Related papers: From quantum Bayesian inference to quantum tomogra…
A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the…
It is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution, that is that its integral is one and that the marginal properties are satisfied.…
Quantum state tomography (QST) is a fundamental task in quantum information science that aims to reconstruct unknown quantum states from measurement data. However, the exponential growth of Hilbert-space dimension with system size makes…
We propose a nonextensive generalization (q parametrized) of the von Neumann equation for the density operator. Our model naturally leads to the phenomenon of decoherence, and unitary evolution is recovered in the limit of q -> 1. The…
We present a general formalism for charecterizing 2-time quantum states, describing pre- and post-selected quantum systems. The most general 2-time state is characterized by a `density vector' that is independent of measurements performed…
Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…
Capturing the correlation emerging between constituents of many-body systems accurately is one of the key challenges for the appropriate description of various systems whose properties are underpinned by quantum mechanical fundamentals.…
In this work, we consider compressed sensing reconstruction from $M$ measurements of $K$-sparse structured signals which do not possess a writable correlation model. Assuming that a generative statistical model, such as a Boltzmann machine,…
Macroscopically populated quantum superpositions pose a question to what extent macroscopic world obeys quantum mechanical laws. Recently such superpositions for light, generated by optimal quantum cloner, were demonstrated. They are of…
Quantum state tomography (QST) for reconstructing pure states requires exponentially increasing resources and measurements with the number of qubits by using state-of-the-art quantum compressive sensing (CS) methods. In this article, QST…
Finite mixture of Gaussian distributions provide a flexible semi-parametric methodology for density estimation when the variables under investigation have no boundaries. However, in practical applications variables may be partially bounded…
We describe an exact, flexible, and computationally efficient algorithm for a joint estimation of the large-scale structure and its power-spectrum, building on a Gibbs sampling framework and present its implementation ARES (Algorithm for…
This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either…
Compressed sensing is triggering a major evolution in signal acquisition. It consists in sampling a sparse signal at low rate and later using computational power for its exact reconstruction, so that only the necessary information is…
This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…
We show that the von Neumann's algorithm of reduction (i.e. the algorithm of calculating the density matrix of the observable subsystem from the density matrix of the closed quantum system) corresponds to the special approximation at which…
A system composed of identical spins and described by a quantum mechanical pure state is analyzed within the statistical framework presented in Part I of this work. We explicitly derive the typical values of the entropy, of the energy, and…
The range of a quantum measurement is the set of outcome probability distributions that can be produced by varying the input state. We introduce data-driven inference as a protocol that, given a set of experimental data as a collection of…
The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…
Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy…