Sequential, successive, and simultaneous decoders for entanglement-assisted classical communication
- First Online:
Bennett et al. showed that allowing shared entanglement between a sender and receiver before communication begins dramatically simplifies the theory of quantum channels, and these results suggest that it would be worthwhile to study other scenarios for entanglement-assisted classical communication. In this vein, the present paper makes several contributions to the theory of entanglement-assisted classical communication. First, we rephrase the Giovannetti–Lloyd–Maccone sequential decoding argument as a more general “packing lemma” and show that it gives an alternate way of achieving the entanglement-assisted classical capacity. Next, we show that a similar sequential decoder can achieve the Hsieh–Devetak–Winter region for entanglement-assisted classical communication over a multiple access channel. Third, we prove the existence of a quantum simultaneous decoder for entanglement-assisted classical communication over a multiple access channel with two senders. This result implies a solution of the quantum simultaneous decoding conjecture for unassisted classical communication over quantum multiple access channels with two senders, but the three-sender case still remains open (Sen recently and independently solved this unassisted two-sender case with a different technique). We then leverage this result to recover the known regions for unassisted and assisted quantum communication over a quantum multiple access channel, though our proof exploits a coherent quantum simultaneous decoder. Finally, we determine an achievable rate region for communication over an entanglement-assisted bosonic multiple access channel and compare it with the Yen-Shapiro outer bound for unassisted communication over the same channel.
KeywordsQuantum information theory Entanglement-assisted communication Quantum simultaneous decoding Quantum multiple access channel Bosonic channel
Unable to display preview. Download preview PDF.
- 11.Dutil, N.: Multiparty quantum protocols for assisted entanglement distillation. PhD thesis, McGill University (2011) arXiv:1105.4657Google Scholar
- 12.Eisert, J., Wolf, M.M.: Quantum Information with Continous Variables of Atoms and Light, chapter Gaussian quantum channels, pp. 23–42. Imperial College Press, London (2007). arXiv:quant-ph/0505151Google Scholar
- 13.El Gamal, A., Kim, Y.-H.: Lecture notes on network information theory (2010). arXiv:1001.3404Google Scholar
- 14.Fawzi, O., Hayden, P., Savov, I., Sen, P., Wilde, M.M.: Classical communication over a quantum interference channel (2011). arXiv:1102.2624Google Scholar
- 18.Giovannetti, V., Lloyd, S., Maccone, L.: Achieving the Holevo bound via sequential measurements (December 2010). arXiv:1012.0386Google Scholar
- 21.Guha, S.: Multiple-User Quantum Information Theory for Optical Communication Channels. PhD thesis, Massachusetts Institute of Technology (2008)Google Scholar
- 33.Sen, P.: Private communication (2011)Google Scholar
- 34.Sen, P.: Sequential decoding for some channels with classical input and quantum output (2011)Google Scholar
- 36.Weedbrook, C., Pirandola, S., Garcia-Patron, R., Cerf, N.J., Ralph, T.C., Shapiro, J.H., Lloyd, S.: Gaussian quantum information (2011 in preparation)Google Scholar
- 37.Wilde, M.M.: From Classical to Quantum Shannon Theory (2011). arXiv:1106.1445Google Scholar