arXiv subjects

Hao-Chung Cheng

Publications and source records attributed to Hao-Chung Cheng.

At least 19 recordsLinked to original sources

arXiv2026

Second-Order Expansion of Privacy Amplification Under f-Divergence Criteria

We derive the second-order asymptotics of randomness extraction from memoryless sources with side information under security criteria based on a broad class of Csisz\`ar f-divergences, treating both a fixed reference side-information marginal and optimization over that marginal. The conditional varentropy decomposes into fluctuations of the conditional entropy across different values of the side information and the average variance of the conditional surprisal for each value. Without marginal optimization, these contributions yield a Gaussian-mixture second-order profile. With marginal optimization, they combine into the total conditional varentropy, yielding a single Gaussian profile. As corollaries, we obtain second-order expansions for R\'enyi-entropy criteria of all orders $\alpha \in (0,1)$ and recover the known expansion for total variation distance.

cs.IT↗

arXiv2026

Minimax games for quantum channel discrimination

Quantum channel discrimination is a primitive task for identifying, verifying, and benchmarking quantum dynamics. Previous studies have primarily considered either the best-case tester-input setting or the worst-case jammer-input setting. Here, we introduce a game-theoretic framework in which both the tester and jammer control separate inputs. Combining three input structures, characterized by whether the tester and jammer use entangled inputs or IID inputs across channel uses, with four information patterns, determined by the visibility of the jammer's strategy and its knowledge of the true hypothesis, yields twelve game models. We provide exact finite blocklength hypothesis testing characterizations of all twelve models in terms of nine minimax hypothesis testing divergences and derive their asymptotic Stein exponents. Notably, for entangled jammers, neither the visibility of the jammer's strategy nor its knowledge of the true hypothesis affects the asymptotic Stein exponent, whereas the information pattern remains consequential for IID jammers. As an example, we study the discrimination of a general channel from a replacer channel and show that all asymptotic Stein exponents coincide with the same additive, single letter quantity. We further develop a general argument that upgrades achievability results to strong converse results, thereby establishing strong converse properties for several game models, resolving an open problem in composite hypothesis testing posed by Berta et al. [Commun. Math. Phys. 385, 55 (2021)], and strengthening several recent results of Lami [arXiv:2510.06340]. The framework and techniques developed here may support future studies of quantum information tasks involving competing roles.

quant-ph↗

arXiv2026

No information transmission through quantum channels above capacity

We show that the capacity of a quantum channel demarcates a phase transition: while reliable transmission below capacity is always possible, any attempt to transmit information above it fails catastrophically. Specifically, we prove exponential strong converse theorems for unassisted quantum and classical communication over arbitrary finite-dimensional memoryless quantum channels. At rates beyond the respective capacity, the entanglement-generation fidelity and the success probability for classical communication decay exponentially with the number of channel uses. This rules out transmission above capacity even when one tolerates arbitrarily large errors. Our proof follows the classical Arimoto strategy, augmented by a crucial new ingredient: integral representations of R\'enyi information measures that lead to asymptotic continuity bounds for R\'enyi capacities.

quant-ph↗

arXiv2026

Strong Converse Exponent of Quantum State Merging

We determine the strong converse exponent for the entanglement cost of quantum state merging, showing that it is characterized by the optimized $\alpha$-$z$ conditional R\'enyi entropies with $z=\alpha/2\in[1/2,1]$. This contrasts with the sandwiched conditional R\'enyi entropies that typically govern strong converse exponents in quantum information theory. As a consequence, we derive the strong converse exponent of the partially smoothed conditional min-entropy in purified distance. This exponent is governed by club-sandwiched conditional entropies, whereas global smoothing leads to a sandwiched expression.

quant-ph↗

arXiv2026

Sharp Continuity of Petz and Sandwiched R\'enyi Conditional Entropies

We determine the sharp modulus of continuity, in trace distance, of the optimized Petz and sandwiched R\'enyi conditional entropies for every order $\alpha\in[\frac12,1)$. If two bipartite states are within trace distance $\delta$, then both conditional entropies differ by at most $\frac{1}{1-\alpha} \log[(1-\varepsilon)^{\alpha} +(D-1)^{1-\alpha}\varepsilon^{\alpha}]$, where $\varepsilon := \min\{\delta,1-1/D\}$ and $D$ is the effective dimension, given by the dimension of the first subsystem times the largest possible Schmidt rank. For every distance constraint $\delta\in[0,1]$, the bound is attained by an isotropic pair with a maximally entangled anchor. Taking $\alpha\uparrow1$ recovers the recent sharp continuity bound of quantum conditional entropy by Berta et al. [arXiv:2607.24687]. The proof linearizes the relevant concave R\'enyi functional at a comparison point dictated by the isotropic equality family. Schmidt-rank domination extends the equality geometry to an arbitrary anchor state, after which trace-distance duality and a noncommutative calibration estimate control the perturbation and anchor term without weakening the sharp constant. The latter estimate requires matrix analysis and is assisted by ChatGPT 5.6 Sol.

quant-ph↗

arXiv2026

Superadditivity for Entanglement-Assisted Communication

The entanglement-assisted capacity of a quantum channel admits an additive single-letter characterization, implying that joint encodings across channel uses cannot increase the ultimate communication rate. Here, we show that this additive picture does not extend to communication reliability. Specifically, we prove that the Petz-R\'enyi channel information can be strictly superadditive for every $\alpha\in[1/2,1)$, yielding a genuine multi-copy enhancement of the entanglement-assisted random-coding error exponent, even though the entanglement-assisted capacity remains additive. We establish this phenomenon analytically already for measurement channels, which are entanglement-breaking and have additive unassisted capacity. Remarkably, this strict superadditivity is witnessed by a separable, classically correlated two-copy channel-input marginal, demonstrating that no entanglement between the transmitted systems is required. Our results show that, although correlations across channel uses cannot increase the ultimate rate of entanglement-assisted communication, they can enhance its reliability.

quant-ph↗

arXiv2026

Device-independent Quantum Key Distribution in the commuting operator framework

Device-independent quantum key distribution (DIQKD) is arguably the gold standard for secure quantum communication, as it aims to rely only on observed input-output statistics of an uncharacterized device which is only assumption to obey the laws of quantum physics. A corresponding security analysis hence demands a description of a quantum experiment from a most general perspective. Under close inspection, existing proof techniques do not always meet this goal as they tend to rely on subtile assumptions on a tensor product structure of the underlying Hilbert space and a 'hidden but finite' dimensionality. In this work, we collect the tools needed for a full analysis of DIQKD in the commuting operator framework, which avoids these subtilities and provides the arguably most general view on a quantum experiment. We rigorously proof the common assumption that in DIQKD measurements can be w.l.o.g. assumed to be projective. Furthermore, we show that task of computing key rates can be casted as a non-commutative polynomial optimization (NPO) problem to which the Navascu\'es-Pironio-Ac\'in (NPA) hierarchy gives a correct and converging relaxation. As a tool, we generalize the integral representation for the relative entropy by Frenkel [Quantum 7, 1102 (2023)] to general von Neumann algebras and apply techniques from Kossmann and Schwonnek [arXiv: 2411.04858] for the approximation in an NPO program.

quant-ph↗

arXiv2026

Multiple Quantum Hypothesis Testing: One-Shot Pairwise Bounds and Sharp Asymptotics

We consider Bayesian discrimination among multiple quantum states and establish a dimension-free one-shot upper bound on the minimum probability of error in terms of the sum of pairwise errors. This resolves a conjecture of Audenaert and Mosonyi [J. Math. Phys. 55 (2014)] and improves the multiple quantum Chernoff bound of Li [Ann. Statist. 44 (2016)] by removing its dimension-dependent prefactor. In the asymptotic many-copy regime, our bound proves the achievability of the multiple quantum Chernoff distance for arbitrary separable Hilbert spaces, thereby settling the previously open infinite-dimensional case, and further yields constant-factor sharp asymptotics for the optimal error probability. In binary quantum hypothesis testing, we prove that the minimum error probability is characterized, up to universal constants, by a trace harmonic-mean quantity. Consequently, the optimal binary quantum error probability is within a factor of two of the optimal classical error probability for the associated Nussbaum-Szko{\l}a distributions, complementing the lower bound of Nussbaum and Szko{\l}a [Ann. Statist. 37 (2009)].

quant-ph↗

arXiv2026

MIDI-Informed Singing Accompaniment Generation in a Compositional Song Pipeline

While end-to-end lyrics-to-song models offer convenience for casual users, professional songwriters require score-to-song systems that allow them to retain authorship over the core melody. However, existing score-to-song methods are limited to short-form snippets and fail to maintain coherence in long-form generation, particularly during vocal-silent sections like intros and bridges. To address this long-form bottleneck, we propose MIDI-informed singing accompaniment generation (MIDI-SAG). Unlike conventional audio-only models, MIDI-SAG utilizes symbolic timing and chord information derived from the vocal MIDI to provide a stable musical roadmap. By incorporating structure planning, which defines temporal boundaries and semantic labels, our framework facilitates consistent generation across both vocal and non-vocal sections. We demonstrate the feasibility of this compositional pipeline by leveraging specialized pre-trained modules, enabling data-efficient training on a single GPU. Our experiments show the potential of this approach for both professional score-to-song and general lyrics-to-song tasks. While an early exploration, MIDI-SAG suggests a promising direction for structured, long-form music synthesis. Audio demos are available, and the code will be open-sourced at https://composerflow.github.io/web_revealed/.

cs.SD↗

arXiv2026

Tight any-shot quantum decoupling

Quantum information decoupling is a fundamental primitive in quantum information theory, underlying various applications in quantum physics. We prove a novel one-shot decoupling theorem formulated in terms of quantum relative entropy distance, with the decoupling error bounded by two sandwiched R\'enyi conditional entropies. In the asymptotic i.i.d. setting of standard information decoupling via partial trace, we show that this bound is ensemble-tight in quantum relative entropy distance and thereby yields a characterization of the associated decoupling error exponent in the low-cost-rate regime. Leveraging this framework, we derive several operational applications formulated in terms of purified distance: (i) single-letter expressions for the exact error exponents of quantum state merging in the low-entanglement-cost and high-entanglement-distillation-rate regimes, in terms of Petz-R\'enyi conditional entropies, and (ii) regularized expressions for achievable error exponents of entanglement distillation and quantum channel coding in terms of Petz-R\'enyi coherent informations. We further prove that these achievable bounds are tight for maximally correlated states and generalized dephasing channels, respectively, for the high distillation-rate/coding-rate regimes.

quant-ph↗

arXiv2026

Adversarial Hypothesis Testing for Quantum Channels

This paper presents a systematic study of adversarial hypothesis testing for both quantum-quantum (QQ) and classical-quantum (CQ) channels. Unlike conventional channel discrimination, we consider a framework where the sender, Alice, selects the channel input adversarially to minimize Bob's distinguishability. We analyze this problem across four settings based on whether Alice employs i.i.d. or general inputs and whether the receiver, Bob, is informed of the specific input choice (allowing his measurement to depend on the input). We characterize the Stein exponents for each setting and reveal a striking distinction in behavior: for QQ channels with i.i.d. inputs, Bob's knowledge of the input significantly enhances distinguishability, yet this advantage vanishes when general inputs are permitted. In contrast, for CQ channels, Bob being informed provides a consistent advantage over the corresponding entanglement-breaking channels for both i.i.d. and general inputs. These results demonstrate a unique phenomenon in adversarial hypothesis testing where the CQ channel does not merely behave as a special case of the QQ channel.

quant-ph↗

arXiv2026

A Mirror-Descent Algorithm for Computing the Petz-R\'enyi Capacity of Classical-Quantum Channels

We study the computation of the $\alpha$-R\'enyi capacity of a classical-quantum (c-q) channel for $\alpha\in(0,1)$. We propose an exponentiated-gradient (mirror descent) iteration that generalizes the Blahut-Arimoto algorithm. Our analysis establishes relative smoothness with respect to the entropy geometry, guaranteeing a global sublinear convergence of the objective values. Furthermore, under a natural tangent-space nondegeneracy condition (and a mild spectral lower bound in one regime), we prove local linear (geometric) convergence in Kullback-Leibler divergence on a truncated probability simplex, with an explicit contraction factor once the local curvature constants are bounded.

quant-ph↗

arXiv2025

The operator layer cake theorem is equivalent to Frenkel's integral formula

The operator layer cake theorem provides an integral representation for the directional derivative of the operator logarithm in terms of a family of projections [arXiv:2507.06232]. Recently, the related work [arXiv:2507.07065] showed that the theorem gives an alternative proof to Frenkel's integral formula for Umegaki's relative entropy [Quantum, 7:1102 (2023)]. In this short note, we find a converse implication, demonstrating that the operator layer cake theorem is equivalent to Frenkel's integral formula.

quant-ph↗

arXiv2025

Sharp estimates of quantum covering problems via a novel trace inequality

In this paper, we prove a novel trace inequality involving two operators. As applications, we sharpen the one-shot achievability bound on the relative entropy error in a wealth of quantum covering-type problems, such as soft covering, privacy amplification, convex splitting, quantum information decoupling, and quantum channel simulation by removing some dimension-dependent factors. Moreover, the established one-shot bounds extend to infinite-dimensional separable Hilbert spaces as well. The proof techniques are based on the recently developed operator layer cake theorem and an operator change-of-variable argument, which are of independent interest.

quant-ph↗

arXiv2025

Layer Cake Representations for Quantum Divergences

Defining suitable quantum extensions of classical divergences often poses a challenge due to the non-commutative nature of quantum information. In this work, we propose a new approach via what we call the layer cake representation. The resulting quantum R\'enyi and $f$-divergences are then proven to be equivalent to those recently defined via integral representations. Nevertheless, the approach can provide several insights. We give an alternative proof of the integral representation of the relative entropy by Frenkel and prove a conjecture regarding a trace expression for the R\'enyi divergence. Additionally, we give applications to error exponents in hypothesis testing, a new Riemann-Stieltjes type integral representation and a variational representation.

quant-ph↗

arXiv2025

Error Exponents for Quantum Packing Problems via An Operator Layer Cake Theorem

In this work, we prove a one-shot random coding bound for classical-quantum channel coding, a problem conjectured by Burnashev and Holevo in 1998. By choosing the optimal input distribution, the bound implies the optimal error exponent (i.e., the reliability function) of classical-quantum channels for rates above the critical rate, even in infinite-dimensional Hilbert spaces. Our result extends to various quantum packing-type problems, including classical communication over any fully quantum channel with or without entanglement-assistance, constant composition codes, and classical data compression with quantum side information via fixed-length or variable-length coding. Our technical ingredient is to establish an operator layer cake theorem - the directional derivative of an operator logarithm admits an integral representation of certain projections. This shows that a kind of pretty-good measurement is equivalent to a randomized Holevo-Helstrom measurement, which provides an operational explanation of why the pretty-good measurement is pretty good.

quant-ph↗

arXiv2025

On Araki-Type Trace Inequalities

In this paper, we prove a trace inequality $\text{Tr}[ f(A) A^s B^s ] \leq \text{Tr}[ f(A) (A^{1/2} B A^{1/2} )^s ]$ for any positive and monotone increasing function $f$, $s\in[0,1]$, and positive semi-definite matrices $A$ and $B$. On the other hand, for $s\in[0,1]$ such that the map $x\mapsto x^s g(x)$ is positive and decreasing, then $ \text{Tr}[ g(A) (A^{1/2} B A^{1/2} )^s ] \leq \text{Tr}[ g(A) A^s B^s ]$.

math-ph↗

arXiv2025

MuseControlLite: Multifunctional Music Generation with Lightweight Conditioners

We propose MuseControlLite, a lightweight mechanism designed to fine-tune text-to-music generation models for precise conditioning using various time-varying musical attributes and reference audio signals. The key finding is that positional embeddings, which have been seldom used by text-to-music generation models in the conditioner for text conditions, are critical when the condition of interest is a function of time. Using melody control as an example, our experiments show that simply adding rotary positional embeddings to the decoupled cross-attention layers increases control accuracy from 56.6% to 61.1%, while requiring 6.75 times fewer trainable parameters than state-of-the-art fine-tuning mechanisms, using the same pre-trained diffusion Transformer model of Stable Audio Open. We evaluate various forms of musical attribute control, audio inpainting, and audio outpainting, demonstrating improved controllability over MusicGen-Large and Stable Audio Open ControlNet at a significantly lower fine-tuning cost, with only 85M trainble parameters. Source code, model checkpoints, and demo examples are available at: https://musecontrollite.github.io/web/.

cs.SD↗