerator experiments T$2$K and NO$ν$A as well as the future experiment DUNE.

hep-ph↗

arXiv2018

Linking Entanglement Detection and State Tomography via Quantum 2-Designs

We present an experimentally feasible and efficient method for detecting entangled states with measurements that extend naturally to a tomographically complete set. Our detection criterion is based on measurements from subsets of a quantum 2-design, e.g., mutually unbiased bases or symmetric informationally complete states, and has several advantages over standard entanglement witnesses. First, as more detectors in the measurement are applied, there is a higher chance of witnessing a larger set of entangled states, in such a way that the measurement setting converges to a complete setup for quantum state tomography. Secondly, our method is twice as effective as standard witnesses in the sense that both upper and lower bounds can be derived. Thirdly, the scheme can be readily applied to measurement-device-independent scenarios.

quant-ph↗

arXiv2015

Twin GHZ-states behave differently

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 C2x4 by entangling two photons in polarisation 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, based on hybrid entangled entanglement, investigates these GHZs properties showing a good stability and fidelity and allowing a scaling in degrees of freedom and advanced operational manipulations.

quant-ph↗

arXiv2015

Contextuality and Nonlocality in Decaying Multipartite Systems

Everyday experience supports the existence of physical properties independent of observation in strong contrast to the predictions of quantum theory. In particular, existence of physical properties that are independent of the measurement context is prohibited for certain quantum systems. This property is known as contextuality. This paper studies whether the process of decay in space-time generally destroys the ability of revealing contextuality. We find that in the most general situation the decay property does not diminish this ability. However, applying certain constraints due to the space-time structure either on the time evolution of the decaying system or on the measurement procedure, the criteria revealing contextuality become inherently dependent on the decay property or an impossibility. In particular, we derive how the context-revealing setup known as Bell's nonlocality tests changes for decaying quantum systems. Our findings illustrate the interdependence between hidden and local hidden parameter theories and the role of time.

quant-ph↗

arXiv2015

A quantum information theoretic analysis of three flavor neutrino oscillations

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 flavour 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 flavour types, shedding light on the quantum-information theoretic aspects of the weak force.

hep-ph↗

arXiv2015

Bringing Bell's theorem back to the domain of Particle Physics & Cosmology

John St. Bell was a physicist working most of his time at CERN and contributing intensively and sustainably to the development of Particle Physics and Collider Physics. As a hobby he worked on so-called "foundations of quantum theory", that was that time very unpopular, even considered to be scientifically taboo. His 1964-theorem, showing that predictions of local realistic theories are different to those of quantum theory, initiated a new field in quantum physics: quantum information theory. The violation of Bell's theorem, for instance, is a necessary and sufficient criterion for generating a secure key for cryptography at two distant locations. This contribution shows how Bell's theorem can be brought to the realm of high energy physics and presents the first conclusive experimental feasible test for weakly decaying neutral mesons on the market. Strong experimental and theoretical limitations make a Bell test in weakly decaying systems such as mesons and hyperons very challenging, however, these systems show an unexpected and puzzling relation to another big open question: why is our Universe dominated by matter, why did the antimatter slip off the map? This long outstanding problem becomes a new perspective via the very idea behind quantum information.

quant-ph↗

arXiv2015

Newtonian Self-Gravitation in the Neutral Meson System

We derive the effect of the Schrödinger--Newton equation, which can be considered as a non-relativistic limit of classical gravity, for a composite quantum system in the regime of high energies. Such meson-antimeson systems exhibit very unique properties, e.g. distinct masses due to strong and electroweak interactions. We find conceptually different physical scenarios due to lacking of a clear physical guiding principle which mass is the relevant one and due to the fact that it is not clear how the flavor wave-function relates to the spatial wave-function. There seems to be no principal contradiction. However, a nonlinear extension of the Schrödinger equation in this manner strongly depends on the relation between the flavor wave-function and spatial wave-function and its particular shape. In opposition to the Continuous Spontaneous Localization collapse models we find a change in the oscillating behavior and not in the damping of the flavor oscillation.

quant-ph↗

arXiv2014

Entangled Entanglement: The Geometry of GHZ States

The familiar Greenberger-Horne-Zeilinger (GHZ) states can be rewritten by entangling the Bell states for two qubits with a state of the third qubit, which is dubbed entangled entanglement. We show that in this way we obtain all 8 independent GHZ states that form the simplex of entangled entanglement, the magic simplex. The construction procedure allows a generalization to higher dimensions both, in the degrees of freedom (considering qudits) as well as in the number of particles (considering n-partite states). Such bases of GHZ-type states exhibit a certain geometry that is relevant for experimental and quantum information theoretic applications. Furthermore, we study the geometry of these particular state spaces, the inherent symmetries, the cyclicity of the phase operations, and the regions of (genuine multi-partite) entanglement and the several classes of separability. We find non-trivial geometrical properties and a conceptually clear procedure to compare state spaces of different dimensions and number of particles.

quant-ph↗

arXiv2013

Mutually Unbiased Bases and Bound Entanglement

In this contribution we relate two different key concepts: mutually unbiased bases (MUBs) and entanglement; in particular we focus on bound entanglement, i.e. highly mixed states which cannot be distilled by local operations and classical communications. For a certain class of states --for which the state-space forms a "magic" simplex-- we analyze the set of bound entangled states detected by the MUB criterion for different dimensions d and number of particles n. We find that the geometry is similar for different d and n, consequently, the MUB criterion opens possibilities to investigate the typicality of PPT-bound and multipartite bound entanglement deeper and provides a simple experimentally feasible tool to detect bound entanglement.

quant-ph↗