Positivity and Nonadditivity of Quantum Capacities Using Generalized Erasure Channels

DOI10.1109/TIT.2021.3080819zbMATH Open1475.81009arXiv2003.00583MaRDI QIDQ5001809

Vikesh Siddhu, Robert B. Griffiths

Publication date: 23 July 2021

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Abstract: We consider various forms of a process, which we call {em gluing}, for combining two or more complementary quantum channel pairs $(mathcalB,mathcalC)$ to form a composite. One type of gluing combines a perfect channel with a second channel to produce a emph{generalized erasure channel} pair $(mathcal{B}_g,mathcal{C}_g)$. We consider two cases in which the second channel is (i) an amplitude-damping, or (ii) a phase-damping qubit channel; (ii) is the emph{dephrasure channel} of Leditzky et al. For both (i) and (ii), $(mathcal{B}_g,mathcal{C}_g)$ depends on the damping parameter $0leqpleq1$ and a parameter $0leqlambdaleq1$ that characterizes the gluing process. In both cases we study $Q^{(1)}(mathcal{B}_g)$ and $Q^{(1)}(mathcal{C}_g)$, where $Q^{(1)}$ is the channel coherent information, and determine the regions in the $(p,lambda)$ plane where each is zero or positive, confirming previous results for (ii). A somewhat surprising result for which we lack any intuitive explanation is that $Q^{(1)}(mathcal{C}_g)$ is zero for $lambdaleq1/2$ when $p=0$, but is strictly positive (though perhaps extremely small) for all values of $lambda>0$ when $p$ is positive by even the smallest amount. In addition we study the nonadditivity of $Q^{(1)}(mathcal{B}_g)$ for two identical channels in parallel. It occurs in a well-defined region of the $(p,lambda)$ plane in case (i). In case (ii) we have extended previous results for the dephrasure channel without, however, identifying the full range of $(p,lambda)$ values where nonadditivity occurs. Again, an intuitive explanation is lacking.

Full work available at URL: https://arxiv.org/abs/2003.00583

zbMATH Keywords

gluingchannel coherent informationcombining two or more complementary quantum channel pairsdephrasure channel

Mathematics Subject Classification ID

Channel models (including quantum) in information and communication theory (94A40) Quantum information, communication, networks (quantum-theoretic aspects) (81P45) Quantum channels, fidelity (81P47)

Related Items (1)

Positivity, discontinuity, finite resources, and nonzero error for arbitrarily varying quantum channels

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