2014/01/31 by H. Boche, J. Nötzel, J. Noetzel
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Channel (broadcasting) #Communication source #Decoding methods #Discontinuity (linguistics) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum capacity #Quantum entanglement #Randomness #Topology (electrical circuits) #Transmission (telecommunications) #Wireless Communication Security Techniques #cs.IT #math-ph #math.IT #math.MP #quant-ph
paper · pdf · doi:10.1063/1.4902930
19 pages, no figures. Corrected typos. Large parts of the introduction are rewritten, especially the historical part from the earlier verions is completely deleted. This version contains an additional theorem (Theorem 5) which summarizes our findings concerning the points of discontinuity of the deterministic message transmission capacity
arxiv created 2014/05/07 · openalex publication_date 2014/12/01 · arxiv updated 2015/06/18 · openalex created_date 2017/10/20 · openalex updated_date 2026/08/05
This work is motivated by a quite general question: Under which circumstances are the capacities of information transmission systems continuous? The research is explicitly carried out on finite arbitrarily varying quantum channels (AVQCs). We give an explicit example that answers the recent question whether the transmission of messages over AVQCs can benefit from assistance by distribution of randomness between the legitimate sender and receiver in the affirmative. The specific class of channels introduced in that example is then extended to show that the unassisted capacity does have discontinuity points, while it is known that the randomness-assisted capacity is always continuous in the channel. We characterize the discontinuity points and prove that the unassisted capacity is always continuous around its positivity points. After having established shared randomness as an important resource, we quantify the interplay between the distribution of finite amounts of randomness between the legitimate sender and receiver, the (nonzero) probability of a decoding error with respect to the average error criterion and the number of messages that can be sent over a finite number of channel uses. We relate our results to the entanglement transmission capacities of finite AVQCs, where the role of shared randomness is not yet well understood, and give a new sufficient criterion for the entanglement transmission capacity with randomness assistance to vanish.