Get Asymptotic theory of quantum statistical inference PDF

By Masahito Hayashi

ISBN-10: 9812560157

ISBN-13: 9789812560155

ISBN-10: 9812563075

ISBN-13: 9789812563071

Quantum statistical inference, a examine box with deep roots within the foundations of either quantum physics and mathematical records, has made impressive development seeing that 1990. specifically, its asymptotic idea has been built in this interval. even if, there has hitherto been no booklet protecting this striking growth after 1990; the recognized textbooks by way of Holevo and Helstrom deal purely with examine leads to the sooner degree (1960s-1970s). This booklet offers the real and up to date result of quantum statistical inference. It specializes in the asymptotic idea, that's one of many relevant problems with mathematical facts and had no longer been investigated in quantum statistical inference until eventually the early Eighties. It comprises impressive papers after Holevo's textbook, a few of that are of significant significance yet should not to be had now. The reader is predicted to have purely trouble-free mathematical wisdom, and as a result a lot of the content material may be obtainable to graduate scholars in addition to examine employees in comparable fields. Introductions to quantum statistical inference were specifically written for the publication. Asymptotic thought of Quantum Statistical Inference: chosen Papers will supply the reader a brand new perception into physics and statistical inference.

Show description

Read or Download Asymptotic theory of quantum statistical inference PDF

Best quantum physics books

Get Theorie quantique des champs experimentale PDF

Un exposé de los angeles théorie quantique des champs clair et concis.

Download PDF by Maurice A De Gosson: The Principles of Newtonian and Quantum Mechanics: The Need

This paintings bargains with the rules of classical physics from the "symplectic" viewpoint, and of quantum mechanics from the "metaplectic" standpoint. The Bohmian interpretation of quantum mechanics is mentioned. part area quantization is accomplished utilizing the "principle of the symplectic camel", that's a lately chanced on deep topological estate of Hamiltonian flows.

New PDF release: Quantum Theory of Motion, The: An account of the De

This ebook provides the 1st entire exposition of the translation of quantum mechanics pioneered via Louis de Broglie and David Bohm. the aim is to provide an explanation for how quantum approaches can be visualized with out ambiguity or confusion when it comes to an easy actual version. Dr. Holland develops the concept that a cloth approach reminiscent of an electron is a particle guided through a surrounding quantum wave.

Negative Quantum Channels: An Introduction to Quantum Maps by James M. McCracken PDF

This e-book is a short advent to destructive quantum channels, i. e. , linear, trace-preserving (and constant) quantum maps that aren't thoroughly optimistic. The flat and sharp operators are brought and defined. entire positivity is gifted as a mathematical estate, however it is argued that entire positivity isn't really a actual requirement of all quantum operations.

Extra resources for Asymptotic theory of quantum statistical inference

Sample text

Hence lim n→∞ 1 βε (2εϕn + (1 − 2ε)ψn , ϕn ) = 0. n (2) Let A = C ⊕ C and ω 1 , ω 2 , ϕ be given with the densities (1, 0), (0, 1), 1 2 (α, 1 − α), respectively, where 0 < α < 1/2. Let ψ = 12 (ω∞ + ω∞ ). By the affinity of SM (·, ϕ∞ ) (see [28]) we get SM (ψ, ϕ∞ ) = 1 1 {S(ω 1 , ϕ) + S(ω 2 , ϕ)} = − {log α + log(1 − α)}. 2 2 But we easily see that Spr (ψn , ϕn ) is the maximum of log 1 = −n log{αn + (1 − α)n }1/n αn + (1 − α)n and 1 1 1 1 1 log n + log = max − log(1 − α), − log α 2 2α 2 2(1 − α)n 2 < SM (ψ, ϕ∞ ).

N (3) Combining the above statement, we can prove Stein’s lemma. The following statement is known as a weaker converse statement. Weak Converse Part: If n → 0, then −1 log βn∗ (p q| n ) ≤ D(p q). n lim (4) Here, for reader’s convenience, we give a proof of classical Stein’s lemma. Proof: For arbitrary real number δ > 0, we choose an acceptance ren gion Tn = ω n = (ω1 , . . , ωn ) pqn (ω n ) ≥ en(D(p q)−δ) . Then, the first error probability 1 − pn (Tn ) = pn ωn 1 n n (log p − log q)(ωi ) < D(p q) − δ i=1 n goes to 0, because the random variable n1 i=1 (log p − log q)(ωi ) goes to D(p q) in pn probability.

Kobayashi, “The strong converse theorem for hypothesis testing,” IEEE Trans. Inform. Theory, 35, 178–180 (1989). [8] F. Hiai and D. Petz, “The proper formula for relative entropy and its asymptotics in quantum probability,” Commun. Math. , 143, 99–114 (1991). (Chap. 3 of this book) [9] E. H. , 11, 267–288 (1973). [10] G. Lindblad, “Completely positive maps and entropy inequalities,” Commun. Math. , 40, 147–151 (1975). [11] T. Ogawa and H. Nagaoka, “Strong converse to the quantum channel coding theorem,” IEEE Trans.

Download PDF sample

Asymptotic theory of quantum statistical inference by Masahito Hayashi

by Thomas

Rated 4.29 of 5 – based on 9 votes