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. Our result implies the sharp Hausdorff--Young constants for the Weyl transform, as well as that for Heisenberg groups. The key ingredient is a novel flow related to the mixed-norm of noncommutative Gabor transform. This, meanwhile, implies a new proof of the classical sharp Hausdorff--Young inequality. We then apply the sharp Hausdorff--Young inequality to establish the sharp Young inequality for noncommutative convolution in the range $1\le p,q\le2\le r\le\infty$, with $1/p+1/q=1+1/r$. After appropriate rescaling and trace normalization, this convolution coincides with beam-splitter convolution for bosonic systems, yielding the corresponding Young inequalities with optimal constants in the same range.

math.FA↗

arXiv2026

Exact exponents for smoothing the max-relative entropy and quantum information decoupling in von Neumann algebras

We establish the exact exponent for smoothing the max-relative entropy on arbitrary von Neumann algebras. The proof first develops the required large-deviation and smoothing estimates in the semifinite setting and then passes to general von Neumann algebras through Haagerup-Junge-Xu reduction. We next study catalytic quantum information decoupling when the reference system is described by an arbitrary von Neumann algebra. A key ingredient is an operator layer-cake formula valid on arbitrary von Neumann algebras. This formula leads to a convex-split estimate for normal states with a general von Neumann algebraic reference system. Combining this estimate with the smoothing exponent result, we obtain lower and upper bounds on the catalytic-decoupling reliability function. These bounds coincide below the corresponding critical rate, yielding the exact decoupling reliability function in that regime.

cs.IT↗

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{é}nyi divergence for all orders $α\in[\frac{1}{2},\infty)$. For $α\in[\frac{1}{2},1)$, the exponent is characterized by the two-parameter club-sandwiched mutual information, whereas for $α\in[1,\infty)$, it is characterized by the order-$α$ sandwiched R{é}nyi mutual information. We also determine the exact strong converse exponent of privacy amplification against quantum side information under the sandwiched R{é}nyi divergence for $α\in(2,\infty)$, expressed in terms of the corresponding order-$α$ sandwiched R{é}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 $α\in[\frac{1}{2},1)$.

quant-ph↗

arXiv2026

Reliability Functions of Quantum Soft Covering and Privacy Amplification via a Mixed-Order Rényi Divergence

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

quant-ph↗