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The resources needed to conventionally characterize a quantum system are overwhelmingly large for high- dimensional systems. This obstacle may be overcome by abandoning traditional cornerstones of quantum measurement, such as general…
As a method to extract information from optical system, imaging can be viewed as a parameter estimation problem. The fundamental precision in locating one emitter or estimating the separation between two incoherent emitters is bounded below…
We consider the quantum field theory for a scalar model of the electromagnetic field interacting with a system of two-level atoms. In this setting, we show that it is possible to uniquely determine the density of atoms from measurements of…
In this paper we propose a method to estimate the density matrix \rho of a d-level quantum system by measurements on the N-fold system. The scheme is based on covariant observables and representation theory of unitary groups and it extends…
In many computational problems in engineering and science, function or model differentiation is essential, but also integration is needed. An important class of computational problems include so-called integro-differential equations which…
Quantum embedding methods enable the study of large, strongly correlated quantum systems by (usually self-consistent) decomposition into computationally manageable subproblems, in the spirit of divide-and-conquer methods. Among these,…
In this paper we consider inverse problems for resistor networks and for models obtained via the Finite Element Method (FEM) for the conductivity equation. These correspond to discrete versions of the inverse conductivity problem of…
The solutions to many problems in the mathematical, computational, and physical sciences often involve multidimensional integrals. A direct numerical evaluation of the integral incurs a computational cost that is exponential in the number…
Detecting entanglement in multipartite quantum states is an inherently probabilistic process, typically with a few measured samples. The level of confidence in entanglement detection quantifies the scheme's validity via the probability that…
Recent work suggests that quantum machine learning techniques can be used for classical image classification by encoding the images in quantum states and using a quantum neural network for inference. However, such work has been restricted…
We consider passive imaging tasks involving discrimination between known candidate objects and investigate the best possible accuracy with which the correct object can be identified. We analytically compute quantum-limited error bounds for…
We address the use of entanglement to improve the precision of generalized quantum interferometry, i.e. of binary measurements aimed to determine whether or not a perturbation has been applied by a given device. For the most relevant…
We introduce two methods for quantum process and detector tomography. In the quantum process tomography method, we develop an analytical procedure for projecting the linear inversion estimation of a quantum channel onto the set of…
We study identifiability for bilinear inverse problems under sparsity and subspace constraints. We show that, up to a global scaling ambiguity, almost all such maps are injective on the set of pairs of sparse vectors if the number of…
We consider the quantum dynamical evolution of a fully-connected quantum system subjected to random projective measurements and study the first detection time of an extended subspace of the Hilbert space. Exact analytical expressions are…
We investigate the quantum state discrimination task for sets of linear independent pure states with an intrinsic ordering. This structured discrimination problems allow for a novel scheme that provides a certified level of error, that is,…
We introduce two families of criteria for detecting and quantifying the entanglement of a bipartite quantum state of arbitrary local dimension. The first is based on measurements in mutually unbiased bases and the second is based on…
Quantum entanglement, after playing a significant role in the development of the foundations of quantum mechanics, has been recently rediscovered as a new physical resource with potential commercial applications such as, for example,…
We consider the problem of constructing quantum operations or channels, if they exist, that transform a given set of quantum states $\{\rho_1, \dots, \rho_k\}$ to another such set $\{\hat\rho_1, \dots, \hat\rho_k\}$. In other words, we must…
This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We introduce the concept of what we define as the optimal projector…