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The detection and characterization of quantum coherence is of fundamental importance both in the foundations of quantum theory as well as for the rapidly developing field of quantum technologies, where coherence has been linked to quantum…
Quantum computers can be considered as a natural means for performing machine learning tasks for inherently quantum labeled data. Many quantum machine learning techniques have been developed for solving classification problems, such as…
The quantum measurement problem considered for the model of measuring system (MS) consist of measured state S (particle), detector D and information processing device (observer) $O$ interacting with S,D. For 'external' observer $O'$ MS…
Quantum theory allows the traversing of multiple channels in a superposition of different orders. When the order in which the channels are traversed is controlled by an auxiliary quantum system, various unknown parameters of the channels…
Estimation of physical observables for unknown quantum states is an important problem that underlies a wide range of fields, including quantum information processing, quantum physics, and quantum chemistry. In the context of quantum…
Measurement in quantum mechanics is generally described as an irreversible process that perturbs the wavefunction describing a quantum system. In this work we establish a formal connection between the measurement description within the…
In quantum information theory, the reliable and effective detection of entanglement is of paramount importance. However, given an unknown state, assessing its entanglement is a challenging task. To attack this problem, we investigate the…
In this paper, we address learning problems for high dimensional data. Previously, oblivious random projection based approaches that project high dimensional features onto a random subspace have been used in practice for tackling…
The concept of randomized measurements on individual particles has proven to be useful for analyzing quantum systems and is central for methods like shadow tomography of quantum states. We introduce $\textit{collective}$ randomized…
Variational algorithms are a promising paradigm for utilizing near-term quantum devices for modeling electronic states of molecular systems. However, previous bounds on the measurement time required have suggested that the application of…
There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity. Unfortunately, they require the use of entangled measurements across many copies of…
Acquiring information about an unknown qubit in a superposition of two states is essential in any computation process. Quantum measurement, or sharp measurement, is usually used to read the information contents of that unknown qubit system.…
Many quantum algorithms contain an important subroutine, the quantum amplitude estimation. As the name implies, this is essentially the parameter estimation problem and thus can be handled via the established statistical estimation theory.…
Quantum mechanics predicts the existence of intrinsically random processes. Contrary to classical randomness, this lack of predictability can not be attributed to ignorance or lack of control. Here we find the optimal method to quantify the…
In quantum metrology, one of the major applications of quantum technologies, the ultimate precision of estimating an unknown parameter is often stated in terms of the Cram\'er-Rao bound. Yet, the latter is no longer guaranteed to carry an…
Quantum contextuality is a limitation on deterministic hidden variable models, testable in measurement scenarios where outcomes differ under quantum or classical descriptions due to a common set of constraints. When considering measurements…
Quantum sensing harnesses the unique properties of quantum systems to enable precision measurements of physical quantities such as time, magnetic and electric fields, acceleration, and gravitational gradients well beyond the limits of…
Measurements are essential for the processing and protection of information in quantum computers. They can also induce long-range entanglement between unmeasured qubits. However, when post-measurement states depend on many non-deterministic…
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.…
We consider statistical learning problems in which data are observed as a set of probability measures. Optimal transport (OT) is a popular tool to compare and manipulate such objects, but its computational cost becomes prohibitive when the…