Related papers: A large-deviation type asymptotics in the quantum …
This paper has been withdrawn, as all conjectures (and one claim) have been proven incorrect. Some of what remains may eventually reappear in a different context.
We reconsider the quantum analogue of Varadhans Theorem proved by Petz, Raggio and Verbeure. They proved this theorem using standard techniques in quantum statistical mechanics of lattice systems to arrive at a variational formula over…
This paper has been withdrawn.
A large deviation function mathematically characterizes the statistical property of atypical events. Recently, in non-equilibrium statistical mechanics, large deviation functions have been used to describe universal laws such as the…
This paper is withdrawn. We found a mistake in Lemma 4.1
The proposition 1 is incomplete. In some of the examples D(a,b) may not obey the triangle inequality. The paper is withdrawn for further elaboration.
This paper has been withdrawn by the author, due to errors in the figures.
This paper proposes a variational principle for the solutions of quantum field theories in which the ``trial functions'' are chosen from the algebra of asymptotic fields, and illustrates this variational principle in simple cases.
We study Mallows random permutations conditioned to avoid a given pattern $\alpha$ of length~$3$. When the bias parameter is of the form $e^{\beta/n}$, we prove that these permutations converge to a non-trivial explicit deterministic…
This paper has been withdrawn by the author(s), due a crucial i-number error in Eqn. 18.
Due to the broad applications of elliptical models, there is a long line of research on goodness-of-fit tests for empirically validating them. However, the existing literature on this topic is generally confined to low-dimensional settings,…
The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.
We extend quantum Stein's lemma in asymmetric quantum hypothesis testing to composite null and alternative hypotheses. As our main result, we show that the asymptotic error exponent for testing convex combinations of quantum states…
This paper has been withdrawn by the author due to a crucial mistakes.
This paper has been withdrawn by the author due to a gap in the proof of the main result.
This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either…
In a recent paper, Nagata [1] claims to derive inconsistencies from quantum mechanics. In this paper, we show that the inconsistencies do not come from quantum mechanics, but from extra assumptions about the reality of observables.
Deviations of the decay law from exponents are discussing for a long time, however, experimental proofs of such deviations are absent. Here in the general form is shown that the conclusions about non-exponential contributions are due to the…
This is a brief pedagogical introduction to the theory of large deviations. It appeared in the ICTS Newsletter 2017 (Volume 3, Issue 2), goo.gl/pZWA6X.
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…