Fair Sampling Research Articles

Fair Sampling in Diffusion Models through Switching Mechanism

Diffusion models have shown their effectiveness in generation tasks by well-approximating the underlying probability distribution. However, diffusion models are known to suffer from an amplified inherent bias from the training data in terms of fairness. While the sampling process of diffusion models can be controlled by conditional guidance, previous works have attempted to find empirical guidance to achieve quantitative fairness. To address this limitation, we propose a fairness-aware sampling method called \textit{attribute switching} mechanism for diffusion models. Without additional training, the proposed sampling can obfuscate sensitive attributes in generated data without relying on classifiers. We mathematically prove and experimentally demonstrate the effectiveness of the proposed method on two key aspects: (i) the generation of fair data and (ii) the preservation of the utility of the generated data.

Extending the fair sampling assumption using causal diagrams

Discarding undesirable measurement results in Bell experiments opens the detection loophole that prevents a conclusive demonstration of nonlocality. As closing the detection loophole represents a major technical challenge for many practical Bell experiments, it is customary to assume the so-called fair sampling assumption (FSA) that, in its original form, states that the collectively postselected statistics are a fair sample of the ideal statistics. Here, we analyze the FSA from the viewpoint of causal inference: We derive a causal structure that must be present in any causal model that faithfully encapsulates the FSA. This provides an easy, intuitive, and unifying approach that includes different accepted forms of the FSA and underlines what is really assumed when using the FSA. We then show that the FSA can not only be applied in scenarios with non-ideal detectors or transmission losses, but also in ideal experiments where only parts of the correlations are postselected, e.g., when the particles' destinations are in a superposition state. Finally, we demonstrate that the FSA is also applicable in multipartite scenarios that test for (genuine) multipartite nonlocality.

Minimum detection efficiency for testing a multi-particle Bell inequality

Bell’s inequality provides a remarkable way to test the consistency between quantum mechanics and classic local realistic theory. However, experimental demonstrations of the loophole-free Bell test are challenging and only recently have been demonstrated with bipartite systems. A central obstacle for the photonic system is that the sampling efficiency, including the collection and detection efficiencies, must be above a certain threshold. We here generalize two-particle Eberhard’s inequality to the n-particle systems and derive a Bell-type inequality for multi-particle systems, which significantly relaxes this threshold. Furthermore, an experimental proposal to achieve a multi-partite Bell test without the fair sampling assumption is presented for the case of three particles. For any given value of the sampling efficiency, we give the optimal configurations for actual implementation, the optimal state, the maximum background noise that the system can tolerate, and the lowest fidelity of the quantum state. We believe our work can serve as a recipe for experimentalists planning to violate local realism using a multi-partite quantum state without the sampling loophole.

Experimental Demonstration that No Tripartite-Nonlocal Causal Theory Explains Nature's Correlations.

Quantum theory predicts the existence of genuinely tripartite-entangled states, which cannot be obtained from local operations over any bipartite-entangled states and unlimited shared randomness. Some of us recently proved that this feature is a fundamental signature of quantum theory. The state |GHZ_{3}⟩=(|000⟩+|111⟩)/sqrt[2] gives rise to tripartite quantum correlations that cannot be explained by any causal theory limited to bipartite nonclassical common causes of any kind (generalizing entanglement) assisted with unlimited shared randomness. Hence, any conceivable physical theory that would reproduce quantum predictions will necessarily include genuinely tripartite resources. In this Letter, we verify that such tripartite correlations are experimentally achievable. We derive a new device-independent witness capable of falsifying causal theories wherein nonclassical resources are merely bipartite. Using a high-performance photonic |GHZ_{3}⟩ state with fidelities of 0.9741±0.002, we provide a clear experimental violation of that witness by more than 26.3 standard deviations, under the locality and fair sampling assumption. We generalize our Letter to the |GHZ_{4}⟩ state, obtaining correlations that cannot be explained by any causal theory limited to tripartite nonclassical common causes assisted with unlimited shared randomness.

How majority-vote crossover and estimation-of-distribution algorithms cope with fitness valleys

The benefits of using crossover in crossing fitness gaps have been studied extensively in evolutionary computation. Recent runtime results show that majority-vote crossover is particularly efficient at optimizing the well-known Jump benchmark function that includes a fitness gap next to the global optimum. Also estimation-of-distribution algorithms (EDAs), which use an implicit crossover, are much more efficient on Jump than typical mutation-based algorithms. However, the allowed gap size for polynomial runtimes with EDAs is at most logarithmic in the problem dimension n.In this paper, we investigate variants of the Jump function where the gap is shifted and appears in the middle of the typical search trajectory. Such gaps can still be overcome efficiently in time O(nlog⁡n) by majority-vote crossover and an estimation-of-distribution algorithm, even for gap sizes almost n. However, if the global optimum is located in the gap instead of the usual all-ones string, majority-vote crossover would nevertheless approach the all-ones string and be highly inefficient. In sharp contrast, an EDA can still find such a shifted optimum efficiently. Thanks to a general property called fair sampling, the EDA will with high probability sample from almost every fitness level of the function, including levels in the gap, and sample the global optimum even though the overall search trajectory points towards the all-ones string. Finally, we derive limits on the gap size allowing efficient runtimes for the EDA.

Phylogeny and evolution of morphological structures in a highly diverse lineage of fruiting-body-forming amoebae, order Trichiales (Myxomycetes, Amoebozoa)

Early phylogenetic studies refuted most previous assumptions concerning the evolution of the morphological traits in the fruiting bodies of the order Trichiales and did not detect discernible evolutionary patterns, yet they were based on a limited number of species. We infer a new Trichiales phylogeny based on three independently inherited genetic regions (nuclear and mitochondrial), with a fair taxonomic sampling encompassing its broad diversity. Besides, we study the evolutionary history of some key morphological characters. According to the new phylogeny, most fruiting body traits in Trichiales systematics do not represent exclusive synapomorphies or autapomorphies for most monophyletic groups. Instead, the evolution of the features derived from the peridium, stalk, capillitium, and spores showed intricate patterns, and character state transitions occurred rather within- than between clades. Thus, we should consider other evolutionary scenarios instead of assuming the homology of some characters. According to these results, we propose a new classification of Trichiales, including the creation of a new genus, Gulielmina, the resurrection of the family Dictydiaethaliaceae and the genus Ophiotheca, and the proposal of 13 new combinations for species of the genera Arcyria (1), Hemitrichia (2), Ophiotheca (2), Oligonema (4), Gulielmina (3), and Perichaena (1).

Experimental Demonstration of Genuine Tripartite Nonlocality under Strict Locality Conditions.

Nonlocality captures one of the counterintuitive features of nature that defies classical intuition. Recent investigations reveal that our physical world's nonlocality is at least tripartite; i.e., genuinely tripartite nonlocal correlations in nature cannot be reproduced by any causal theory involving bipartite nonclassical resources and unlimited shared randomness. Here, by allowing the fair sampling assumption and postselection, we experimentally demonstrate such genuine tripartite nonlocality in a network under strict locality constraints that are ensured by spacelike separating all relevant events and employing fast quantum random number generators and high-speed polarization measurements. In particular, for a photonic quantum triangular network we observe a locality-loophole-free violation of the Bell-type inequality by 7.57 standard deviations for a postselected tripartite Greenberger-Horne-Zeilinger state of fidelity (93.13±0.24)%, which convincingly disproves the possibility of simulating genuine tripartite nonlocality by bipartite nonlocal resources with globally shared randomness.

Fair Sampling Error Analysis on NISQ Devices

We study the status of fair sampling on Noisy Intermediate Scale Quantum (NISQ) devices, in particular the IBM Q family of backends. Using the recently introduced Grover Mixer-QAOA algorithm for discrete optimization, we generate fair sampling circuits to solve six problems of varying difficulty, each with several optimal solutions, which we then run on twenty backends across the IBM Q system. For a given circuit evaluated on a specific set of qubits, we evaluate: how frequently the qubits return an optimal solution to the problem, the fairness with which the qubits sample from all optimal solutions, and the reported hardware error rate of the qubits. To quantify fairness, we define a novel metric based on Pearson’s χ 2 test. We find that fairness is relatively high for circuits with small and large error rates, but drops for circuits with medium error rates. This indicates that structured errors dominate in this regime, while unstructured errors, which are random and thus inherently fair, dominate in noisier qubits and longer circuits. Our results show that fairness can be a powerful tool for understanding the intricate web of errors affecting current NISQ hardware.

Quantum spatial correlations imaging through thick scattering media: experiments and comparison with simulations of the biphoton wave function

We first extend our recent experiments of spatial quantum correlations imaging through thin scattering media to the case where two phase scattering plates placed respectively in the image and the Fourier planes of the biphoton source, mimics a thick scattering medium. Spatial correlations between twin photons are still detected at the quantum level but no more in the form of two-photon speckle-like patterns. However, we show that spatial entanglement of very-high dimensionality can be retrieved through thick scattering media with moderate losses and without any fair sampling assumption in the space and time domains. Second, a numerical simulation of the biphoton wave function is developed and applied to our experimental situation, with a good agreement.

Analysis of Assumptions in BIG Bell Test Experiments

AbstractRecently, a group of experiments tested local realism with random choices prepared by humans. These various tests were subject to additional assumptions, which lead to loopholes in the interpretations of almost all of the experiments. Among these assumptions are fair sampling, no signaling, and faithful reproduction of a Bell‐type quantum model. The data from 9 of 13 experiments were examined and occurring anomalies were analyzed in view of the above assumptions. It is concluded that further tests of local realism need better setup calibration to avoid apparent signaling or necessity of the complicated underlying quantum model.

Bell nonlocality with intensity information only

We address the problem of detecting bipartite Bell nonlocality whenever the only experimental information are the intensities produced in each run of the experiment by an unknown number of particles. We point out that this scenario naturally occurs in Bell experiments with parametric down-conversion when the crystal is pumped by strong pulses, in Bell tests with distant sources and in which particles suffer different delays during their flight, in Bell experiments using living cells as photo detectors, and in Bell experiments where the pairing information is physically removed. We show that, although Bell nonlocality decreases as the number of particles increases, if the parties can distinguish arbitrarily small differences of intensities and the visibility is larger than $0.98$, then Bell nonlocality can still be experimentally detected with fluxes of up to $15$ particles. We show that this prediction can be tested with current equipment in a Bell experiment where pairing information is physically removed, but requires the assumption of fair sampling.

Generating entangled Schrödinger cat states using a number state and a beam splitter

Passing a photon number state through a balanced beam splitter will produce an entangled state in which the phases of the two output beams are highly correlated. This entangled state can be viewed as a generalized form of a Schrodinger cat state where there is an equal probability amplitude for all possible phases. We show that Bell's inequality can be violated using this entangled state and two distant measuring devices that consist of a single-photon interferometer with a Kerr medium in one path, a set of single-photon detectors, and postselection based on a homodyne measurement. These entangled states are sensitive to photon loss and a violation of Bell's inequality requires either that the losses are inherently small or that their effects have been minimized using linear optics techniques [M. Micuda et al., Phys. Rev. Lett. 109, 180503 (2012)]. Somewhat surprisingly, the use of the fair sampling assumption is not required for a violation of Bell's inequality despite the use of postselection if the measurements are made in the correct order.

Rapid fair sampling of the XY spin Hamiltonian with a laser simulator

Coupled oscillators such as lasers, OPO's and BEC polaritons can rapidly and efficiently dissipate into a stable phase locked state that can be mapped onto the minimal energy (ground state) of classical spin Hamiltonians. However, for degenerate or near degenerate ground state manifolds, statistical fair sampling is required to obtain a complete knowledge of the minimal energy state, which needs many repetitions of simulations under identical conditions. We show that with dissipatively coupled lasers such fair sampling can be achieved rapidly and accurately by exploiting the many longitudinal modes of each laser to form an ensemble of identical but independent simulators, acting in parallel. We fairly sampled the ground state manifold of square, triangular and Kagome lattices by measuring their coherence function identifying manifolds composed of a single, doubly degenerate, and highly degenerate ground states, respectively.

Entanglement-based secure quantum cryptography over 1,120 kilometres.

Quantum key distribution (QKD)1-3 is a theoretically secure way of sharing secret keys between remote users. It has been demonstrated in a laboratory over a coiled optical fibre up to 404 kilometres long4-7. In the field, point-to-point QKD has been achieved from a satellite to a ground station up to 1,200 kilometres away8-10. However, real-world QKD-based cryptography targets physically separated users on the Earth, for which the maximum distance has been about 100 kilometres11,12. The use of trusted relays can extend these distances from across a typical metropolitan area13-16 to intercity17 and even intercontinental distances18. However, relays pose security risks, which can be avoided by using entanglement-based QKD, which has inherent source-independent security19,20. Long-distance entanglement distribution can be realized using quantum repeaters21, but the related technology is still immature for practical implementations22. The obvious alternative for extending the range of quantum communication without compromising its security is satellite-based QKD, but so far satellite-based entanglement distribution has not been efficient23 enough to support QKD. Here we demonstrate entanglement-based QKD between two ground stations separated by 1,120 kilometres at a finite secret-key rate of 0.12 bits per second, without the need for trusted relays. Entangled photon pairs were distributed via two bidirectional downlinks from the Micius satellite to two ground observatories in Delingha and Nanshan in China. The development of a high-efficiency telescope and follow-up optics crucially improved the link efficiency. The generated keys are secure for realistic devices, because our ground receivers were carefully designed to guarantee fair sampling and immunity to all known side channels24,25. Our method not only increases the secure distance on the ground tenfold but also increases the practical security of QKDto an unprecedented level.

Sphetcher: Spherical Thresholding Improves Sketching of Single-Cell Transcriptomic Heterogeneity

SummaryThe massive size of single-cell RNA sequencing datasets often exceeds the capability of current computational analysis methods to solve routine tasks such as detection of cell types. Recently, geometric sketching was introduced as an alternative to uniform subsampling. It selects a subset of cells (the sketch) that evenly cover the transcriptomic space occupied by the original dataset, to accelerate downstream analyses and highlight rare cell types. Here, we propose algorithm Sphetcher that makes use of the thresholding technique to efficiently pick representative cells within spheres (as opposed to the typically used equal-sized boxes) that cover the entire transcriptomic space. We show that the spherical sketch computed by Sphetcher constitutes a more accurate representation of the original transcriptomic landscape. Our optimization scheme allows to include fairness aspects that can encode prior biological or experimental knowledge. We show how a fair sampling can inform the inference of the trajectory of human skeletal muscle myoblast differentiation.

How post-selection affects device-independent claims under the fair sampling assumption

Device-independent certifications employ Bell tests to guarantee the proper functioning of an apparatus from the sole knowledge of observed measurement statistics, i.e. without assumptions on the internal functioning of the devices. When these Bell tests are implemented with devices having too low efficiency, one has to post-select the events that lead to successful detections and thus rely on a fair sampling assumption. The question that we address in this paper is what remains of a device-independent certification under fair sampling. We provide an intuitive description of post-selections in terms offiltersand define the fair sampling assumption as a property of these filters, equivalent to the definition introduced in Ref. \cite{Berry10}. When this assumption is fulfilled, the post-selected data is reproduced by an ideal experiment where lossless devices measure afilteredstate which can be obtained from theactualstate via local probabilistic maps. Trusted conclusions can thus be obtained on the quantum properties of this filtered state and the corresponding measurement statistics can reliably be used, e.g., for randomness generation or quantum key distribution. We also explore a stronger notion of fair sampling leading to the conclusion that the post-selected data is a fair representation of the data that would be obtained with lossless detections. Furthermore, we show that our conclusions hold in cases of small deviations from exact fair sampling. Finally, we describe setups previously or potentially used in Bell-type experiments under fair sampling and identify the underlying device-specific assumptions.

Fair Sampling by Simulated Annealing on Quantum Annealer

Conventional quantum annealing does not sample all ground states fairly. We demonstrate that fair sampling can be achieved by performing simulated annealing on a quantum annealer. We discuss the problems that occur when implementing this method and propose an alternative way to overcome them. We numerically verify the fair sampling ability of our method in a small-scale toy model.

Experimental certification of an informationally complete quantum measurement in a device-independent protocol

Minimal informationally complete positive operator-valued measures (MIC-POVMs) are special kinds of measurement in quantum theory in which the statistics of their d 2 -outcomes are enough to reconstruct any d -dimensional quantum state. For this reason, MIC-POVMs are referred to as standard measurements for quantum information. Here, we report an experiment with entangled photon pairs that certifies, for what we believe is the first time, a MIC-POVM for qubits following a device-independent protocol (i.e., modeling the state preparation and the measurement devices as black boxes, and using only the statistics of the inputs and outputs). Our certification is achieved under the assumption of freedom of choice, no communication, and fair sampling.

Poor taxonomic sampling undermines nomenclatural stability: A reply to Roxo et al. (2019).

A recent study based on genomic data by Roxo et al. (2019) provided a phylogeny of the Loricariidae, the largest catfish family and second largest Neotropical fish family with approximately 1,000 species. The study represents a valuable and innovative contribution for understanding higher-level relationships within the family. The phylogenetic tree inferred by Roxo et al. (2019) thoroughly corroborates the monophyly and relationships of most currently accepted subfamilies of Loricariidae, based on a fair taxon sampling (nearly 14% of the species in the family) representing most genera of each but one of the subfamilies, the Lithogeninae, the sister-group of the remaining members of the family (Pereira & Reis, 2017; Reis et al., 2017). In addition to a hypothesis of relationships, Roxo et al. (2019) also proposed a series of lower-level taxonomic changes, which are deemed premature considering that the taxonomic sampling of the study targeted higher-level clades, and go against one of the pillars of biological classification: nomenclatural stability (e.g., Heterick & Majer, 2018; Beninger & Backeljau, 2019). Here we (1) discuss implications of inadequate taxonomic sampling as a basis for changes in classification of species; (2) explain why the taxonomic sampling design of Roxo et al. (2019) is inadequate for the proposed nomenclatural changes; and (3) advocate that changes to classifications must be grounded on phylogenies with dense sampling of taxa at the relevant level.

Uncertain fate of fair sampling in quantum annealing

Recently, it was demonstrated both theoretically and experimentally on the D-Wave quantum annealer that transverse-field quantum annealing does not find all ground states with equal probability. In particular, it was proposed that more complex driver Hamiltonians beyond transverse fields might mitigate this shortcoming. Here, we investigate the mechanisms of (un)fair sampling in quantum annealing. While higher-order terms can improve the sampling for selected small problems, we present multiple counterexamples where driver Hamiltonians that go beyond transverse fields do not remove the sampling bias. Using perturbation theory we explain why this is the case. In addition, we present large-scale quantum Monte Carlo simulations for spin glasses with known degeneracy in two space dimensions and demonstrate that the fair-sampling performance of quadratic driver terms is comparable to standard transverse-field drivers. Our results suggest that quantum annealing machines are not well suited for sampling applications, unless post-processing techniques to improve the sampling are applied.