404 research outputs found
Distributed Task Encoding
The rate region of the task-encoding problem for two correlated sources is
characterized using a novel parametric family of dependence measures. The
converse uses a new expression for the -th moment of the list size, which
is derived using the relative -entropy.Comment: 5 pages; accepted at ISIT 201
On the quantum Renyi relative entropies and related capacity formulas
We show that the quantum -relative entropies with parameter
can be represented as generalized cutoff rates in the sense
of [I. Csiszar, IEEE Trans. Inf. Theory 41, 26-34, (1995)], which provides a
direct operational interpretation to the quantum -relative entropies.
We also show that various generalizations of the Holevo capacity, defined in
terms of the -relative entropies, coincide for the parameter range
, and show an upper bound on the one-shot epsilon-capacity of
a classical-quantum channel in terms of these capacities.Comment: v4: Cutoff rates are treated for correlated hypotheses, some proofs
are given in greater detai
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
Finite-key security analysis for multilevel quantum key distribution
We present a detailed security analysis of a d-dimensional quantum key
distribution protocol based on two and three mutually unbiased bases (MUBs)
both in an asymptotic and finite key length scenario. The finite secret key
rates are calculated as a function of the length of the sifted key by (i)
generalizing the uncertainly relation-based insight from BB84 to any d-level
2-MUB QKD protocol and (ii) by adopting recent advances in the second-order
asymptotics for finite block length quantum coding (for both d-level 2- and
3-MUB QKD protocols). Since the finite and asymptotic secret key rates increase
with d and the number of MUBs (together with the tolerable threshold) such QKD
schemes could in principle offer an important advantage over BB84. We discuss
the possibility of an experimental realization of the 3-MUB QKD protocol with
the orbital angular momentum degrees of freedom of photons.Comment: v4: close to the published versio
- …