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Self-testing is a method to certify devices from the result of a Bell test. Although examples of noise tolerant self-testing are known, it is not clear how to deal efficiently with a finite number of experimental trials to certify the…
We consider the task of quantum state certification: given a description of a hypothesis state $\sigma$ and multiple copies of an unknown state $\rho$, a tester aims to determine whether the two states are equal or $\epsilon$-far in trace…
The generation of certifiable randomness is one of the most promising applications of quantum technologies. Furthermore, the intrinsic non-locality of quantum correlations allow us to certify randomness in a device-independent way, i.e. one…
While quantum state tomography is notoriously hard, most states hold little interest to practically-minded tomographers. Given that states and unitaries appearing in Nature are of bounded gate complexity, it is natural to ask if efficient…
Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data…
Within psychology, neuroscience and artificial intelligence, there has been increasing interest in the proposal that the brain builds probabilistic models of sensory and linguistic input: that is, to infer a probabilistic model from a…
Measurement-device-independent quantum key distribution (MDI-QKD), which is immune to all detector side-channel attacks, is the most promising solution to the security issues in practical quantum key distribution systems. Though several…
A particularly challenging problem in AI safety is providing guarantees on the behavior of high-dimensional autonomous systems. Verification approaches centered around reachability analysis fail to scale, and purely statistical approaches…
Key distribution plays a fundamental role in cryptography. Currently, the quantum scheme stands as the only known method for achieving unconditionally secure key distribution. This method has been demonstrated over distances of 508 and 1002…
Using the previously shared Einstein-Podolsky-Rosen pairs, a proposal which can be used to distribute a quantum key and identify the user's identification simultaneously is presented. In this scheme, two local unitary operations and the…
The performance of quantum key distribution (QKD) is severely limited by multiphoton emissions, due to the photon-number-splitting attack. The most efficient solution, the decoy-state method, requires that the phases of all transmitted…
We investigate a fundamental property of device independent security in quantum cryptography by characterizing probability distributions which are necessarily independent of the measurement results of any eavesdropper. We show that…
Self-testing is a method of quantum state and measurement estimation that does not rely on assumptions about the inner working of the used devices. Its experimental realization has been limited to sources producing single quantum states so…
Hypothesis testing is a central problem in statistical analysis, and there is currently a lack of differentially private tests which are both statistically valid and powerful. In this paper, we develop several new differentially private…
Numerical security proofs offer a versatile approach for evaluating the secret-key generation rate of quantum key distribution (QKD) protocols. However, existing methods typically require perfect source characterization, which is…
We study distributed goodness-of-fit testing for discrete distribution under bandwidth and differential privacy constraints. Information constraint distributed goodness-of-fit testing is a problem that has received considerable attention…
In the near future, there will likely be special-purpose quantum computers with 40-50 high-quality qubits. This paper lays general theoretical foundations for how to use such devices to demonstrate "quantum supremacy": that is, a clear…
Quantum key distribution promises unconditionally secure communications. However, as practical devices tend to deviate from their specifications, the security of some practical systems is no longer valid. In particular, an adversary can…
Pattern recognition is a central topic in Learning Theory with numerous applications such as voice and text recognition, image analysis, computer diagnosis. The statistical set-up in classification is the following: we are given an i.i.d.…
In classical stochastic theory, the joint probability distributions of a stochastic process obey by definition the Kolmogorov consistency conditions. Interpreting such a process as a sequence of physical measurements with probabilistic…