Rényi Extrapolation of Shannon Entropy

  • Authors:
  • Karol Życzkowski

  • Affiliations:
  • Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagielloński ul. Reymonta 4, 30-059 Kraków, Poland and Centrum Fizyki Teoretycznej, Polska Akademia Nauk Al. Lotników 32/44, 02-668 ...

  • Venue:
  • Open Systems & Information Dynamics
  • Year:
  • 2003

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Abstract

Relations between Shannon entropy and Rényi entropies of integer order are discussed. For any N-point discrete probability distribution for which the Rényi entropies of order two and three are known, we provide a lower and an upper bound for the Shannon entropy. The average of both bounds provide an explicit extrapolation for this quantity. These results imply relations between the von Neumann entropy of a mixed quantum state, its linear entropy and traces.