3 research outputs found
Achievable error exponents of data compression with quantum side information and communication over symmetric classical-quantum channels
A fundamental quantity of interest in Shannon theory, classical or quantum,
is the optimal error exponent of a given channel W and rate R: the constant
E(W,R) which governs the exponential decay of decoding error when using ever
larger codes of fixed rate R to communicate over ever more (memoryless)
instances of a given channel W. Here I show that a bound by Hayashi [CMP 333,
335 (2015)] for an analogous quantity in privacy amplification implies a lower
bound on the error exponent of communication over symmetric classical-quantum
channels. The resulting bound matches Dalai's [IEEE TIT 59, 8027 (2013)]
sphere-packing upper bound for rates above a critical value, and reproduces the
well-known classical result for symmetric channels. The argument proceeds by
first relating the error exponent of privacy amplification to that of
compression of classical information with quantum side information, which gives
a lower bound that matches the sphere-packing upper bound of Cheng et al. [IEEE
TIT 67, 902 (2021)]. In turn, the polynomial prefactors to the sphere-packing
bound found by Cheng et al. may be translated to the privacy amplification
problem, sharpening a recent result by Li, Yao, and Hayashi [arXiv:2111.01075
[quant-ph]], at least for linear randomness extractors.Comment: Comments very welcome