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A Correlation Measure Based on Vector-Valued Lp -Norms

Mojahedian, M. M ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1109/TIT.2019.2937099
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2019
  4. Abstract:
  5. In this paper, we introduce a new measure of correlation for bipartite quantum states. This measure depends on a parameter α , and is defined in terms of vector-valued Lp -norms. The measure is within a constant of the exponential of α -Rényi mutual information, and reduces to the trace norm (total variation distance) for α =1. We will prove some decoupling type theorems in terms of this measure of correlation, and present some applications in privacy amplification as well as in bounding the random coding exponents. In particular, we establish a bound on the secrecy exponent of the wiretap channel (under the total variation metric) in terms of the α -Rényi mutual information according to Csiszár's proposal. © 1963-2012 IEEE
  6. Keywords:
  7. Correlation measure ; Decoupling-type theorems ; Vector-valued L p-norms ; Correlation measures ; Entanglement generation ; Privacy amplification ; Random binning ; Secrecy exponent ; Vector valued ; Quantum optics
  8. Source: IEEE Transactions on Information Theory ; Volume 65, Issue 12 , 2019 , Pages 7985-8004 ; 00189448 (ISSN)
  9. URL: https://ieeexplore.ieee.org/document/8811607