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We show that an information-theoretic property of Shannon's entropy power, known as concavity of entropy power, can be fruitfully employed to prove inequalities in sharp form. In particular, the concavity of entropy power implies the…
The half-line one-dimensional Coulomb potential is possibly the simplest D-dimensional model with physical solutions which has been proved to be successful to describe the behaviour of Rydberg atoms in external fields and the dynamics of…
Strong and general entropic and geometric Heisenberg limits are obtained, for estimates of multiparameter unitary displacements in quantum metrology, such as the estimation of a magnetic field from the induced rotation of a probe state in…
The notion of complexity of quantum states is quite different from uncertainty or information contents, and involves the tradeoff between its classical and quantum features. In this work, we we introduce a quantifier of complexity of…
Informationally complete measurements form the foundation of universal quantum state reconstruction, while quantum parameter estimation is based on the local structure of the manifold of quantum states. Here we establish a general link…
The information provided by a classical measurement is unambiguously determined by the mutual information between the output results and the measured quantity. However, quantum mechanically there are at least two notions of information…
We prove an inequality between the free entropy and the mutual free Fisher information for two projections, regarded as a free analog of the logarithmic Sobolev inequality. The proof is based on the random matrix approximation procedure via…
Entropic Dynamics (ED) is a framework in which Quantum Mechanics (QM) is derived as an application of entropic methods of inference. The magnitude of the wave function is manifestly epistemic: its square is a probability distribution. The…
We introduce a geometric formulation of quantum indeterminacy from which the standard uncertainty inequalities emerge as necessary consequences. Our approach is based on convex geometry in phase space and on methods from symplectic…
Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e.…
This Chapter develops a realist information-theoretic interpretation of the nonclassical features of quantum probabilities. On this view, what is fundamental in the transition from classical to quantum physics is the recognition that…
The thermodynamic uncertainty relation is an inequality stating that it is impossible to attain higher precision than the bound defined by entropy production. In statistical inference theory, information inequalities assert that it is…
Motivated by the corrected form of the entropy-area law, and with the help of von Neumann entropy of quantum matter, we construct an emergent spacetime by the virtue of the geometric language of statistical information manifolds. We discuss…
We summarise important recent advances in quantum metrology, in connection to experiments in cold gases, trapped cold atoms and photons. First we review simple metrological setups, such as quantum metrology with spin squeezed states, with…
We propose an extension of the quantum entropy power inequality for finite dimensional quantum systems, and prove a conditional quantum entropy power inequality by using the majorization relation as well as the concavity of entropic…
The invariant information introduced by Brukner and Zeilinger, Phys. Rev. Lett. 83, 3354 (1999), is reconsidered from the point of view of quantum state estimation. We show that it is directly related to the mean error of the standard…
Many-body states described by a Schr\"{o}dinger equation include states of overlapping waves of non-vanishing interaction energies. These peculiar states formed in many-body transitions remain in asymptotic regions, and lead a new component…
We apply geometric phase ideas to coherent states to shed light on interference phenomenon in the phase space description of continuous variable Cartesian quantum systems. In contrast to Young's interference characterized by path lengths,…
Quantum inequalities are lower bounds for local averages of quantum observables that have positive classical counterparts, such as the energy density or the Wick square. We establish such inequalities in general (possibly interacting)…
We establish an exact information-geometric inequality that remains valid regardless of the underlying dynamics, encompassing both Markovian and non-Markovian evolutions within the mixed-state domain. This inequality can be viewed as an…