Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Symposium on Information Theory and its Applications

Formula of channel matrix for coded quantum signals by classical linear codes over Zm

Masaki Ota, Hideyuki Kumazawa, Keisuke Shiromoto, Tsuyoshi Sasaki Usuda

Published Oct 1, 2010• 0 citations
Publisher

Abstract

A formula of channel matrix for linear codes over Zmis presented. m-ary PSK coherent-states are used as letter states and the square-root measurement (SRM) is used as a decoding. First, arbitrary linear codes over Zmare shown to group covariant. Then the formula of channel matrix is derived by generalizing [T.S. Usuda, S. Usami, I. Takumi, and M. Hata, Phys. Lett. A305, pp.125-134, (2002)]. Furthermore, the usefulness of the formula is considered.

DOI
10.1109/isita.2010.5649495

Related papers

4PSK coherent-state signals can be narrow sense group covariant with respect to F 4 by coding

Minami Tanaka, Asuka Ohashi, Tsuyoshi Sasaki Usuda

The formula of the channel matrix for group co-variant signals for classical-quantum communication has been studied to calculate the channel matrix analytically. However, despite its importance, the formula derived previously cannot be applied to coded q-ary phase shift keying (PSK) signals by linear codes over an extension field F q . To derive the formula for codes over F q , we focus on the 4PSK signals coded by the codes over F 4 . In the present paper, we propose a construction method of a code of length 2n over F 4 from a code of length n. If the original code is a group code, the coded 4PSK signals by the constructed code is narrow sense group covariant.

International Symposium on Information Theory and its Applications•Oct 1, 2016•0 citations

Simplification of the Calculation of the Channel Matrix for AMPM Coherent-state Signals

Ryusuke Miyazaki, Mana Yoshida, Tiancheng Wang +1 more

The square-root measurement (SRM) is regarded as the optimum quantum measurement for symmetric signals and quasi-optimum measurements for any quantum signals. Therefore, deriving formulae for the channel matrix by using SRM is crucial in developing a theory of quantum communications. To date, formulae for these matrices are known for symmetric and group-covariant signals. However, there are important non-symmetric signals such as ASK, AMPM, and QAM signals, etc. In this paper, we demonstrate that the calculation of the channel matrix for 4m-ary AMPM signals can be simplified by using their partial symmetry.

International Symposium on Information Theory and its Applications•Oct 24, 2020•2 citations

Analytical expression of s-th power of Gram matrix for group covariant signals and its application

Tsuyoshi Sasaki Usuda, Keisuke Shiromoto, Timothy C. Ralph +1 more

Analytical expression of s‐th power of the Gram matrix is shown when the quantum signals are group covariant. An application of the formula to coded quantum signals by classical linear codes over a finite field is also shown.

AIP conference proceedings•Jan 1, 2011•7 citations

Error Exponents of Quantum Communication System with M-ary PSK Coherent State Signal

Kentaro Kato

The optimal distributions on a channel input that yield the random coding exponent, the expurgation exponent, and the zero-rate reliability function for a discrete classical-quantum channel with M-ary Phase Shift Keying (PSK) coherent state signal are analytically derived. In each case, the optimal distributions are given by a uniform distribution over the channel input alphabet. As a result, the expressions of the error exponents for M-ary PSK coherent state signal are simplified. By using this result, typical behavior of the error exponents is sketched in the case of M = 16.

•Jan 1, 2011•2 citations

Group Covariant Signals in Quantum Information Theory

Tsuyoshi Sasaki Usuda, Ichi Takumi

Necessary and sufficient condition for group covariant signals is given. This condition shows what kind of signals correspond to “group covariant signals.” We show by applying this condition that many signals, such as arbitrary binary signals, PPM, FSK, and PSK coherent-state signals, equidistant codes, and binary linear codes, are all group covariant.

Kluwer Academic Publishers eBooks•Dec 19, 2005•8 citations

Property of Classical Reliability Function for BPSK Signals Coded by Simplex Codes with SRM

Ken Masaki, Tiancheng Wang, Shogo Usami +2 more

There is a gap between properties of quantum and classical reliability functions. That is, the upper bound of the quantum reliability function diverges, whereas that of classical one does not, even if the same coherent signal is used. We are interested in the origin of this gap. In this paper, we investigate the upper bound of the reliability function for quantum signals coded by simplex codes when using square-root measurement (SRM). The reliability function in this case has a much steeper slope with respect to the rate than in the uncoded case. This result suggests the divergence of the upper bound of the quantum reliability function in the previous study.

International Symposium on Information Theory and its Applications•Nov 10, 2024•0 citations
A formula of channel matrix for linear codes over Zmis presented. m-ary PSK coherent-states are used as letter states and the square-root measurement (SRM) is used as a decoding. First, arbitrary linear codes over Zmare shown to group covariant. Then the formula of channel matrix is derived by generalizing [T.S. Usuda, S. Usami, I. Takumi, and M. Hata, Phys. Lett. A305, pp.125-134, (2002)]. Furthermore, the usefulness of the formula is considered.
The formula of the channel matrix for group co-variant signals for classical-quantum communication has been studied to calculate the channel matrix analytically. However, despite its importance, the formula derived previously cannot be applied to coded q-ary phase shift keying (PSK) signals by linear codes over an extension field F q . To derive the formula for codes over F q , we focus on the 4PSK signals coded by the codes over F 4 . In the present paper, we propose a construction method of a code of length 2n over F 4 from a code of length n. If the original code is a group code, the coded 4PSK signals by the constructed code is narrow sense group covariant.
The square-root measurement (SRM) is regarded as the optimum quantum measurement for symmetric signals and quasi-optimum measurements for any quantum signals. Therefore, deriving formulae for the channel matrix by using SRM is crucial in developing a theory of quantum communications. To date, formulae for these matrices are known for symmetric and group-covariant signals. However, there are important non-symmetric signals such as ASK, AMPM, and QAM signals, etc. In this paper, we demonstrate that the calculation of the channel matrix for 4m-ary AMPM signals can be simplified by using their partial symmetry.
The optimal distributions on a channel input that yield the random coding exponent, the expurgation exponent, and the zero-rate reliability function for a discrete classical-quantum channel with M-ary Phase Shift Keying (PSK) coherent state signal are analytically derived. In each case, the optimal distributions are given by a uniform distribution over the channel input alphabet. As a result, the expressions of the error exponents for M-ary PSK coherent state signal are simplified. By using this result, typical behavior of the error exponents is sketched in the case of M = 16.
There is a gap between properties of quantum and classical reliability functions. That is, the upper bound of the quantum reliability function diverges, whereas that of classical one does not, even if the same coherent signal is used. We are interested in the origin of this gap. In this paper, we investigate the upper bound of the reliability function for quantum signals coded by simplex codes when using square-root measurement (SRM). The reliability function in this case has a much steeper slope with respect to the rate than in the uncoded case. This result suggests the divergence of the upper bound of the quantum reliability function in the previous study.