Superadditivity of Quantum Channel Coding Rate With Finite Blocklength Joint Measurements

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The maximum rate at which classical information can be reliably transmitted per use of a quantum channel strictly increases in general with N, the number of channel outputs that are detected jointly by the quantum joint-detection receiver (JDR). This phenomenon is known as superadditivity of the maximum achievable information rate over a quantum channel. We study this phenomenon for a pure-state classical-quantum channel and provide a lower bound on C-N/N, the maximum information rate when the JDR is restricted to making joint measurements over no more than N quantum channel outputs, while allowing arbitrary classical error correction. We also show the appearance of a superadditivity phenomenon-of mathematical resemblance to the aforesaid problem-in the channel capacity of a classical discrete memoryless channel when a concatenated coding scheme is employed, and the inner decoder is forced to make hard decisions on N-length inner codewords. Using this correspondence, we develop a unifying framework for the above two notions of superadditivity, and show that for our lower bound to C-N/N to be equal to a given fraction of the asymptotic capacity C of the respective channel, N must be proportional to V/C-2, where V is the respective channel dispersion quantity.
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Issue Date
2016-10
Language
English
Article Type
Article
Citation

IEEE TRANSACTIONS ON INFORMATION THEORY, v.62, no.10, pp.5938 - 5959

ISSN
0018-9448
DOI
10.1109/TIT.2016.2597285
URI
http://hdl.handle.net/10203/224574
Appears in Collection
EE-Journal Papers(저널논문)
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