Quantum theory based on real numbers can be experimentally falsified.

Although complex numbers are essential in mathematics, they are not needed to describe physical experiments, as those are expressed in terms of probabilities, hence real numbers. Physics, however, aims to explain, rather than describe, experiments through theories. Although most theories of physics are based on real numbers, quantum theory was the first to be formulated in terms of operators acting on complex Hilbert spaces1,2. This has puzzled countless physicists, including the fathers of the theory, for whom a real version of quantum theory, in terms of real operators, seemed much more natural3. In fact, previous studies have shown that such a 'real quantum theory' can reproduce the outcomes of any multipartite experiment, as long as the parts share arbitrary real quantum states4. Here we investigate whether complex numbers are actually needed in the quantum formalism. We show this to be case by proving that real and complex Hilbert-space formulations of quantum theory make different predictions in network scenarios comprising independent states and measurements. This allows us to devise a Bell-like experiment, the successful realization of which would disprove real quantum theory, in the same way as standard Bell experiments disproved local physics.

Self-Testing in Prepare-and-Measure Scenarios and a Robust Version of Wigner's Theorem.

We consider communication scenarios where one party sends quantum states of known dimensionality D, prepared with an untrusted apparatus, to another, distant party, who probes them with uncharacterized measurement devices. We prove that, for any ensemble of reference pure quantum states, there exists one such prepare-and-measure scenario and a linear functional W on its observed measurement probabilities, such that W can only be maximized if the preparations coincide with the reference states, modulo a unitary or an antiunitary transformation. In other words, prepare-and-measure scenarios allow one to "self-test" arbitrary ensembles of pure quantum states. Arbitrary extreme D-dimensional quantum measurements, or sets thereof, can be similarly self-tested. Our results rely on a robust generalization of Wigner's theorem, a well-known result in particle physics that characterizes physical symmetries.

Testing Real Quantum Theory in an Optical Quantum Network.

Quantum theory is commonly formulated in complex Hilbert spaces. However, the question of whether complex numbers need to be given a fundamental role in the theory has been debated since its pioneering days. Recently it has been shown that tests in the spirit of a Bell inequality can reveal quantum predictions in entanglement swapping scenarios that cannot be modeled by the natural real-number analog of standard quantum theory. Here, we tailor such tests for implementation in state-of-the-art photonic systems. We experimentally demonstrate quantum correlations in a network of three parties and two independent EPR sources that violate the constraints of real quantum theory by over 4.5 standard deviations, hence disproving real quantum theory as a universal physical theory.

Optimized Detection of High-Dimensional Entanglement.

Entanglement detection is one of the most conventional tasks in quantum information processing. While most experimental demonstrations of high-dimensional entanglement rely on fidelity-based witnesses, these are powerless to detect entanglement within a large class of entangled quantum states, the so-called unfaithful states. In this Letter, we introduce a highly flexible automated method to construct optimal tests for entanglement detection given a bipartite target state of arbitrary dimension, faithful or unfaithful, and a set of local measurement operators. By restricting the number or complexity of the considered measurement settings, our method outputs the most convenient protocol which can be implemented using a wide range of experimental techniques such as photons, superconducting qudits, cold atoms, or trapped ions. With an experimental quantum optics setup that can prepare and measure arbitrary high-dimensional mixed states, we implement some three-setting protocols generated by our method. These protocols allow us to experimentally certify two- and three-unfaithful entanglement in four-dimensional photonic states, some of which contain well above 50% of noise.

Genuine Network Multipartite Entanglement.

The standard definition of genuine multipartite entanglement stems from the need to assess the quantum control over an ever-growing number of quantum systems. We argue that this notion is easy to hack: in fact, a source capable of distributing bipartite entanglement can, by itself, generate genuine k-partite entangled states for any k. We propose an alternative definition for genuine multipartite entanglement, whereby a quantum state is genuinely network k-entangled if it cannot be produced by applying local trace-preserving maps over several (k-1)-partite states distributed among the parties, even with the aid of global shared randomness. We provide analytic and numerical witnesses of genuine network entanglement, and we reinterpret many past quantum experiments as demonstrations of this feature.

Bounding the Sets of Classical and Quantum Correlations in Networks.

We present a method that allows the study of classical and quantum correlations in networks with causally independent parties, such as the scenario underlying entanglement swapping. By imposing relaxations of factorization constraints in a form compatible with semidefinite programing, it enables the use of the Navascués-Pironio-Acín hierarchy in complex quantum networks. We first show how the technique successfully identifies correlations not attainable in the entanglement-swapping scenario. Then we use it to show how the nonlocal power of measurements can be activated in a network: there exist measuring devices that, despite being unable to generate nonlocal correlations in the standard Bell scenario, provide a classical-quantum separation in an entanglement swapping configuration.

Structure of multilocus genetic diversity in predominantly selfing populations.

Predominantly selfing populations are expected to have reduced effective population sizes due to nonrandom sampling of gametes, demographic stochasticity (bottlenecks or extinction-recolonization), and large scale hitchhiking (reduced effective recombination). Thus, they are expected to display low genetic diversity, which was confirmed by empirical studies. The structure of genetic diversity in predominantly selfing species is dramatically different from outcrossing ones, with populations often dominated by one or a few multilocus genotypes (MLGs) coexisting with several rare genotypes. Therefore, multilocus diversity indices are relevant to describe diversity in selfing populations. Here, we use simulations to provide analytical expectations for multilocus indices and examine whether selfing alone can be responsible for the high-frequency MLGs persistent through time in the absence of selection. We then examine how combining single and multilocus indices of diversity may be insightful to distinguish the effects of selfing, population size, and more complex demographic events (bottlenecks, migration, admixture, or extinction-recolonization). Finally, we examine how temporal changes in MLG frequencies can be insightful to understand the evolutionary trajectory of a given population. We show that combinations of selfing and small demographic sizes can result in high-frequency MLGs, as observed in natural populations. We also show how different demographic scenarios can be distinguished by the parallel analysis of single and multilocus indices of diversity, and we emphasize the importance of temporal data for the study of predominantly selfing populations. Finally, the comparison of our simulations with empirical data on populations of Medicago truncatula confirms the pertinence of our simulation framework.

Almost-Quantum Correlations Violate the No-Restriction Hypothesis.

To identify which principles characterize quantum correlations, it is essential to understand in which sense this set of correlations differs from that of almost-quantum correlations. We solve this problem by invoking the so-called no-restriction hypothesis, an explicit and natural axiom in many reconstructions of quantum theory stating that the set of possible measurements is the dual of the set of states. We prove that, contrary to quantum correlations, no generalized probabilistic theory satisfying the no-restriction hypothesis is able to reproduce the set of almost-quantum correlations. Therefore, any theory whose correlations are exactly, or very close to, the almost-quantum correlations necessarily requires a rule limiting the possible measurements. Our results suggest that the no-restriction hypothesis may play a fundamental role in singling out the set of quantum correlations among other nonsignaling ones.

Entanglement and Nonlocality in Infinite 1D Systems.

We consider the problem of detecting entanglement and nonlocality in one-dimensional (1D) infinite, translation-invariant (TI) systems when just near-neighbor information is available. This issue is deeper than one might think a priori, since, as we show, there exist instances of local separable states (classical boxes) which admit only entangled (nonclassical) TI extensions. We provide a simple characterization of the set of local states of multiseparable TI spin chains and construct a family of linear witnesses which can detect entanglement in infinite TI states from the nearest-neighbor reduced density matrix. Similarly, we prove that the set of classical TI boxes forms a polytope and devise a general procedure to generate all Bell inequalities which characterize it. Using an algorithm based on matrix product states, we show how some of them can be violated by distant parties conducting identical measurements on an infinite TI quantum state. All our results can be easily adapted to detect entanglement and nonlocality in large (finite, not TI) 1D condensed matter systems.

Increased fire frequency promotes stronger spatial genetic structure and natural selection at regional and local scales in Pinus halepensis Mill.

Background and Aims: The recurrence of wildfires is predicted to increase due to global climate change, resulting in severe impacts on biodiversity and ecosystem functioning. Recurrent fires can drive plant adaptation and reduce genetic diversity; however, the underlying population genetic processes have not been studied in detail. In this study, the neutral and adaptive evolutionary effects of contrasting fire regimes were examined in the keystone tree species Pinus halepensis Mill. (Aleppo pine), a fire-adapted conifer. The genetic diversity, demographic history and spatial genetic structure were assessed at local (within-population) and regional scales for populations exposed to different crown fire frequencies. Methods: Eight natural P. halepensis stands were sampled in the east of the Iberian Peninsula, five of them in a region exposed to frequent crown fires (HiFi) and three of them in an adjacent region with a low frequency of crown fires (LoFi). Samples were genotyped at nine neutral simple sequence repeats (SSRs) and at 251 single nucleotide polymorphisms (SNPs) from coding regions, some of them potentially important for fire adaptation. Key Results: Fire regime had no effects on genetic diversity or demographic history. Three high-differentiation outlier SNPs were identified between HiFi and LoFi stands, suggesting fire-related selection at the regional scale. At the local scale, fine-scale spatial genetic structure (SGS) was overall weak as expected for a wind-pollinated and wind-dispersed tree species. HiFi stands displayed a stronger SGS than LoFi stands at SNPs, which probably reflected the simultaneous post-fire recruitment of co-dispersed related seeds. SNPs with exceptionally strong SGS, a proxy for microenvironmental selection, were only reliably identified under the HiFi regime. Conclusions: An increasing fire frequency as predicted due to global change can promote increased SGS with stronger family structures and alter natural selection in P. halepensis and in plants with similar life history traits.

Bounding the Set of Finite Dimensional Quantum Correlations.

We describe a simple method to derive high performance semidefinite programing relaxations for optimizations over complex and real operator algebras in finite dimensional Hilbert spaces. The method is very flexible, easy to program, and allows the user to assess the behavior of finite dimensional quantum systems in a number of interesting setups. We use this method to bound the strength of quantum nonlocality in Bell scenarios where the dimension of the parties is bounded from above. We derive new results in quantum communication complexity and prove the soundness of the prepare-and-measure dimension witnesses introduced in Gallego et al., Phys. Rev. Lett. 105, 230501 (2010). Finally, we propose a new dimension witness that can distinguish between classical, real, and complex two-level systems.

Nonthermal Quantum Channels as a Thermodynamical Resource.

Quantum thermodynamics can be understood as a resource theory, whereby thermal states are free and the only allowed operations are unitary transformations commuting with the total Hamiltonian of the system. Previous literature on the subject has just focused on transformations between different state resources, overlooking the fact that quantum operations which do not commute with the total energy also constitute a potentially valuable resource. In this Letter, given a number of nonthermal quantum channels, we study the problem of how to integrate them in a thermal engine so as to distill a maximum amount of work. We find that, in the limit of asymptotically many uses of each channel, the distillable work is an additive function of the considered channels, computable for both finite dimensional quantum operations and bosonic channels. We apply our results to bound the amount of distillable work due to the natural nonthermal processes postulated in the Ghirardi-Rimini-Weber (GRW) collapse model. We find that, although GRW theory predicts the possibility of extracting work from the vacuum at no cost, the power which a collapse engine could, in principle, generate is extremely low.

Distinguishing migration from isolation using genes with intragenic recombination: detecting introgression in the Drosophila simulans species complex.

BACKGROUND: Determining the presence or absence of gene flow between populations is the target of some statistical methods in population genetics. Until recently, these methods either avoided the use of recombining genes, or treated recombination as a nuisance parameter. However, genes with recombination contribute additional information for the detection of gene flow (i.e. through linkage disequilibrium). METHODS: We present three summary statistics based on the spatial arrangement of fixed differences, and shared and exclusive polymorphisms that are sensitive to the presence and direction of gene flow. Power and false positive rate for tests based on these statistics are studied by simulation. RESULTS: The application of these tests to populations from the Drosophila simulans species complex yielded results consistent with migration between D. simulans and its two endemic sister species D. mauritiana and D. sechellia, and between populations D. mauritiana on the islands of the Mauritius and Rodrigues. CONCLUSIONS: We demonstrate the sensitivity of the developed statistics to the presence and direction of gene flow, and characterize their power as a function of differentiation level and recombination rate. The properties of these statistics make them especially suitable for analyzing high-throughput sequencing data or for their integration within the approximate Bayesian computation framework.

How energy conservation limits our measurements.

Observations in quantum mechanics are subject to complex restrictions arising from the principle of energy conservation. Determining such restrictions, however, has been so far an elusive task, and only partial results are known. In this Letter, we discuss how constraints on the energy spectrum of a measurement device translate into limitations on the measurements which we can effect on a target system with a nonconstant energy operator. We provide efficient algorithms to characterize such limitations and, in case the target is a two-level quantum system, we quantify them exactly. Our Letter, thus, identifies the boundaries between what is possible or impossible to measure, i.e., between what we can see or not, when energy conservation is at stake.

Quantifying Einstein-Podolsky-Rosen steering.

Einstein-Podolsky-Rosen steering is a form of bipartite quantum correlation that is intermediate between entanglement and Bell nonlocality. It allows for entanglement certification when the measurements performed by one of the parties are not characterized (or are untrusted) and has applications in quantum key distribution. Despite its foundational and applied importance, Einstein-Podolsky-Rosen steering lacks a quantitative assessment. Here we propose a way of quantifying this phenomenon and use it to study the steerability of several quantum states. In particular, we show that every pure entangled state is maximally steerable and the projector onto the antisymmetric subspace is maximally steerable for all dimensions; we provide a new example of one-way steering and give strong support that states with positive-partial transposition are not steerable.

Robust and versatile black-box certification of quantum devices.

Self-testing refers to the fact that, in some quantum devices, both states and measurements can be assessed in a black-box scenario, on the sole basis of the observed statistics, i.e., without reference to any prior device calibration. Only a few examples of self-testing are known, and they just provide nontrivial assessment for devices performing unrealistically close to the ideal case. We overcome these difficulties by approaching self-testing with the semidefinite programing hierarchy for the characterization of quantum correlations. This allows us to improve dramatically the robustness of previous self-testing schemes; e.g., we show that a Clauser-Horne-Shimony-Holt violation larger than 2.57 certifies a singlet fidelity of more than 70%. In addition, the versatility of the tool brings about self-testing of hitherto impossible cases, such as the robust self-testing of nonmaximally entangled two-qutrit states in the Collins-Gisin-Linden-Massar-Popescu scenario.

Dimension witnesses and quantum state discrimination.

Dimension witnesses allow one to test the dimension of an unknown physical system in a device-independent manner, that is, without placing assumptions about the functioning of the devices used in the experiment. Here we present simple and general dimension witnesses for quantum systems of arbitrary Hilbert space dimension. Our approach is deeply connected to the problem of quantum state discrimination, hence establishing a strong link between these two research topics. Finally, our dimension witnesses can distinguish between classical and quantum systems of the same dimension, making them potentially useful for quantum information processing.

Genome Scan of Rice Landrace Populations Collected Across Time Revealed Climate Changes' Selective Footprints in the Genes Network Regulating Flowering Time.

Analyses of the genetic bases of plant adaptation to climate changes, using genome-scan approaches, are often conducted on natural populations, under hypothesis of out-crossing reproductive regime. We report here on a study based on diachronic sampling (1980 and 2011) of the autogamous crop species, Oryza sativa and Oryza glaberrima, in the tropical forest and the Sudanian savannah of West Africa. First, using historical meteorological data we confirmed changes in temperatures (+ 1 °C on average) and rainfall regime (less predictable and reduced amount) in the target areas. Second, phenotyping the populations for phenology, we observed significantly earlier heading time in the 2010 samples. Third, implementing two genome-scan methods (one of which specially developed for selfing species) on genotyping by sequencing genotypic data of the two populations, we detected 31 independent selection footprints. Gene ontology analysis detected significant enrichment of these selection footprints in genes involved in reproductive processes. Some of them bore known heading time QTLs and genes, including OsGI, Hd1 and OsphyB. This rapid adaptive evolution, originated from subtle changes in the standing variation in genetic network regulating heading time, did not translate into predominance of multilocus genotypes, as it is often the case in selfing plants, and into notable selective sweeps. The high adaptive potential observed results from the multiline genetic structure of the rice landraces, and the rather large and imbricated genetic diversity of the rice meta-population at the farm, the village and the region levels, that hosted the adaptive variants in multiple genetic backgrounds before the advent of the environmental selective pressure. Our results illustrate the evolution of in situ diversity through processes of human and natural selection, and provide a model for rice breeding and cultivars deployment strategies aiming resilience to climate changes. It also calls for further development of population genetic models for adaptation of plant populations to environmental changes. To our best knowledge, this is the first study dealing with climate-changes' selective footprint in crops.

Quantum steering and spacelike separation.

In nonrelativistic quantum mechanics, measurements performed by separate observers are modeled via tensor products. In algebraic quantum field theory, though, local observables corresponding to spacelike separated parties are just required to commute. The problem of determining whether these two definitions of separation lead to the same set of bipartite correlations is known in nonlocality as Tsirelson's problem. In this article, we prove that the analog of Tsirelson's problem in steering scenarios is false. That is, there exists a steering inequality that can or cannot be violated depending on how we define spacelike separation at the operator level.

Operational framework for nonlocality.

Because of the importance of entanglement for quantum information purposes, a framework has been developed for its characterization and quantification as a resource based on the following operational principle: entanglement among N parties cannot be created by local operations and classical communication, even when N-1 parties collaborate. More recently, nonlocality has been identified as another resource, alternative to entanglement and necessary for device-independent quantum information protocols. We introduce an operational framework for nonlocality based on a similar principle: nonlocality among N parties cannot be created by local operations and allowed classical communication even when N-1 parties collaborate. We then show that the standard definition of multipartite nonlocality, due to Svetlichny, is inconsistent with this operational approach: according to it, genuine tripartite nonlocality could be created by two collaborating parties. We finally discuss alternative definitions for which consistency is recovered.