Related papers: Inequalities for Quantum Entropy: A Review with Co…
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are…
The two surprising features of gravity are (a) the principle of equivalence and (b) the connection between gravity and thermodynamics. Using principle of equivalence and special relativity in the {\it local inertial frame}, one could obtain…
The approach to extend the notion of entanglement for characterizing the properties of quantum correlations in the state of a single qudit is presented. New information and entropic inequalities, such as the subadditivity condition, strong…
In this essay, we argue that certain aspects of the measurement require revision in Quantum Gravity. Using entropic arguments, we propose that the number of measurement outcomes and the accuracy (or the range) of the measurement are limited…
For quantum lattice systems with local interactions, the Lieb-Robinson bound acts as an alternative for the strict causality of relativistic systems and allows to prove many interesting results, in particular when the energy spectrum…
The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this work, we provide a family of…
We derive the strong subadditivity of the von Neumann entropy with a strict lower bound dependent on the distribution of quantum correlation in the system. We investigate the structure of states saturating the bounded subadditivity and…
Planck-scale quantum spacetime undergoes probabilistic local curvature fluctuations whose distributions cannot explicitly depend on position otherwise vacuum's small-scale quantum structure would fail to be statistically homogeneous. Since…
We derive entropic Bell inequalities from considering entropy Venn diagrams. These entropic inequalities, akin to the Braunstein-Caves inequalities, are violated for a quantum mechanical Einstein-Podolsky-Rosen pair, which implies that the…
To find the essential nature of quantum theory has been an important problem for not only theoretical interest but also applications to quantum technologies. In those studies on quantum foundations, the notion of uncertainty plays a primary…
We consider the entropy of sums of independent discrete random variables, in analogy with Shannon's Entropy Power Inequality, where equality holds for normals. In our case, infinite divisibility suggests that equality should hold for…
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…
The so-called "Quantum Inequalities", and the "Quantum Interest Conjecture", use quantum field theory to impose significant restrictions on the temporal distribution of the energy density measured by a time-like observer, potentially…
We consider a randomly forced Ginzburg-Landau equation on an unbounded domain. The forcing is smooth and homogeneous in space and white noise in time. We prove existence and smoothness of solutions, existence of an invariant measure for the…
Experimentally quantifying entanglement and coherence are extremely important for quantum resource theory. However, because the quantum state tomography requires exponentially growing measurements with the number of qubits, it is hard to…
In this paper, we characterize the saturation of four universal inequalities in quantum information theory, including a variant version of strong subadditivity inequality for von Neumann entropy, the coherent information inequality, the…
We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area…
A key test of any quantum theory of gravity is its ability to reproduce the known thermodynamic properties of black holes. A statistical mechanical description of the Bekenstein-Hawking entropy once seemed remote, but today we suffer an…
Quantum coherence is a fundamental manifestation of the quantum superposition principle. Recently, Baumgratz \emph{et al}. [Phys. Rev. Lett. \textbf{113}, 140401 (2014)] presented a rigorous framework to quantify coherence from the view of…
We develop a new framework for establishing approximate factorization of entropy on arbitrary probability spaces, using a geometric notion known as non-negative sectional curvature. The resulting estimates are equivalent to entropy…