arXiv subjects

Shi-Bing Li

Publications and source records attributed to Shi-Bing Li.

4 recordsLinked to original sources

arXiv2026

Strong Converse Exponents of Quantum Soft Covering and Privacy Amplification

We determine the exact strong converse exponent of quantum soft covering under the sandwiched R{\'e}nyi divergence for all orders $\alpha\in[\frac{1}{2},\infty)$. For $\alpha\in[\frac{1}{2},1)$, the exponent is characterized by the two-parameter club-sandwiched mutual information, whereas for $\alpha\in[1,\infty)$, it is characterized by the order-$\alpha$ sandwiched R{\'e}nyi mutual information. We also determine the exact strong converse exponent of privacy amplification against quantum side information under the sandwiched R{\'e}nyi divergence for $\alpha\in(2,\infty)$, expressed in terms of the corresponding order-$\alpha$ sandwiched R{\'e}nyi conditional entropy. To the best of our knowledge, these results provide the first exact characterization of the strong converse exponent of quantum soft covering and the first precise operational interpretation of the two-parameter club-sandwiched mutual information in the quantum setting. The key ingredient is that we establish the exponential rate of the $K$-functional, which is instrumental in deriving the strong converse exponent of quantum soft covering for $\alpha\in[\frac{1}{2},1)$.

quant-ph↗

arXiv2026

Reliability Functions of Quantum Soft Covering and Privacy Amplification via a Mixed-Order R\'enyi Divergence

In this paper, we introduce a novel mixed-order R\'enyi divergence and investigate its fundamental properties. Using this divergence, we define a family of mixed-order order-two R\'enyi mutual information and R\'enyi conditional entropy. We derive exact reliability functions of quantum soft covering and privacy amplification under the sandwiched R\'enyi divergence with order $\alpha\in[2,\infty)$. The former is jointly characterized by the sandwiched and mixed-order order-two R\'enyi mutual information quantities, while the latter is characterized by the corresponding conditional entropies. These results provide operational interpretations of the proposed mixed-order R\'enyi divergence. To the best of our knowledge, this is the first exact characterization of the reliability function for quantum soft covering.

quant-ph↗

arXiv2025

Two-Parameter Rényi Information Quantities with Applications to Privacy Amplification and Soft Covering

There are no universally accepted definitions of Rényi conditional entropy and Rényi mutual information, although motivated by different applications, several definitions have been proposed in the literature. In this paper, we consider a family of two-parameter Rényi conditional entropy and a family of two-parameter Rényi mutual information. By performing a change of variables for the parameters, the two-parameter Rényi conditional entropy we study coincides precisely with the definition introduced by Hayashi and Tan [IEEE Trans. Inf. Theory, 2016], and it also emerges naturally as the classical specialization of the three-parameter quantum Rényi conditional entropy recently put forward by Rubboli, Goodarzi, and Tomamichel [arXiv:2410.21976 (2024)]. We establish several fundamental properties of the two-parameter Rényi conditional entropy, including monotonicity with respect to the parameters and variational expression. The associated two-parameter Rényi mutual information considered in this paper is new and it unifies three commonly used variants of Rényi mutual information. For this quantity, we prove several important properties, including the non-negativity, additivity, data processing inequality, monotonicity with respect to the parameters, variational expression, as well as convexity and concavity. Finally, we demonstrate that these two-parameter Rényi information quantities can be used to characterize the strong converse exponents in privacy amplification and soft covering problems under Rényi divergence of order $α\in (0, \infty)$.

cs.IT↗

arXiv2025

Large Deviation Analysis for the Reverse Shannon Theorem

Channel simulation is to simulate a noisy channel using noiseless channels with unlimited shared randomness. This can be interpreted as the reverse problem to Shannon's noisy coding theorem. In contrast to previous works, our approach employs Rényi divergence (with the parameter $α\in(0,\infty)$) to measure the level of approximation. Specifically, we obtain the reverse Shannon theorem under the Rényi divergence, which characterizes the Rényi simulation rate, the minimum communication cost rate required for the Rényi divergence vanishing asymptotically. We also investigate the behaviors of the Rényi divergence when the communication cost rate is above or below the Rényi simulation rate. When the communication cost rate is above the Rényi simulation rate, we provide a complete characterization of the convergence exponent, called the reliability function. When the communication cost rate is below the Rényi simulation rate, we determine the linear increasing rate for the Rényi divergence with parameter $α\in(0,\infty]$, which implies the strong converse exponent for the $α$-order fidelity.

cs.IT↗