arXiv subjects

Hongsen Qiu

Publications and source records attributed to Hongsen Qiu.

5 recordsLinked to original sources

arXiv2026

Noncommutative sharp Hausdorff-Young inequality

We prove the sharp Hausdorff--Young inequality on the quantum Euclidean space. Meanwhile, our result implies the sharp Hausdorff-Young constants for the Weyl transform, as well as that for the Heisenberg group. The key ingredient is a novel operator-valued flow related to the Gabor transform. Our method is mainly based on operator calculus and hence generally applicable to similar problems. Finally, we give the definition of noncommutative convolution and include the partial results for the sharp Young's inequality.

math.FA↗

arXiv2026

Sharp Quasi-Reverse Minkowski Inequality for Schatten Norms

Let $\|\cdot\|_p$ denote the Schatten $p$-norm and let $|A|=(A^*A)^{1/2}$. For $2\leq p<\infty$, let $x_{p,m}>1$ be the unique solution of $x_{p,m}^p=2x_{p,m}+m-1$, and set \[ C_{p,m}=\frac{\sqrt{x_{p,m}(x_{p,m}+m-1)}}{(x_{p,m}^p+m-1)^{1/p}}. \] We prove the sharp inequality \[ \|A_1+\cdots+A_m\|_p\leq C_{p,m}\bigl\||A_1|+\cdots+|A_m|\bigr\|_p \] for arbitrary complex matrices of arbitrary size. Equivalently, if $q=p/(p-1)$ and $R,X_1,\cdots,+X_m$ are positive semidefinite, then \[ \|RX_1\|_1+\cdots\|RX_m\|_1 \leq C_{p,m}\|R\|_q\|X_1+\cdots X_m\|_p. \] For $1<p<2$, we also show that the formula proposed for the optimal constant fails. We give both a numerical counterexample and a systematic analytic construction.oposed for the optimal constant fails. We give both a numerical counterexample and a systematic analytic construction.

math.FA↗

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↗

arXiv2026

Smoothing Exponents and Decoupling in Semifinite von Neumann Algebras

We study the smoothing exponent of the max-relative entropy in semifinite von Neumann algebras. Our main result gives an exact exponent formula in this setting. The proof develops operator-algebraic replacements for the dimension-dependent tools used in finite-dimensional arguments. These ingredients show that the smoothing exponent is governed by the underlying von Neumann algebraic structure rather than by matrix dimension estimates. As an application, we formulate catalytic quantum information decoupling with a semifinite von Neumann algebraic reference system. We prove an intrinsic layer-cake lemma for von Neumann algebras, which removes the countable spectrum assumption in the finite-dimensional proof and yields the corresponding semifinite estimate. Consequently, the decoupling reliability exponent is described by the same sandwiched R\'enyi mutual information formula as in the finite-dimensional theory.

cs.IT↗