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IEEE International Symposium on Information Theory (ISIT)

On intrinsic information

Matthias Christandl, Renato Renner

Published Dec 23, 2004• 15 citations
Publisher

Abstract

This paper introduces the public Eve scenario and shows that the secret key rate in this scenario is bounded by the intrinsic information. This elucidates previous results and gives new insights in the gap between formation and extraction of secret information. Intrinsic information, in its function as an upper bound on the secret key rate, is generalized to secret key agreement from arbitrary tripartite quantum states.

DOI
10.1109/isit.2004.1365175

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This paper introduces the public Eve scenario and shows that the secret key rate in this scenario is bounded by the intrinsic information. This elucidates previous results and gives new insights in the gap between formation and extraction of secret information. Intrinsic information, in its function as an upper bound on the secret key rate, is generalized to secret key agreement from arbitrary tripartite quantum states.
This paper is concerned with secret-key agreement by public discussion. Assume that two parties Alice and Bob and an adversary Eve have access to independent realizations of random variables X, Y, and Z, respectively, with joint distribution P/sub XYZ/. The secret-key rate S(X;Y/spl par/Z) has been defined as the maximal rate at which Alice and Bob can generate a secret key by communication over an insecure, but authenticated channel such that Eve's information about this key is arbitrarily small. We define a new conditional mutual information measure, the intrinsic conditional mutual information between S and Y when given Z, denoted by I(X;Y/spl darr/Z), which is an upper bound on S(X;Y/spl par/Z). The special scenarios are analyzed where X, Y, and Z are generated by sending a binary random variable R, for example a signal broadcast by a satellite, over independent channels, or two scenarios in which Z is generated by sending X and Y over erasure channels. In the first two scenarios it can be shown that the secret-key rate is strictly positive if and only if I(X;Y/spl darr/Z) is strictly positive. For the third scenario, a new protocol is presented which allows secret-key agreement even when all the previously known protocols fail.
This paper is concerned with secret-key agreement by public discussion: two parties Alice and Bob and an adversary Eve have access to independent realizations of random variables X , Y , and Z, respectively, with joint distribution PXY Z . The secret key rate S(X ; Y jjZ) has been defined as the maximal rate at which Alice and Bob can generate a secret key by communication over an insecure, but authenticated channel such that Eve's information about this key is arbitrarily small. We define a new conditional mutual information measure, the intrinsic conditional mutual information between X and Y when given Z, denoted by I(X ; Y#Z), which is an upper bound on S(X ; Y jjZ). The special scenarios where X , Y , and Z are generated by sending a binary random variable R, for example a signal broadcast by a satellite, over independent channels, or where Z is generated by sending X and Y over erasure channels, are analyzed. In the first scenario it can be shown that the secret key rate is str...
We propose a new conditional mutual information measure, called the reduced intrinsic in- formation, and show its significance in the context of determining the number of secret-key bits that can be extracted from distributed information by public communication. I. THE REDUCED INTRINSIC INFORMATION The secret-key rate S(X; YllZ) of a tripartite probability distribution PXYZ is the rate at which two parties, knowing realizations of X and Y, respectively, can generate, by pub- lic communication, common bits about which a third party, who has access to 2, remains almost completely ignorant (l). It is a fundamental problem to express S(X;YllZ) in terms of Pxyz. In (2), the intrinsic information I(X;YJ. Z) := infpZlz(I(X;YIZ)) was shown to be an upper bound on S(X; YllZ). (Here, the infimum is taken over all possible ways the third party Eve can process her information 2.)
We prove the conjectured existence of bound information, a classical analog of bound entanglement, in the multipartite scenario. We give examples of tripartite probability distributions from which it is impossible to extract any kind of secret key, even in the asymptotic regime, although they cannot be created by local operations and public communication. Moreover, we show that bound information can be activated: three honest parties can distill a common secret key from different distributions having bound information. Our results demonstrate that quantum information theory can provide useful insight for solving open problems in classical information theory.
Consider a scenario in which two parties Alice and Bob as well as an opponent Eve receive the output of a binary symmetric source (e,g. installed in a satellite) over individual, not necessarily independent binary symmetric channels. Alice and Bob share no secret key initially and can only communicate over a public channel completely accessible to Eve. The authors derive a lower bound on the rate at which Alice and Bob can generate secret-key bits about which Eve has arbitrarily little information, This lower bound is strictly positive as long as Eve's binary symmetric channel is not perfect, even if Alice's and Bob's channels are by orders of magnitude less reliable than Eve's channel.>