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It is commonly believed that failures of tomographic completeness undermine assessments of nonclassicality in noncontextuality experiments. In this work, we study how such failures can indeed lead to mistaken assessments of nonclassicality. We then show that proofs of the failure of noncontextuality are robust to a very broad class of failures of tomographic completeness, including the kinds of failures that are likely to occur in real experiments. We do so by showing that such proofs actually rely on a much weaker assumption that we term relative tomographic completeness: namely, that one's experimental procedures are tomographic for each other. Thus, the failure of noncontextuality can be established even with coarse-grained, effective, emergent, or virtual degrees of freedom. This also implies that the existence of a deeper theory of nature (beyond that being probed in one's experiment) does not in and of itself pose any challenge to proofs of nonclassicality. To prove these results, we first introduce a number of useful new concepts within the framework of generalized probabilistic theories (GPTs). Most notably, we introduce the notion of a GPT subsystem, generalizing a range of preexisting notions of subsystems (including those arising from tensor products, direct sums, decoherence processes, virtual encodings, and more). We also introduce the notion of a shadow of a GPT fragment, which captures the information lost when one's states and effects are unknowingly not tomographic for one another., Comment: 21 pages plus appendices; Many figures and diagrams

We provide the first systematic technique for deriving witnesses of contextuality in prepare-transform-measure scenarios. More specifically, we show how linear quantifier elimination can be used to compute a polytope of correlations consistent with generalized noncontextuality in such scenarios. This polytope is specified as a set of noncontextuality inequalities that are necessary and sufficient conditions for observed data in the scenario to admit of a classical explanation relative to any linear operational identities, if one ignores some constraints from diagram preservation. While including these latter constraints generally leads to tighter inequalities, it seems that nonlinear quantifier elimination would be required to systematically include them. We also provide a linear program which can certify the nonclassicality of a set of numerical data arising in a prepare-transform-measure experiment. We apply our results to get a robust noncontextuality inequality for transformations that can be violated within the stabilizer subtheory. Finally, we give a simple algorithm for computing all the linear operational identities holding among a given set of states, of transformations, or of measurements., Comment: 15 pages + appendices; 3 figures

Building upon the Chatterjee correlation (2021: J. Am. Stat. Assoc. 116, p2009) for two real-valued variables, this study introduces a generalized measure of directed association between two vector variables, real or complex-valued, and of possibly different dimensions. The new measure is denoted as the "distance-based Chatterjee correlation", owing to the use here of the "distance transformed data" defined in Szekely et al (2007: Ann. Statist. 35, p2769) for the distance correlation. A main property of the new measure, inherited from the original Chatterjee correlation, is its predictive and asymmetric nature: it measures how well one variable can be predicted by the other, asymmetrically. This allows for inferring the causal direction of the association, by using the method of Blobaum et al (2019: PeerJ Comput. Sci. 1, e169). Since the original Chatterjee correlation is based on ranks, it is not available for complex variables, nor for general multivariate data. The novelty of our work is the extension to multivariate real and complex-valued pairs of vectors, offering a robust measure of directed association in a completely non-parametric setting. Informally, the intuitive assumption used here is that distance correlation is mathematically equivalent to Pearson's correlation when applied to "distance transformed" data. The next logical step is to compute Chatterjee's correlation on the same "distance transformed" data, thereby extending the analysis to multivariate vectors of real and complex valued data. As a bonus, the new measure here is robust to outliers, which is not true for the distance correlation of Szekely et al. Additionally, this approach allows for inference regarding the causal direction of the association between the variables., Comment: program code (pascal language) and executables at https://osf.io/ty6sc/ ; version2: updated header with DOI link to paper

Generalised contextuality is the notion of nonclassicality powering up a myriad of quantum tasks, among which is the celebrated case of a two-party information processing task where classical information is compressed in a quantum channel, the parity-oblivious multiplexing (POM) task. The success rate is the standard quantifier of resourcefulness for this task, while robustness-based quantifiers are as operationally motivated and have known general properties. In this work, we leverage analytical and numerical tools to estimate robustness of contextuality in POM scenarios under different types of noise. We conclude that for the 3-to-1 case robustness of contextuality to depolarisation, as well as a minimisation of robustness of contextuality to dephasing over all bases, are good quantifiers for the nonclassical advantage of this scenario. Moreover, we obtain a general relation between robustness of contextuality to depolarisation and the success rate in any $n$-to-1 POM scenario and show how it can be used to bound the number of bits encoded in this task., Comment: 11 pages, 7 figures. Comments are welcome

Kirkwood-Dirac representations of quantum states are increasingly finding use in many areas within quantum theory. Usually, representations of this sort are only applied to provide a representation of quantum states (as complex functions over some set). We show how standard Kirkwood-Dirac representations can be extended to a fully compositional representation of all of quantum theory (including channels, measurements and so on), and prove that this extension satisfies the essential features of functoriality (namely, that the representation commutes with composition of channels), linearity, and quasistochasticity. Interestingly, the representation of a POVM element is uniquely picked out to be the collection of weak values for it relative to the bases defining the representation. We then prove that if one can find any Kirkwood-Dirac representation that is everywhere real and nonnegative for a given experimental scenario or fragment of quantum theory, then the scenario or fragment is consistent with the principle of generalized noncontextuality, a key notion of classicality in quantum foundations. We also show that the converse does not hold: even if one verifies that all Kirkwood-Dirac representations (as defined herein) of an experiment require negativity or imaginarity, one cannot generally conclude that the experiment witnesses contextuality., Comment: 5 pages; comments welcome!

Measures of association between cortical regions based on activity signals provide useful information for studying brain functional connectivity. Difficulties occur with signals of electric neuronal activity, where an observed signal is a mixture, i.e. an instantaneous weighted average of the true, unobserved signals from all regions, due to volume conduction and low spatial resolution. This is why measures of lagged association are of interest, since at least theoretically, "lagged association" is of physiological origin. In contrast, the actual physiological instantaneous zero-lag association is masked and confounded by the mixing artifact. A minimum requirement for a measure of lagged association is that it must not tend to zero with an increase of strength of true instantaneous physiological association. Such biased measures cannot tell apart if a change in its value is due to a change in lagged or a change in instantaneous association. An explicit testable definition for frequency domain lagged connectivity between two multivariate time series is proposed. It is endowed with two important properties: it is invariant to non-singular linear transformations of each vector time series separately, and it is invariant to instantaneous association. As a first sanity check: in the case of two univariate time series, the new definition leads back to the bivariate lagged coherence of 2007 (eqs 25 and 26 in https://doi.org/10.48550/arXiv.0706.1776). As a second stronger sanity check: in the case of a univariate and multivariate vector time series, the new measure presented here leads back to the original multivariate lagged coherence of 2007 (eq 31 in https://doi.org/10.48550/arXiv.0711.1455), which again trivially includes the bivariate case., Comment: - (2023-11-24): First original version #1. - (2023-11-27): Second version #2: Added subsection "8. Lagged association of a univariate time series with a multivariate vector time series". - (2024-01-07): Third version #3: Current version. Eq. 44 now correct without "logarithm"

KS-contextuality is a crucial feature of quantum theory. Previous research demonstrated the vanishing of $N$-cycle KS-contextuality in setups where multiple independent observers measure sequentially on the same system, which we call Public Systems. This phenomenon can be explained as the additional observers' measurements degrading the state and depleting the quantum resource. This explanation would imply that state-independent contextuality should survive in such a system. In this paper, we show that this is not the case. We achieved this result by simulating an observer trying to violate the Peres-Mermin noncontextuality inequality in a Public System. Additionally, we provide an analytical description of our setup, explaining the loss of contextuality even in the state-independent case. Ultimately, these results show that state-independent contextuality is not independent of what happens to the system in-between the measurements of a context., Comment: 8+3 pages, 5 figures. Revised justification for Eq. (11), results unchanged

The control of the magnetization inversion dynamics is one of the main challenges driving the design of new nanostructured magnetic materials for magnetoelectronic applications. Nanoparticles with onion-like architecture offer a unique opportunity to expand the possibilities allowing to combine different phases at the nanoscale and also modulate the coupling between magnetic phases by introducing spacers in the same structure. Here we report the fabrication, by a three-step high temperature decomposition method, of Fe3O4/MgO/CoFe2O4 onio-like nanoparticles and their detailed structural analysis, elemental compositional maps and magnetic response. The core/shell/shell nanoparticles present epitaxial growth and cubic shape with overall size of (29+-6) nm. These nanoparticles are formed by cubic iron oxide core of (22+-4) nm covered by two shells, the inner of magnesium oxide and the outer of cobalt ferrite of ~1 and ~2.5 nm of thickness, respectively. The magnetization measurements show a single reversion magnetization curve and the enhancement of the coercivity field, from HC~608 Oe for the Fe3O4/MgO to HC~5890 Oe to the Fe3O4/MgO/CoFe2O4 nanoparticles at T=5 K, ascribed to the coupling between both ferrimagnetic phases with a coupling constant of =2 erg/cm2. The system also exhibits exchange bias effect, where the exchange bias field increases up to HEB~2850 Oe at 5 K accompanied with the broadening of the magnetization loop of HC~6650 Oe. This exchange bias effect originates from the freezing of the surface spins below the freezing temperature TF=32 K that pinned the magnetic moment of the cobalt ferrite shell., Comment: 39 pages, 8 figures

Power spectra of awake resting state EEG recordings in humans typically have an Alpha peak at around 10 Hz riding a decreasing background "Xi process". Normal and pathological variations may have more than one peak or none. The single channel Xi-Alpha model (Pascual-Marqui et al 1988, https://doi.org/10.3109/00207458808985730) separated these two processes, providing a low-dimensional parametric description of EEG spectra. Currently lacking is a generative whole cortex model for activity spectra and intracortical functional connectivity. Here we introduce the "cortical Xi-Alpha model". The cross-spectral density matrices are modeled as additive components, each one consisting of a scalar spectrum that multiplies a frequency invariant Hermitian covariance matrix. This simple "separation of variables" form offers a very rich repertoire of spatio-spectral properties, as well as diverse whole cortex functional connectivity patterns. The scalp EEG model conserves the same form, allowing simple estimation from scalp to cortex. Two independent open-access, resting state eyes open and closed EEG data sets (203 participants with 61 electrodes, and 47 participants with 26 electrodes) were used to demonstrate, test, and validate the model. Results summary: - The average dimension of cross-spectra lies between 1.7 and 2.6, indicating two processes. - Non-negative matrix factorization of population power spectra sampled at 6239 cortical voxels with only two components (identified as Xi and Alpha) explains 99% of the variance. - The median value of explained variance was 95% for the "cortical Xi-Alpha model" across all datasets and conditions. - Alpha process generators more occipital, Xi more frontal. - Xi cortical lagged connectivities are isotropic with interdistance. - Laminar recordings suggest layers 2/3 pyramidal neurons generate Xi; layers 5/6 pyramidal neurons generate Alpha.

Brain function as measured by multichannel EEG recordings can be described to a high level of accuracy by microstates, characterized as a sequence of time intervals within which the sign invariant normalized scalp electric potential field remains quasi-stable, concatenated by fast transitions. Filtering the EEG has a small effect on the spatial microstate scalp maps, but a large effect on the dynamics (e.g. duration, frequency of occurrence, and transition rates). In addition, spectral power has been found to be strongly correlated with microstate dynamics. And yet, the nature of the relation between spectra and microstates remains poorly understood. Here we show that the multivariate EEG cross-spectrum contains sufficient generative information for estimating the microstate scalp maps and their dynamics, demonstrating an underlying fundamental link between the microstate model and the multivariate cross-spectrum. Empirically, based on EEG recordings from 203 participants in eyes-closed resting state, their cross-spectral matrices were computed, from which stochastic EEG was generated. No significant differences were found for the microstate model (maps and dynamics) estimated from the actual EEG and from the stochastic EEG based solely on the cross-spectra. In addition, with the aim of quantifying the spatio-cross-spectral properties of the microstate model, we introduce here the topographic likelihood spectrum, based on the Watson distribution, which provides a frequency-by-frequency account of the contribution of a normalized microstate map to the normalized EEG cross-spectrum, independent of power. The topographic likelihood spectra are distinct for the different microstate maps. In a comparison between eyes-closed and eyes open conditions, they are shown to be significantly different in frequency specific patterns., Comment: version 2 fixes some spelling mistakes, and fixes table order. adds in header info on citing this preprint

Quantum Darwinism proposes that the proliferation of redundant information plays a major role in the emergence of objectivity out of the quantum world. Is this kind of objectivity necessarily classical? We show that if one takes Spekkens' notion of noncontextuality as the notion of classicality and the approach of Brand\~{a}o, Piani and Horodecki to quantum Darwinism, the answer to the above question is `yes', if the environment encodes sufficiently well the proliferated information. Moreover, we propose a threshold on this encoding, above which one can unambiguously say that classical objectivity has emerged under quantum Darwinism., Comment: Essentially the accepted version. Enhanced clarity, but main results stand the same. Addition of two new subsections: 1- a cutoff for classical objectivity 2-state spectrum broadcasting case (+ the relative subsections to the appendix). For the final version, please look at PRX Quantum. 8 pages, 2 figures in the main text + 7 pages, 1 figure in the Appendix. Comments are welcome!

In Specific Power Absorption (SPA) models for Magnetic Fluid Hyperthermia (MFH) experiments, the magnetic relaxation time of the nanoparticles (NPs) is known to be a fundamental descriptor of the heating mechanisms. The relaxation time is mainly determined by the interplay between the magnetic properties of the NPs and the rheological properties of NPs environment. Although the role of magnetism in MFH has been extensively studied, the thermal properties of the NPs medium and their changes during of MFH experiments have been so far underrated. Here, we show that ZnxFe3-xO4 NPs dispersed through different with phase transition in the temperature range of the experiment: clarified butter oil (CBO) and paraffin. These systems show non-linear behavior of the heating rate within the temperature range of the MFH experiments. For CBO, a fast increase at $306 K$ associated to changes in the viscosity (\texteta(T)) and specific heat (c_p(T)) of the medium below and above its melting temperature. This increment in the heating rate takes place around $318 K$ for paraffin. Magnetic and morphological characterizations of NPs together with the observed agglomeration of the nanoparticles above $306 K$ indicate that the fast increase in MFH curves could not be associated to a change in the magnetic relaxation mechanism, with N\'eel relaxation being dominant. In fact, successive experiment runs performed up to temperatures below and above the CBO melting point resulted in different MFH curves due to agglomeration of NPs driven by magnetic field inhomogeneity during the experiments. Similar effects were observed for paraffin. Our results highlight the relevance of the NPs medium's thermodynamic properties for an accurate measurement of the heating efficiency for in vitro and in vivo environments, where the thermal properties are largely variable within the temperature window of MFH experiments., Comment: 36 pages, 8 figures

We employ the resource theory of generalized contextuality as a tool for analyzing the structure of prepare-and-measure scenarios. We argue that this framework simplifies proofs of quantum contextuality in complex scenarios and strengthens existing arguments regarding robustness of experimental implementations. As a case study, we demonstrate quantum contextuality associated with any nontrivial noncontextuality inequality for a class of useful scenarios by noticing a connection between the resource theory and measurement simulability. Additionally, we expose a formal composition rule that allows engineering complex scenarios from simpler ones. This approach provides insights into the noncontextual polytope structure for complex scenarios and facilitates the identification of possible quantum violations of noncontextuality inequalities., Comment: 11 pages (+9 page Appendix), 2 figures (+1 figure and 3 tables in appendix)

Entangled quantum states play an important role in quantum information science and also in quantum mechanics fundamental investigations. Implementation and characterization of techniques allowing for easy preparation of entangled states are important steps in such fields. Here we generated entangled quantum states encoded in photons transversal paths, obtained by pumping a non-linear crystal with multiple transversal Gaussian beams. Such approach allows us to generate entangled states of two qubits and two qutrits encoded in Gaussian transversal path of twin photons. We make a theoretical analyses of this source, considering the influence of the pump angular spectrum on the generated states, further characterizing those by their purity and entanglement degree. Our experimental results reveals that the generated states presents both high purity and entanglement, and the theoretical analysis elucidates how the pump beams profile can be used to manipulate such photonic states., Comment: 6.5 pages +1 page refs. Comments are welcome!

Quantum Darwinism posits that the emergence of a classical reality relies on the spreading of classical information from a quantum system to many parts of its environment. But what are the essential physical principles of quantum theory that make this mechanism possible? We address this question by formulating the simplest instance of Darwinism - CNOT-like fan-out interactions - in a class of probabilistic theories that contain classical and quantum theory as special cases. We determine necessary and sufficient conditions for any theory to admit such interactions. We find that every theory with non-classical features that admits this idealized spreading of classical information must have both entangled states and entangled measurements. Furthermore, we show that Spekkens' toy theory admits this form of Darwinism, and so do all probabilistic theories that satisfy principles like strong symmetry, or contain a certain type of decoherence processes. Our result suggests the counter-intuitive general principle that in the presence of local non-classicality, a classical world can only emerge if this non-classicality can be "amplified" to a form of entanglement., Comment: 17+4 pages, 6 figures. Roberto D. Baldijao and Marius Krumm share first authorship of this paper. v2: added several clarifications; accepted by Quantum

Magnetic fluid hyperthermia (MFH), the procedure of raising the temperature of tumor cells using magnetic nanoparticles (MNPs) as heating agents, has proven successful in treating some types of cancer. However, the low heating power generated under physiological conditions makes necessary a high local concentration of MNPs at tumor sites. Here, we report how the in vitro heating power of magnetically soft MnFe$_2$O$_4$ nanoparticles can be enhanced by intracellular low-dimensional clusters through a strategy that includes: a) the design of the MNPs to retain N\'eel magnetic relaxation in high viscosity media, and b) culturing MNP-loaded cells under magnetic fields to produce elongated intracellular agglomerates. Our direct in vitro measurements demonstrated that the specific loss power (SLP) of elongated agglomerates ($SLP=576\pm33$ W/g) induced by culturing BV2 cells in situ under a dc magnetic field was increased by a factor of 2 compared to the $SLP=305\pm25$ W/g measured in aggregates freely formed within cells. A numerical mean-field model that included dipolar interactions quantitatively reproduced the SLPs of these clusters both in phantoms and in vitro, suggesting that it captures the relevant mechanisms behind power losses under high-viscosity conditions. These results indicate that in situ assembling of MNPs into low-dimensional structures is a sound possible way to improve the heating performance in MFH., Comment: 63 pages, 19 figures

We report the precise control of tunneling magnetoresistance (TMR) in devices of self-assembled core/shell Fe$_3$O$_4$/Co$_{1-x}$Zn$_x$Fe$_2$O$_4$ nanoparticles ($0\leq x\leq 1$). Adjusting the magnetic anisotropy through the content of Co$^{2+}$ in the shell, provides an accurate tool to control the switching field between the bistable states of the TMR. In this way, different combinations of soft/hard and hard/soft core/shell configurations can be envisaged for optimizing devices with the required magnetotransport response., Comment: 25 pages, 7 figures