The Operational Meaning of Min- and Max-Entropy

In this paper, we show that the conditional min-entropy H min ( A | B ) of a bipartite state rhoAB is directly related to the maximum achievable overlap with a maximally entangled state if only local actions on the B -part of rhoAB are allowed. In the special case where A is classical, this overlap corresponds to the probability of guessing A given B . In a similar vein, we connect the conditional max-entropy H max ( A | B ) to the maximum fidelity of rhoAB with a product state that is completely mixed on A . In the case where A is classical, this corresponds to the security of A when used as a secret key in the presence of an adversary holding B . Because min- and max-entropies are known to characterize…

• NS
  National Science Foundation

  Awards: 0803371, 0456720, PHY-0803371
• EC
  European Commission

  Award: 015848
• SN
  Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

  Awards: 200021-, 119868, 200021
• NO
  Nederlandse Organisatie voor Wetenschappelijk Onderzoek