Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T07:49:54.281Z Has data issue: false hasContentIssue false
  • English
  • Français

A separation between divergence and Holevo information for ensembles

Published online by Cambridge University Press:  27 October 2010

RAHUL JAIN ,
ASHWIN NAYAK  and
YI SU
RAHUL JAIN
Affiliation:
Centre for Quantum Technologies, and Department of Computer Science, National University of Singapore, Block S15, 3 Science Drive 2, Singapore 11754 Email: rahul@comp.nus.edu.sg
ASHWIN NAYAK
Affiliation:
Department of Combinatorics and Optimization, and Institute for Quantum Computing, University of Waterloo, and Perimeter Institute for Theoretical Physics., 200 University Ave. W., Waterloo, ON N2L 3G1, Canada Email: ashwin.nayak@uwaterloo.ca
YI SU
Affiliation:
Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, MI 48109-1043, U.S.A. Email: yisu@umich.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

The notion of divergence information of an ensemble of probability distributions was introduced by Jain, Radhakrishnan and Sen in Jain et al. (2002; 2009) in the context of the ‘substate theorem’. Since then, divergence has been recognised as a more natural measure of information in several situations in both quantum and classical communication.

We construct ensembles of probability distributions for which divergence information may be significantly smaller than the more standard Holevo information. As a result, we establish that bounds previously shown for Holevo information are weaker than similar ones shown for divergence information.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 20 , Special Issue 5: Theory and Applications of Models of Computation (TAMC 2008–2009) , October 2010 , pp. 977 - 993
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Buhrman, H., Christandl, M., Hayden, P., Lo, H.-K. and Wehner, S. (2006) Security of quantum bit string commitment depends on the information measure. Phys. Rev. Lett. 97 (25) (article 250501).CrossRefGoogle ScholarPubMed
Cover, T. M. and Thomas, J. A. (1991) Elements of Information Theory, Wiley Series in Telecommunications, John Wiley & Sons.Google Scholar
Jain, R. (2006) Communication complexity of remote state preparation with entanglement. Quantum Inf. Comput. 6 (4-5)461–464.Google Scholar
Jain, R. (2008) New binding-concealing trade-offs for quantum string commitment. J. Cryptol. 24 (4)579–592.CrossRefGoogle Scholar
Jain, R., Radhakrishnan, J. and Sen, P. (2002) Privacy and interaction in quantum communication complexity and a theorem about the relative entropy of quantum states. In: Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press 429–438.Google Scholar
Jain, R., Radhakrishnan, J. and Sen, P. (2005) Prior entanglement, message compression and privacy in quantum communication. In: Proceedings of the 20th Annual IEEE Conference on Computational Complexity, IEEE Computer Society Press 285–296.Google Scholar
Jain, R., Radhakrishnan, J. and Sen, P. (2009) A new information-theoretic property about quantum states with an application to privacy in quantum communication. J. ACM 56 (6) (article 33).CrossRefGoogle Scholar
Kent, A. (2003) Quantum bit string commitment. Phys. Rev. Lett. 90 (article 237901).CrossRefGoogle ScholarPubMed
Lo, H.-K. and Chau, H.-F. (1997) Is quantum bit commitment really possible? Phys. Rev. Lett. 78 3410–3413.CrossRefGoogle Scholar
Mayers, D. (1997) Unconditionally secure quantum bit commitment is impossible. Phys. Rev. Lett. 78 (17)3414–3417.CrossRefGoogle Scholar
Nielsen, M. A. and Chuang, I. L. (2000) Quantum Computation and Quantum Information, Cambridge University Press.Google Scholar