Related papers: Geometric inequalities from phase space translatio…
We obtain large sieve type inequalities for the Rayleigh quotient of the restriction of phase space representations of higher rank operators, via an operator analogue of the short-time Fourier transform (STFT). The resulting bounds are…
The coupling between internal degrees of freedom of quantum systems and their overall motion in an external gravitational field plays a central role in multiple extensions of Einstein's equivalence principle to quantum physics. While…
We apply the classical data processing inequality to quantum metrology to show that manipulating the classical information from a quantum measurement cannot aid in the estimation of parameters encoded in quantum states. We further derive a…
In most quantum technologies, measurements need to be performed on the parametrized quantum states to transform the quantum information to classical information. The measurements, however, inevitably distort the information. The…
In recent years, various quantum inequalities have been established on quantum symmetries in the framework of quantum Fourier analysis. We provide a detailed introduction to quantum inequalities including Hausdorff-Young inequality, Young's…
There are several inequalities in physics which limit how well we can process physical systems to achieve some intended goal, including the second law of thermodynamics, entropy bounds in quantum information theory, and the uncertainty…
This paper considers an entropy-power inequality (EPI) of Costa and presents a natural vector generalization with a real positive semidefinite matrix parameter. This new inequality is proved using a perturbation approach via a fundamental…
The classical statistics indication for the impossibility to derive quantum mechanics from classical mechanics is proved. The formalism of the statistical Fisher information is used. Next the Fisher information as a tool of the construction…
Quantum channel estimation and discrimination are fundamentally related information processing tasks of interest in quantum information science. In this paper, we analyze these tasks by employing the right logarithmic derivative Fisher…
It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is…
Divergences often play important roles for study in information science so that it is indispensable to investigate their fundamental properties. There is also a mathematical significance of such results. In this paper, we introduce some…
Markov Random Field models are powerful tools for the study of complex systems. However, little is known about how the interactions between the elements of such systems are encoded, especially from an information-theoretic perspective. In…
Quantum generalizations of the Fisher information are important in quantum information science, with applications in high energy and condensed matter physics and in quantum estimation theory, machine learning, and optimization. One can…
This paper is twofold. In the first part, we present a refinement of the R\'enyi Entropy Power Inequality (EPI) recently obtained in \cite{BM16}. The proof largely follows the approach in \cite{DCT91} of employing Young's convolution…
Sobolev-type inequalities have been extensively studied in the frameworks of real-valued functions and non-commutative $\mathbb{L}_p$ spaces, and have proven useful in bounding the time evolution of classical/quantum Markov processes, among…
In this study, we obtained the position-momentum uncertainties and some uncertainty relations for the P\"oschl-Teller-type potential for any $\ell$. The radial expectation values of $r^{-2}$, $r^{2}$ and $p^{2}$ are obtained from which the…
We prove a lower bound on the relative entropy between two finite-dimensional states in terms of their entropy difference and the dimension of the underlying space. The inequality is tight in the sense that equality can be attained for any…
We strengthen the connection between Information Theory and quantum-mechanical systems using a recently developed dequantization procedure whereby quantum fluctuations latent in the quantum momentum are suppressed. The dequantization…
Quantum mechanics gives a new breakthrough to the field of parameter estimation. In the realm of quantum metrology, the precision of parameter estimation is limited by the quantum Fisher information. We introduce the measures of partial…
The interferometric power of a bipartite quantum state quantifies the precision, measured by quantum Fisher information, that such a state enables for the estimation of a parameter embedded in a unitary dynamics applied to one subsystem…