2011/05/31 by Mark M. Wilde, Patrick Hayden, Saikat Guha · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Coding (social sciences) #Computer science #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Statistics #cs.IT #math.IT #quant-ph
paper · pdf · doi:10.1103/physreva.86.062306
published as Physical Review A 86, 062306 (2012) · 20 pages, 7 figures, v2 has a new figure and a proof that the regions are optimal for the lossy bosonic channel if the entropy photon-number inequality is true; v3, submission to Physical Review A (see related work at http://link.aps.org/doi/10.1103/PhysRevLett.108.140501); v4, final version accepted into Physical Review A
arxiv created 2012/11/22 · openalex publication_date 2012/12/06 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The trade-off capacity region of a quantum channel characterizes the optimal net rates at which a sender can communicate classical, quantum, and entangled bits to a receiver by exploiting many independent uses of the channel, along with the help of the same resources. Similarly, one can consider a trade-off capacity region when the noiseless resources are public, private, and secret-key bits. We identified [see Wilde, Hayden, and Guha, Phys. Rev. Lett. 108, 140501 (2012)] these trade-off rate regions for the pure-loss bosonic channel and proved that they are optimal provided that a long-standing minimum-output entropy conjecture is true. Additionally, we showed that the performance gains of a trade-off coding strategy when compared to a time-sharing strategy can be quite significant. In this paper, we provide detailed derivations of the results announced there, and we extend the application of these ideas to thermal-noise and amplifying bosonic channels. We also derive a ``rule of thumb'' for trade-off coding, which determines how to allocate photons in a coding strategy if a large mean photon number is available at the channel input. Our results on the amplifying bosonic channel also apply to the ``Unruh channel'' considered in the context of relativistic quantum information theory.