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The Heisenberg-Robertson uncertainty relation quantitatively expresses the impossibility of jointly sharp preparation of incompatible observables. However it does not capture the concept of incompatible observables because it can be trivial…

We associate to every entanglement measure a family of measures which depend on a precision parameter, and which we call epsilon-measures of entanglement. Their definition aims at addressing a realistic scenario in which we need to estimate…

This work proposes a novel theoretical framework of robust limit analysis i.e. the computation of limit loads of structures in presence of uncertainties using limit analysis and robust optimization theories. We first derive generic robust…

A new measure of non-classical correlations is introduced and characterized. It tests the ability of using a state {\rho} of a composite system AB as a probe for a quantum illumination task [e.g. see S. Lloyd, Science 321, 1463 (2008)], in…

The robustness of multipartite entanglement of systems undergoing decoherence is of central importance to the area of quantum information. Its characterization depends however on the measure used to quantify entanglement and on how one…

Incompatible, i.e. non-jointly measurable quantum measurements are a necessary resource for many information processing tasks. It is known that increasing the number of distinct measurements usually enhances the incompatibility of a…

This dissertation will serve as an introduction to entanglement quantification, containing highly detailed proofs ensuring solid understanding of the subject. Specifically, we will review the properties of entanglement that should be…

Infinite determinantal measures introduced in this note are inductive limits of determinantal measures on an exhausting family of subsets of the phase space. Alternatively, an infinite determinantal measure can be described as a product of…

The paper deals with measures of nonlinearity. In state estimation, they are utilized i) to select a suitable state estimation algorithm by assessing the nonlinearity of a system model, ii) to adapt the estimation algorithm structure or…

We identify a phase transition between two kinds of volume-law entangled phases in non-local but few-body unitary dynamics with local projective measurements. In one phase, a finite fraction of the system belongs to a fully-entangled state,…

In the paper, we devote to defining an available measure to quantify the nonbilocal correlation in the entanglement-swapping experiment. Then we obtain analytical formulas to calculate the quantifier when the inputs are pure states. For the…

We propose a family of lower bounds for concurrence in quantum systems using mutually unbiased measurements, which prove more effective in entanglement estimation compared to existing methods. Through analytical and numerical examples, we…

We discuss entanglement of multiparticle quantum systems. We propose a potential measure of a type of entanglement of pure states of n qubits, the n-tangle. For a system of two qubits the n-tangle is equal to the square of the concurrence,…

An adjoint-based procedure to determine weaknesses, or, more generally the material properties of structures is developed and tested. Given a series of force and deformation/strain measurements, the material properties are obtained by…

The basin entropy is a simple idea that aims to measure the the final state unpredictability of multistable systems. Since 2016, the basin entropy has been widely used in different contexts of physics, from cold atoms to galactic dynamics.…

The entanglement content of superpositions of quantum states is investigated based on a measure called {\it concurrence}. Given a bipartite pure state in arbitrary dimension written as the quantum superposition of two other such states, we…

We develop a new entanglement measure by extending Jaeger's Minkowskian norm entanglement measure. This measure can be applied to a much wider class of multipartite mixed states, although still "quasi" in the sense that it is still…

We derive an experimentally observable lower bound on concurrence of mixed quantum states in terms of an entanglement witness, relating measurements on single states with those on two copies.

Problem of classification of all the set of entangled states is considered. Invariance of entangled states relative to transformations from a group of symmetry of qubit space leads to classification of all states of the system through…

It is shown that, despite strong nonlinearity, entanglement of formation of two-qubit state can be measured without prior state reconstruction. Collective measurements on small number of copies are provided that allow to determine quantum…