The DOI matches its Crossref record; 21 of the 21 references it cites were found in a registry or an index.
The Operational Meaning of Min- and Max-Entropy
Open accessAbstract
In this paper, we show that the conditional min-entropyHmin(A|B) of a bipartite staterhoABis directly related to the maximum achievable overlap with a maximally entangled state if only local actions on theB-part ofrhoABare allowed. In the special case whereAis classical, this overlap corresponds to the probability of guessingAgivenB. In a similar vein, we connect the conditional max-entropyHmax(A|B) to the maximum fidelity ofrhoABwith a product state that is completely mixed onA. In the case whereAis classical, this corresponds to the security ofAwhen used as a secret key in the presence of an adversary holdingB. Because min- and max-entropies are known to characterize information-processing tasks such as randomness extraction and state merging, our results establish a direct connection between these tasks and basic operational problems. For example, they imply that the (logarithm of the) probability of guessingAgivenBis a lower bound on the number of uniform secret bits that can be extracted fromArelative to an adversary holdingB.
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Cites
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Cited by
Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., & Wehner, S. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.419 · Cited by 2,688
Random numbers certified by Bell’s theorem
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The thermodynamic meaning of negative entropy
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Self-citationSelf-Testing Quantum Random Number Generator
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“tropy Hmin(R|E)ρ = max σE Hmin(R|E)ρ|σ , (3) where the maximisation is over normalised states σE and Hmin(R|E)ρ|σ = −log2 min{λ ∈ R: ρRE λIR ⊗σE}. (4) For a cq-state of the form (1), it is shown in [13] that Hmin(R|E)ρ = −log2 pguess(R|E), (5) 2 where pguess(R|E) = max ME X r P(r)tr[ρr EM r E] , (6) is the probability…”
BackgroundMethod
Metadata
- Authors
- Konig, R., Renner, R., & Schaffner, C.
- Venue
- IEEE Transactions on Information Theory
- Published
- 2009-09
- Volume
- 55
- Issue
- 9
- Pages
- 4337-4347
- ISSN
- 0018-9448 (ISSN-L)
- OpenAlex
- W2164253138
- Cited by
- 659
- References
- 21
- FWCI
- 33.25
- Type
- journal article
- Language
- en
- Open access
- green
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