Get A Group Theoretic Approach to Quantum Information PDF

By Masahito Hayashi

ISBN-10: 3319452398

ISBN-13: 9783319452395

ISBN-10: 331945241X

ISBN-13: 9783319452418

This ebook is the 1st one addressing quantum details from the point of view of crew symmetry. Quantum platforms have a bunch symmetrical constitution. This constitution permits to address systematically quantum details processing. even if, there isn't any different textbook targeting crew symmetry for quantum info even if there exist many textbooks for crew illustration. After the mathematical coaching of quantum details, this e-book discusses quantum entanglement and its quantification through the use of team symmetry. crew symmetry vastly simplifies the calculation of a number of entanglement measures even if their calculations are typically very tough to deal with. This e-book treats optimum info strategies together with quantum kingdom estimation, quantum kingdom cloning, estimation of staff motion and quantum channel and so forth. often it's very tough to derive the optimum quantum details strategies with no asymptotic atmosphere of those themes. even though, team symmetry permits to derive those optimum suggestions with no assuming the asymptotic atmosphere. subsequent, this booklet addresses the quantum blunders correcting code with the symmetric constitution of Weyl-Heisenberg teams. This constitution ends up in comprehend the quantum errors correcting code systematically. ultimately, this ebook specializes in the quantum common details protocols by utilizing the gang SU(d). This subject should be considered as a quantum model of the Csiszar-Korner's common coding conception with the kind approach. the necessary mathematical wisdom approximately workforce illustration is summarized within the better half e-book, workforce illustration for Quantum conception.

Show description

Read or Download A Group Theoretic Approach to Quantum Information PDF

Similar abstract books

Algèbre commutative: Chapitres 1 à 4 by N. Bourbaki PDF

Les Éléments de mathématique de Nicolas Bourbaki ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce greatest quantity du Livre d Algèbre commutative, septième Livre du traité, est consacré aux suggestions fondamentaux de l algèbre commutative.

Read e-book online An Introduction to Group Representation Theory PDF

During this publication, we research theoretical and sensible facets of computing tools for mathematical modelling of nonlinear platforms. a couple of computing thoughts are thought of, reminiscent of equipment of operator approximation with any given accuracy; operator interpolation thoughts together with a non-Lagrange interpolation; tools of method illustration topic to constraints linked to thoughts of causality, reminiscence and stationarity; equipment of procedure illustration with an accuracy that's the most sensible inside of a given type of types; equipment of covariance matrix estimation;methods for low-rank matrix approximations; hybrid tools in response to a mixture of iterative tactics and most sensible operator approximation; andmethods for info compression and filtering lower than situation clear out version should still fulfill regulations linked to causality and sorts of reminiscence.

Read e-book online New Trends in Quantum Structures PDF

D. Hilbert, in his recognized application, formulated many open mathematical difficulties that have been stimulating for the advance of arithmetic and a fruitful resource of very deep and basic rules. in the course of the complete twentieth century, mathematicians and experts in different fields were fixing difficulties which are traced again to Hilbert's application, and this present day there are lots of uncomplicated effects influenced through this software.

New PDF release: Abstract State Machines, B and Z: First International

This e-book constitutes the refereed lawsuits of the 1st foreign convention of summary country Machines, B and Z, ABZ 2008, held in London, united kingdom, in September 2008. The convention concurrently included the fifteenth overseas ASM Workshop, the seventeenth foreign convention of Z clients and the eighth overseas convention at the B strategy.

Additional resources for A Group Theoretic Approach to Quantum Information

Example text

As another type of measures, we can measure the difference between two density matrices ρ1 and ρ2 by modifying the information quantity in the previous subsection. Firstly, based on von Neumann entropy, we define relative entropy D(ρ1 ρ2 ) := s Tr ρ1 (log ρ1 − log ρ2 ). Also, we define ψ(s|ρ1 ρ2 ) := log Tr ρ1−s 1 ρ2 . Using this function, we define relative Renyi entropy of order 1 − s: D1−s (ρ1 ρ2 ) := − ψ(s|ρs1 ρ2 ) . Taking the limit s → 0, we can recover the relative entropy D(ρ1 ρ2 ) = lims→0 D1−s (ρ1 ρ2 ).

When a POVM can be realized by one-way LOCC, two-way LOCC, or separable, it is called a one-way LOCC POVM, a two-way LOCC POVM, or a separable POVM, respectively. 1 Locality Conditions 41 separable operation two-way LOCC one-way LOCC Fig. 1 Relation among local operations where M m,l is a positive semi definite matrix on the system Hm . Now, we recall the j majorization relation between two density matrices ρ1 and ρ2 defined in Sect. 2. 1 (Nielsen [100]) Given two vector states |Φ and |Ψ on the composite system H A ⊗ H B , we define the two states ρ1 := Tr B |Φ Φ| and ρ2 := Tr B |Ψ Ψ |.

58) hold for R ∈ [0, log k]. 54). 54) also guarR )) antees that S R = R−ψ(s(S . 56). 57). 59) 34 2 Quantum Channel, and Information Quantity, and Their Mathematical Structure and − H (ρ ) + H (ρs ) = Tr ρ log ρ − log ρ1−s Tr ρ1−s =D(ρ ρs ) + (1 − s) Tr ρ − + Tr ρ − ρ1−s Tr ρ1−s ρ1−s Tr ρ1−s log ρ1−s Tr ρ1−s log ρ. 54) implies H (ρs(SR ) ) = R. 60) imply D(ρ ρs(SR ) ) = − Tr ρ − ρs(SR ) log ρ 1 − s(S R ) D(ρ ρ) − D(ρs(SR ) ρ) − D(ρ ρs(SR ) ) . = s(S R ) That is, we have D(ρ ρ) − D(ρs(SR ) ρ) = 1 D(ρ ρs(SR ) ) ≥ 0.

Download PDF sample

A Group Theoretic Approach to Quantum Information by Masahito Hayashi


by Kevin
4.4

Rated 4.75 of 5 – based on 46 votes