Related papers: The Converse Part of The Theorem for Quantum Hoeff…
We study the behaviors of quantum groups under an edge contraction. We show that there exists an explicit embedding induced by an edge contraction operation. We further conjecture that this explicit embedding is a section of an explicit…
In this paper we look at a particular realization of Popper's thought experiment with correlated quantum particles and argue that, from the point of view of a nonlinear quantum physics and contrary to the orthodox interpretation,…
We derive the monotonicity of the quantum relative entropy by an elementary operational argument based on Stein's lemma in quantum hypothesis testing. For the latter we present an elementary and short proof that requires the law of large…
We use the smooth entropy approach to treat the problems of binary quantum hypothesis testing and the transmission of classical information through a quantum channel. We provide lower and upper bounds on the optimal type II error of quantum…
We propose a theory of quantum (statistical) measurement which is close, in spirit, to Hepp's theory, which is centered on the concepts of decoherence and macroscopic (classical) observables, and apply it to a model of the Stern-Gerlach…
We introduce the notion of reduced relative quantum entropy and prove that it is convex. This result is then used to give a simplified proof of a theorem of Lieb and Seiringer.
We uncover the quantum fluctuation-response inequality, which, in the most general setting, establishes a bound for the mean difference of an observable at two different quantum states, in terms of the quantum relative entropy. When the…
An analysis using classical stochastic processes is used to construct a consistent system of quantum counterfactual reasoning. When applied to a counterfactual version of Hardy's paradox, it shows that the probabilistic character of quantum…
In two articles, the authors claim that the Heisenberg uncertainty principle limits the precision of simultaneous measurements of the position and velocity of a particle and refer to experimental evidence that supports their claim. It is…
A quantum theory of gravity is described in the case of a positive cosmological constant in 3+1 dimensions. Both old and new results are described, which support the case that loop quantum gravity provides a satisfactory quantum theory of…
We prove quasipolynomial bounds on the inverse theorem for the Gowers $U^{s+1}[N]$-norm. The proof is modeled after work of Green, Tao, and Ziegler and uses as a crucial input recent work of the first author regarding the equidistribution…
Recently, a new definition for quantum $f$-divergences was introduced based on an integral representation. These divergences have shown remarkable properties, for example when investigating contraction coefficients under noisy channels. At…
Quantum Lefschetz theorem by Coates and Givental gives a relationship between the genus 0 Gromov-Witten theory of X and the twisted theory by a line bundle L on X. We prove the convergence of the twisted theory under the assumption that the…
The Bousso bound requires that one quarter the area of a closed codimension two spacelike surface exceeds the entropy flux across a certain lightsheet terminating on the surface. The bound can be violated by quantum effects such as Hawking…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous…
The aim of the present paper is to give axiomatic characterization of quantum relative entropy utilizing resource conversion scenario. We consider two sets of axioms: non-asymptotic and asymptotic. In the former setting, we prove that the…
The aim of the present paper is to give axiomatic characterization of quantum relative entropy utilizing resource conversion scenario. We consider two sets of axioms: non-asymptotic and asymptotic. In the former setting, we prove that the…
We present a new method for proving lower bounds on quantum query algorithms. The new method is an extension of adversary method, by analyzing the eigenspace structure of the problem. Using the new method, we prove a strong direct product…
In this essay it will be shown that the introduction of a modification to Heisenberg algebra (here this feature means the existence of a minimal obserlvable length), as a fundamental part of the quantization process of the electrodynamical…