Common Randomness Research Articles

Multi-User Distillation of Common Randomness and Entanglement From Quantum States

We construct new protocols for the tasks of converting noisy multipartite quantum correlations into noiseless classical and quantum ones using local operations and classical communication (LOCC). The former task is known as common randomness (CR) distillation, and it requires offsetting the amount of classical communication against the randomness created. We obtain a new lower bound on the “distillable common randomness,” an operational measure of the total genuine (classical) correlations in a quantum state. Our proof relies on a generalization of communication for omniscience (CO) [Csiszár and Narayan, IEEE Trans. Inf. Theory 50:3047-3061, 2004], and our contribution here is a novel simultaneous decoder for the compression of correlated classical sources by random binning with quantum side information at the decoder. For the latter task, we derive two lower bounds on the rate at which Greenberger-Horne-Zeilinger (GHZ) states can be asymptotically distilled from any given pure state under LOCC. Our approach consists in “making coherent” the proposed CR distillation protocols and recycling of resources [Devetak <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> IEEE Trans. Inf. Theory 54(10):4587-4618, 2008]. The first lower bound is identical to a recent result by Vrana and Christandl [IEEE Trans. Inf. Theory 65(9):5945-5958, 2019], which is based on a combinatorial method to achieve the same rate. Our second lower bound generalises and improves upon this result, and unifies a number of other known lower bounds on GHZ distillation.

Arbitrarily varying multiple access channels with conferencing encoders: List decoding and finite coordination resources

Communication over channels that may vary in an arbitrary and unknown manner from channel use to channel use is studied. Such channels fall in the framework of arbitrarily varying channels (AVCs), for which it has been shown that the classical deterministic approaches with pre-specified encoder and decoder fail if the AVC is symmetrizable. However, more sophisticated strategies such as common randomness (CR) assisted codes or list decoding are capable to resolve the ambiguity induced by symmetrizable AVCs. AVCs further serve as the indispensable basis for modeling adversarial attacks such as jamming in information theoretic security related communication problems. In this paper, we study the arbitrarily varying multiple access channel (AVMAC) with conferencing encoders, which models the communication scenario with two cooperating transmitters and one receiver. This can be motivated for example by cooperating base stations or access points in future systems. The capacity region of the AVMAC with conferencing encoders is established and it is shown that list decoding allows for reliable communication also for symmetrizable AVMACs. The list capacity region equals the CR-assisted capacity region for large enough list size. Finally, for fixed probability of decoding error the amount of resources, i.e., CR or list size, is quantified and shown to be finite.

Capacity results and super-activation for wiretap channels with active wiretappers

The classical wiretap channel models secure communication in the presence of a nonlegitimate wiretapper who has to be kept ignorant. Traditionally, the wiretapper is passive in the sense that he only tries to eavesdrop the communication using his received channel output. In this paper, more powerful active wiretappers are studied. In addition to eavesdropping, these wiretappers are able to influence the communication conditions of all users by controlling the corresponding channel states. Since legitimate transmitters and receivers do not know the actual channel realization or the wiretapper's strategy of influencing the channel states, they are confronted with arbitrarily varying channel (AVC) conditions. The corresponding secure communication scenario is, therefore, given by the arbitrarily varying wiretap channel (AVWC). In the context of AVCs, common randomness (CR) has been shown to be an important resource for establishing reliable communication, in particular, if the AVC is symmetrizable. But availability of CR also affects the strategy space of an active wiretapper as he may or may not exploit the common randomness for selecting the channel states. Several secrecy capacity results are derived for the AVWC. In particular, the CR-assisted secrecy capacity of the AVWC with an active wiretapper exploiting CR is established and analyzed in detail. Finally, it is demonstrated for active wiretappers how two orthogonal AVWCs, each useless for transmission of secure messages, can be super-activated to a useful channel allowing for secure communication at nonzero secrecy rates. To the best of our knowledge, this is not possible for passive wiretappers and, further, provides the first example of such super-activation, which has been expected to appear only in the area of quantum communication. Such knowledge is particularly important as it provides valuable insights for the design and the medium access control of future wireless communication systems.

Common randomness and secret key generation with a helper

Summary form only given. We consider the generation of common randomness (CR), secret or not secret, by two user terminals with aid from a terminal. Each terminal observes a different component of a discrete memoryless multiple source. The helper aids the users by transmitting information to them over a noiseless public channel subject to a rate constraint. Furthermore, one of the users is allowed to transmit to the other user over a public channel under a similar rate constraint. We study the maximum rate of the CR which can be thus generated, and also under additional secrecy conditions when it must be concealed from an eavesdropper and from a wiretapper. Single-letter capacity formulae are obtained for several special cases of interest. Connections are shown between CR capacity and identification capacity in specific situations.

Common randomness in information theory and cryptography. II. CR capacity

For pt.I see ibid., vol.39, p.1121, 1993. The common randomness (CR) capacity of a two-terminal model is defined as the maximum rate of common randomness that the terminals can generate using resources specified by the given model. We determine CR capacity for several models, including those whose statistics depend on unknown parameters. The CR capacity is shown to be achievable robustly, by common randomness of nearly uniform distribution no matter what the unknown parameters are. Our CR capacity results are relevant for the problem of identification capacity, and also yield a new result on the regular (transmission) capacity of arbitrarily varying channels with feedback.