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arXiv:quant-ph/0311064 · Physical Review Letters

Multipartite Bound Information Exists and Can Be Activated

Antonio Acín, J. I. Cirac, Lluís Masanes

Published Mar 12, 2004• 46 citations
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Abstract

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.

DOI
10.1103/physrevlett.92.107903

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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.
We demonstrate the existence of Gaussian multipartite bound information which is a classical analog of Gaussian multipartite bound entanglement. We construct a tripartite Gaussian distribution from which no secret key can be distilled, but which cannot be created by local operations and public communication. Further, we show that the presence of bound information is conditional on the presence of a part of the adversary's information creatable only by private communication. Existence of this part of the adversary's information is found to be a more generic feature of classical analogs of quantum phenomena obtained by mapping of nonclassically correlated separable quantum states.
Bound information, a cryptographic classical analog of bound entanglement, is defined as classical secret correlations from which no secret key can be extracted. Its existence was conjectured and shown in a multipartite case. In this work, we provide an example of bound information in a four-partite scenario. Later, using this example, we prove that bound information can be superactivated and moreover unlockable in a finite-copy scenario. We also show that bound entangled states (bound information) can be used to distribute multipartite pure-state entanglements (secret keys).
There exist bipartite quantum states that cost entanglement to create, yet from which no singlet can be distilled. This extreme irreversibility is known as bound entanglement. A quarter-century ago, Gisin and Wolf asked whether classical information theory admits the same phenomenon. Are there correlations, shared by two parties and an eavesdropper, that cost secret bits to create, yet from which none can be distilled? This question is part of a broader program exploring the relation between quantum and classical information theory. We answer it in the affirmative, providing a simple example, a distribution of two bits and a trit. Bound entanglement thus has a classical counterpart, bound information. An even more direct correspondence was originally conjectured, namely that measuring purifications of bound-entangled states yields distributions with bound information. The very states that motivated the conjecture, however, yield no bound information when measured in the standard basis, whereas suitable measurements of purifications of separable states do. The analogy between bound entanglement and bound information thus lies in the accounting of resources, not in a correspondence between individual quantum states and the classical probability distributions induced by measuring them.
One big problem of the communication between two parties is the secrecy. That means how\nmuch information a third party can obtain by intercepting the messages transmitted from\none honest party to the other one. Therefore cryptography offers a wide range of protocols\nto ensure security with assumptions on the eavesdropper. So one was looking for an\ninformation-theoretical description of the scenario to get unconditional secure communication.\nIn this scenario we are considering two honest parties that want to communicate over\nan authenticated channel that the eavesdropper is wiretapping. This scenario introduced the definition of the intrinsic information and the secret-key rate which are a measure of the secrecy in this setting. Later because of strong analogies to quantum mechanics it turned out that this description was lacking a phenomena called bound information which is the disability of a probability distribution to create a secret-key even though it has predicted secrecy.\nNearly ten years of research have shown the existence of bound information for the multipartite case where several parties are communicating but not yet for the bipartite case.\nHence the approach of non-distillability seems a very promising one to find this conjecture.\nMotivated by this the approach we implemented this tool and simulated some distributions that have conjectured bound information. Thereby we improved the tool to reduce its calculationtime and to get closer to the aim.
Non-additivity is one of the distinctive traits of Quantum Information Theory: the combined use of quantum objects may be more advantageous than the sum of their individual uses. Non-additivity effects have been proven, for example, for quantum channel capacities, entanglement distillation or state estimation. In this work, we consider whether non-additivity effects can be found in Classical Information Theory. We work in the secret-key agreement scenario in which two honest parties, having access to correlated classical data that are also correlated to an eavesdropper, aim at distilling a secret key. Exploiting the analogies between the entanglement and the secret-key agreement scenario, we provide some evidence that the secret-key rate may be a non-additive quantity. In particular, we show that correlations with conjectured bound information become secret-key distillable when combined. Our results constitute a new instance of the subtle relation between the entanglement and secret-key agreement scenario.