Graphstate basis for Pauli channels
Abstract
Quantum capacities of Pauli channels are not additive, a degenerate quantum code may improve the hashing bound of the capacity. The difficulty in approaching the capacity is how to calculate the coherent information of a generic degenerate quantum code. Using graph state basis, we greatly reduce the problem for the input of quantum errorcorrecting code. We show that for a graph diagonal state passing through a Pauli channel the output state is diagonalizable and the joint output state of the system and ancilla is block diagonalizable. When the input state is an equal probable mixture of codewords of a stabilizer code, the coherent information can be analytically obtained.
 Authors:
 College of Information and Electronic Engineering, Zhejiang Gongshang University, Hangzhou, 310018 (China)
 Publication Date:
 OSTI Identifier:
 21546733
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. A; Journal Volume: 83; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.83.052316; (c) 2011 American Institute of Physics
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTER CODES; ERRORS; GRAPH THEORY; PAULI PRINCIPLE; QUANTUM INFORMATION; QUANTUM OPERATORS; INFORMATION; MATHEMATICAL OPERATORS; MATHEMATICS
Citation Formats
Chen Xiaoyu, and Jiang Lizhen. Graphstate basis for Pauli channels. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.83.052316.
Chen Xiaoyu, & Jiang Lizhen. Graphstate basis for Pauli channels. United States. doi:10.1103/PHYSREVA.83.052316.
Chen Xiaoyu, and Jiang Lizhen. 2011.
"Graphstate basis for Pauli channels". United States.
doi:10.1103/PHYSREVA.83.052316.
@article{osti_21546733,
title = {Graphstate basis for Pauli channels},
author = {Chen Xiaoyu and Jiang Lizhen},
abstractNote = {Quantum capacities of Pauli channels are not additive, a degenerate quantum code may improve the hashing bound of the capacity. The difficulty in approaching the capacity is how to calculate the coherent information of a generic degenerate quantum code. Using graph state basis, we greatly reduce the problem for the input of quantum errorcorrecting code. We show that for a graph diagonal state passing through a Pauli channel the output state is diagonalizable and the joint output state of the system and ancilla is block diagonalizable. When the input state is an equal probable mixture of codewords of a stabilizer code, the coherent information can be analytically obtained.},
doi = {10.1103/PHYSREVA.83.052316},
journal = {Physical Review. A},
number = 5,
volume = 83,
place = {United States},
year = 2011,
month = 5
}
Other availability
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Minimax discrimination of two Pauli channels
We consider the problem of optimally discriminating two Pauli channels in the minimax strategy, maximizing the smallest of the probabilities of correct identification of the channel. We find the optimal input state at the channel and show the conditions under which using entanglement strictly enhances distinguishability. We finally compare the minimax strategy with the Bayesian one. 
Entanglementenhanced transmission of classical information in Pauli channels with memory: Exact solution
The amount of classical information that is reliably transmitted over two uses of general Pauli channels with memory, modeled as a correlated noise between a single pair of uses, is investigated. The maximum of the mutual information between the input and the output is proven to be achieved by a class of product states that is explicitly given in terms of the relevant channel parameters below some memory threshold, and by maximally entangled states above this threshold. In particular, this proves a conjecture on the depolarizing channel by Macchiavello and Palma [Phys. Rev. A 65, 050301(R) (2002)]. Furthermore, it alsomore » 
Convergence of BreitPauli spinorbit matrix elements with basis set size and configuration interaction space: The halogen atoms F, Cl, and Br
Systematic sequences of basis sets are used to calculate the spinorbit splittings of the halogen atoms F, Cl, and Br in the framework of firstorder perturbation theory with the BreitPauli operator and internally contracted configuration interaction wave functions. The effects of both higher angular momentum functions and the presence of tight functions are studied. By systematically converging the oneparticle basis set, an unambiguous evaluation of the effects of correlating different numbers of electrons in the Cl treatment is carried out. Correlation of the 2pelectrons in chlorine increases the spinorbit splitting by {approx}80 cm1, while in bromine we observe incremental increasesmore » 
Graph theoretical ordering of structures as a basis for systematic searches for regularities in molecular data
Selected molecular data on alkanes have been reexamined in a search for general regularities in isomeric variations. In contrast to the prevailing approaches concerned with fitting data by searching for optimal parameterization, the present work is primarily aimed at established trends, i.e., searching for relative magnitudes and their regularities among the isomers. Such an approach is complementary to curve fitting or correlation seeking procedures. It is particularly useful when there are incomplete data which allow trends to be recognized but no quantitative correlation to be established. One proceeds by first ordering structures. One way is to consider molecular graphs andmore »