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Quantum theory is notoriously counterintuitive, and yet remains entirely self-consistent when applied universally. Here we uncover a new manifestation of its unusual consequences. We demonstrate, theoretically and experimentally (by means…
Recently, Hajirasouliha and Raphael (WABI 2014) proposed a model for deconvoluting mixed tumor samples measured from a collection of high-throughput sequencing reads. This is related to understanding tumor evolution and critical cancer…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
Statistical hypothesis testing serves as statistical evidence for scientific innovation. However, if the reported results are intentionally biased, hypothesis testing no longer controls the rate of false discovery. In particular, we study…
We consider symmetries and reduction in non-relativistic many-body quantum mechanics, with the aim of identifying physically meaningful observables in systems such as molecules and crystalline solids. To this end, we propose a unified…
Making fair decisions is crucial to ethically implementing machine learning algorithms in social settings. In this work, we consider the celebrated definition of counterfactual fairness [Kusner et al., NeurIPS, 2017]. We begin by showing…
I raise some doubts concerning a protocol recently applied in an experiment (Walborn et al, Nature) to measure entanglement. The protocol is much simpler than other known entanglement-verification methods, but, I argue, needs assumptions…
From a quantum information perspective, verifying quantum coherence in a quantum experiment typically requires adjusting measurement settings or changing inputs. A paradigmatic example is that of a double-slit experiment, where observing…
Suppose that multiple experts (or learning algorithms) provide us with alternative Bayesian network (BN) structures over a domain, and that we are interested in combining them into a single consensus BN structure. Specifically, we are…
The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. Despite the reputation of learned NN models to behave as black boxes and…
Heisenberg's uncertainty principle was originally posed for the limit of the accuracy of simultaneous measurement of non-commuting observables as stating that canonically conjugate observables can be measured simultaneously only with the…
We study the computation complexity of Boolean functions in the quantum black box model. In this model our task is to compute a function $f:\{0,1\}\to\{0,1\}$ on an input $x\in\{0,1\}^n$ that can be accessed by querying the black box.…
Clustering methods such as k-means have found widespread use in a variety of applications. This paper proposes a formal testing procedure to determine whether a null hypothesis of a single cluster, indicating homogeneity of the data, can be…
We study the problem of testing composite hypotheses versus composite alternatives, using a convex duality approach. In contrast to classical results obtained by Krafft and Witting (Z. Wahrsch. Verw. Gebiete 7 (1967) 289--302), where…
Conformal Prediction (CP) stands out as a robust framework for uncertainty quantification, which is crucial for ensuring the reliability of predictions. However, common CP methods heavily rely on data exchangeability, a condition often…
Numerous algorithms have been produced for the fundamental problem of clustering under many different notions of fairness. Perhaps the most common family of notions currently studied is group fairness, in which proportional group…
In three papers Colbeck and Renner (Nature Communications 2:411, (2011); Phys. Rev. Lett. 108, 150402 (2012); arXiv:1208.4123) argued that "no alternative theory compatible with quantum theory and satisfying the freedom of choice assumption…
We investigate the structure of quantum proof systems by establishing collapse results that reveal simplifications in their complexity landscape. By extending classical theorems such as the Karp-Lipton theorem to quantum settings and…
State-of-the-art posted-price mechanisms for submodular bidders with $m$ items achieve approximation guarantees of $O((\log \log m)^3)$ [Assadi and Singla, 2019]. Their truthfulness, however, requires bidders to compute an NP-hard…
In the modern Bayesian view classical probability theory is simply an extension of conventional logic, i.e., a quantitative tool that allows for consistent reasoning in the presence of uncertainty. Classical theory presupposes, however,…