Duality between source coding with quantum side information and c-q channel coding

Abstract

In this paper, we establish an interesting duality between two different quantum informationprocessing tasks, namely, classical source coding with quantum side information, and channel coding over c-q channels. The duality relates the optimal error exponents of these two tasks, generalizing the classical results of Ahlswede and Dueck. We establish duality both at the operational level and at the level of the entropic quantities characterizing these exponents. For the latter, the duality is given by an exact relation, whereas for the former, duality manifests itself in the following sense: an optimal coding strategy for one task can be used to construct an optimal coding strategy for the other task. Along the way, we derive a bound on the error exponent for c-q channel coding with constant composition codes which might be of independent interest.

Quantum Sphere-Packing Bounds With Polynomial Prefactors

“…(1) and (1), and discusses their generalizations to c-q channels. We remark that the established finite blocklength bounds and the polynomial prefactor are crucial for the analysis of coding performance in the medium error probability regime (more commonly known as moderate deviation analysis) [28,29,30], classical data compression with quantum side information [31,32], and joint source-channel coding with quantum side information [33].…”

Refined Strong Converse for the Constant Composition Codes

“…Thus Arimoto's bound is tight, in terms of the exponential decay rate of the probability of correct decoding with block length, for all rates above the channel capacity. An analogous result is derived for constant composition codes on DSPCs in [22], for the Gaussian channel in [23], for classical-quantum channels in [18], for classical data compression with quantum side information in [20], and for constant composition codes on classical-quantum channels in [24]. Although Arimoto's bound, given in (1), is tight in terms of the exponential decay rate of the correct decoding probability with block length, the prefactor multiplying the exponentially decaying term can be improved.…”

Classical State Masking over a Quantum Channel

“…for all x n ∈ A δ1 (p X ), by ( 40), ( 46), (48), and (49), respectively. Thus, by Lemma 6, there exists a POVM D k such that Pr (E 2 | E c 1 ) ≤ 2 −n(I(X;B)ρ− R−ε3(δ)) , which tends to zero as n → ∞, provided that…”

“…compression with SSI is also studied in [43][44][45][46][47][48][49]. Compression with SSI given entanglement assistance was recently considered by Khanian and Winter [50][51][52].…”