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Considered is a network of parallel wireless channels in which individual parties are engaged in secret communication under the protection of cooperative jamming. A strategic eavesdropper selects the most vulnerable channels to attack. Existing works usually suggest the defender allocate limited cooperative jamming power to various channels. However, it usually requires some strong assumptions and complex computation to find such an optimal power control policy. This paper proposes a probabilistic cooperative jamming scheme such that the defender focuses on protecting randomly selected channels. Two different cases regarding each channel’s eavesdropping capacity are discussed. The first case studies the general scenario where each channel has different eavesdropping capacity. The second case analyzes an extreme scenario where all channels have the same eavesdropping capacity. Two non-zero-sum Nash games model the competition between the network defender and an eavesdropper in each case. Furthermore, considering the case that the defender does not know the eavesdropper’s channel state information (CSI) leads to a Bayesian game. For all three games, we derive conditions for the existence of a unique Nash equilibrium (NE), and obtain the equilibria and the value functions in closed form.
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Entropic singularities give rise to quantum transmission
Abstract When can noiseless quantum information be sent across noisy quantum devices? And at what maximum rate? These questions lie at the heart of quantum technology, but remain unanswered because of non-additivity— a fundamental synergy which allows quantum devices (aka quantum channels) to send more information than expected. Previously, non-additivity was known to occur in very noisy channels with coherent information much smaller than that of a perfect channel; but, our work shows non-additivity in a simple low-noise channel. Our results extend even further. We prove a general theorem concerning positivity of a channel’s coherent information. A corollary of this theorem gives a simple dimensional test for a channel’s capacity. Applying this corollary solves an open problem by characterizing all qubit channels whose complement has non-zero capacity. Another application shows a wide class of zero quantum capacity qubit channels can assist an incomplete erasure channel in sending quantum information. These results arise from introducing and linking logarithmic singularities in the von-Neumann entropy with quantum transmission: changes in entropy caused by this singularity are a mechanism responsible for both positivity and non-additivity of the coherent information. Analysis of such singularities may be useful in other physics problems.
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- PAR ID:
- 10305964
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- Nature Communications
- Volume:
- 12
- Issue:
- 1
- ISSN:
- 2041-1723
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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