arXiv subjects

Hao-Chung Cheng

Publications and source records attributed to Hao-Chung Cheng.

At least 37 records · Page 2Linked to original sources

arXiv2024

Resolvability of classical-quantum channels

Channel resolvability concerns the minimum resolution for approximating the channel output. We study the resolvability of classical-quantum channels in two settings, for the channel output generated from the worst input, and form the fixed independent and identically distributed (i.i.d.) input. The direct part of the worst-input setting is derived from sequential hypothesis testing as it involves of non-i.i.d.~inputs. The strong converse of the worst-input setting is obtained via the connection to identification codes. For the fixed-input setting, while the direct part follows from the known quantum soft covering result, we exploit the recent alternative quantum Sanov theorem to solve the strong converse.

quant-ph↗

arXiv2024

Distributed Quantum Hypothesis Testing under Zero-rate Communication Constraints

The trade-offs between error probabilities in quantum hypothesis testing are by now well-understood in the centralized setting, but much less is known for distributed settings. Here, we study a distributed binary hypothesis testing problem to infer a bipartite quantum state shared between two remote parties, where one of these parties communicates to the tester at (asymptotic) zero-rate, while the other party communicates to the tester at zero-rate or higher. As our main contribution, we derive an efficiently computable single-letter formula for the Stein's exponent of this problem, when the state under the alternative is the product of their marginals. For proving the converse direction of our result, we utilize a novel technique based on reverse hypercontractivity of a quantum markov semigroup combined with the pinching method. For the general case with vanishing type I error probability, we show that the Stein's exponent when (at least) one of the parties communicates classically at zero-rate is given by a multi-letter expression involving regularized measured relative entropy maximized over a sub-class of binary outcome separable measurements. When the state under the alternative commutes with a product eigenbasis of the marginal states under the null and has a larger support, we show that the exponent is characterized as a max-min optimization of regularized measured relative entropy over a sub-class of local binary outcome projective measurements. While this expression becomes single-letter for the fully classical case, we further prove that this already does not happen in the same way for classical-quantum states in general. The converse proof of the max-min characterization relies on an extension of the classical blowing-up lemma to bipartite quantum states satisfying the aforementioned commutativity condition, which could be of independent interest.

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arXiv2024

Exponents for Shared Randomness-Assisted Channel Simulation

We determine the exact error and strong converse exponents of shared randomness-assisted channel simulation in worst case total-variation distance. Namely, we find that these exponents can be written as simple optimizations over the R\'enyi channel mutual information. Strikingly, and in stark contrast to channel coding, there are no critical rates, allowing a tight characterization for arbitrary rates below and above the simulation capacity. We derive our results by asymptotically expanding the meta-converse for channel simulation [Cao {\it et al.}, IEEE Trans.~Inf.~Theory (2024)], which corresponds to non-signaling assisted codes. We prove this to be asymptotically tight by employing the approximation algorithms from [Berta {\it et al.}, Proc.~IEEE ISIT (2024)], which show how to round any non-signaling assisted strategy to a strategy that only uses shared randomness. Notably, this implies that any additional quantum entanglement-assistance does not change the error or the strong converse exponents.

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arXiv2024

Global Coherence in Quantum Discord as a Resource

This work addresses which aspect of \textit{bipartite coherence} in \textit{quantum discord} is essential for \textit{genuinely quantum correlation}. To this end, \textit{global coherence} of bipartite states is defined as a form of bipartite coherence that is not local coherence in either of the subsystems or in both subsystems alone, and we identify it as being indicated by a witness of discord. With \textit{global coherence} as \textit{a resource}, \textit{any local operations} of the form $\Phi_A \otimes \Phi_B$, which may create coherence locally, are \textit{free operations}. This implies that with global coherence as a resource for operational tasks, any local operations can be freely used, but require \textit{classical randomness not to be freely} available. Using this identification, we demonstrate that \textit{global coherence} is a \textit{necessary resource} for the task of \textit{semi-device-independent steerability} of quantum discord. On the other hand, for the task of \textit{remote state preparation} using \textit{quantum discord} in two-qubit states, a \textit{necessary and sufficient quantum resource} is identified by invoking a \textit{witness of global coherence}.

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arXiv2024

Joint State-Channel Decoupling and One-Shot Quantum Coding Theorem

In this work, we consider decoupling a bipartite quantum state via a general quantum channel. We propose a joint state-channel decoupling approach to obtain a one-shot error exponent bound without smoothing, in which trace distance is used to measure how good the decoupling is. The established exponent is expressed in terms of a sum of two sandwiched R{\'e}nyi entropies, one quantifying the amount of initial correlation between the state and environment, while the other characterizing the effectiveness of the quantum channel. This gives an explicit exponential decay of the decoupling error in the whole achievable region, which was missing in the previous results [Commun. Math. Phys. 328, 2014]. Moreover, it strengthens the error exponent bound obtained in a recent work [IEEE Trans. Inf. Theory, 69(12), 2023], for exponent from the channel part. As an application, we establish a one-shot error exponent bound for quantum channel coding given by a sandwiched R\'enyi coherent information.

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arXiv2024

Linear Convergence in Hilbert's Projective Metric for Computing Augustin Information and a R\'{e}nyi Information Measure

Consider the problems of computing the Augustin information and a R\'{e}nyi information measure of statistical independence, previously explored by Lapidoth and Pfister (IEEE Information Theory Workshop, 2018) and Tomamichel and Hayashi (IEEE Trans. Inf. Theory, 64(2):1064--1082, 2018). Both quantities are defined as solutions to optimization problems and lack closed-form expressions. This paper analyzes two iterative algorithms: Augustin's fixed-point iteration for computing the Augustin information, and the algorithm by Kamatsuka et al. (arXiv:2404.10950) for the R\'{e}nyi information measure. Previously, it was only known that these algorithms converge asymptotically. We establish the linear convergence of Augustin's algorithm for the Augustin information of order $\alpha \in (1/2, 1) \cup (1, 3/2)$ and Kamatsuka et al.'s algorithm for the R\'{e}nyi information measure of order $\alpha \in [1/2, 1) \cup (1, \infty)$, using Hilbert's projective metric.

math.OC↗

arXiv2024

Audio Prompt Adapter: Unleashing Music Editing Abilities for Text-to-Music with Lightweight Finetuning

Text-to-music models allow users to generate nearly realistic musical audio with textual commands. However, editing music audios remains challenging due to the conflicting desiderata of performing fine-grained alterations on the audio while maintaining a simple user interface. To address this challenge, we propose Audio Prompt Adapter (or AP-Adapter), a lightweight addition to pretrained text-to-music models. We utilize AudioMAE to extract features from the input audio, and construct attention-based adapters to feedthese features into the internal layers of AudioLDM2, a diffusion-based text-to-music model. With 22M trainable parameters, AP-Adapter empowers users to harness both global (e.g., genre and timbre) and local (e.g., melody) aspects of music, using the original audio and a short text as inputs. Through objective and subjective studies, we evaluate AP-Adapter on three tasks: timbre transfer, genre transfer, and accompaniment generation. Additionally, we demonstrate its effectiveness on out-of-domain audios containing unseen instruments during training.

cs.SD↗

arXiv2024

MusiConGen: Rhythm and Chord Control for Transformer-Based Text-to-Music Generation

Existing text-to-music models can produce high-quality audio with great diversity. However, textual prompts alone cannot precisely control temporal musical features such as chords and rhythm of the generated music. To address this challenge, we introduce MusiConGen, a temporally-conditioned Transformer-based text-to-music model that builds upon the pretrained MusicGen framework. Our innovation lies in an efficient finetuning mechanism, tailored for consumer-grade GPUs, that integrates automatically-extracted rhythm and chords as the condition signal. During inference, the condition can either be musical features extracted from a reference audio signal, or be user-defined symbolic chord sequence, BPM, and textual prompts. Our performance evaluation on two datasets -- one derived from extracted features and the other from user-created inputs -- demonstrates that MusiConGen can generate realistic backing track music that aligns well with the specified conditions. We open-source the code and model checkpoints, and provide audio examples online, https://musicongen.github.io/musicongen_demo/.

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arXiv2024

Sample Complexity of Locally Differentially Private Quantum Hypothesis Testing

Quantum state discrimination is an important problem in many information processing tasks. In this work we are concerned with finding its best possible sample complexity when the states are preprocessed by a quantum channel that is required to be locally differentially private. To that end we provide achievability and converse bounds for different settings. This includes symmetric state discrimination in various regimes and the asymmetric case. On the way, we also prove new sample complexity bounds for the general unconstrained setting. An important tool in this endeavor are new entropy inequalities that we believe to be of independent interest.

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arXiv2024

An invitation to the sample complexity of quantum hypothesis testing

Quantum hypothesis testing (QHT) has been traditionally studied from the information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of samples of an unknown state. In this paper, we study the sample complexity of QHT, wherein the goal is to determine the minimum number of samples needed to reach a desired error probability. By making use of the wealth of knowledge that already exists in the literature on QHT, we characterize the sample complexity of binary QHT in the symmetric and asymmetric settings, and we provide bounds on the sample complexity of multiple QHT. In more detail, we prove that the sample complexity of symmetric binary QHT depends logarithmically on the inverse error probability and inversely on the negative logarithm of the fidelity. As a counterpart of the quantum Stein's lemma, we also find that the sample complexity of asymmetric binary QHT depends logarithmically on the inverse type II error probability and inversely on the quantum relative entropy, provided that the type II error probability is sufficiently small. We then provide lower and upper bounds on the sample complexity of multiple QHT, with it remaining an intriguing open question to improve these bounds. The final part of our paper outlines and reviews how sample complexity of QHT is relevant to a broad swathe of research areas and can enhance understanding of many fundamental concepts, including quantum algorithms for simulation and search, quantum learning and classification, and foundations of quantum mechanics. As such, we view our paper as an invitation to researchers coming from different communities to study and contribute to the problem of sample complexity of QHT, and we outline a number of open directions for future research.

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arXiv2024

Optimal Second-Order Rates for Quantum Information Decoupling

In this paper, we consider the standard quantum information decoupling, in which Alice aims to decouple her system from the environment by local operations and discarding some of her systems. To achieve an $\varepsilon$-decoupling with trace distance as the error criterion, we establish a near-optimal one-shot characterization for the largest dimension of the remainder system in terms of the conditional $(1-\varepsilon)$-hypothesis-testing entropy. When the underlying system is independent and identically prepared, our result leads to the matched second-order rate as well as the matched moderate deviation rate. As an application, we find an achievability bound in entanglement distillation protocol, where the objective is for Alice and Bob to transform their quantum state to maximally entangled state with largest possible dimension using only local operations and one-way classical communications.

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arXiv2024

Maximal $\alpha$-Leakage for Quantum Privacy Mechanisms

In this work, maximal $\alpha$-leakage is introduced to quantify how much a quantum adversary can learn about any sensitive information of data upon observing its disturbed version via a quantum privacy mechanism. We first show that an adversary's maximal expected $\alpha$-gain using optimal measurement is characterized by measured conditional R\'enyi entropy. This can be viewed as a parametric generalization of K\"onig et al.'s famous guessing probability formula [IEEE Trans. Inf. Theory, 55(9), 2009]. Then, we prove that the $\alpha$-leakage and maximal $\alpha$-leakage for a quantum privacy mechanism are determined by measured Arimoto information and measured R\'enyi capacity, respectively. Various properties of maximal $\alpha$-leakage, such as data processing inequality and composition property are established as well. Moreover, we show that regularized $\alpha$-leakage and regularized maximal $\alpha$-leakage for identical and independent quantum privacy mechanisms coincide with $\alpha$-tilted sandwiched R\'enyi information and sandwiched R\'enyi capacity, respectively.

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arXiv2024

On Strong Converse Theorems for Quantum Hypothesis Testing and Channel Coding

Strong converse theorems refer to the study of impossibility results in information theory. In particular, Mosonyi and Ogawa established a one-shot strong converse bound for quantum hypothesis testing [Comm. Math. Phys, 334(3), 2014], which servers as a primitive tool for establishing a variety of tight strong converse theorems in quantum information theory. In this short note, we demonstrate an alternative one-line proof for this bound via the variational expression of measured R\'enyi divergences [Lett. Math. Phys, 107(12), 2017]. Then, we show that the variational expression is a direct consequence of H\"older's inequality.

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arXiv2024

Computing Augustin Information via Hybrid Geodesically Convex Optimization

We propose a Riemannian gradient descent with the Poincar\'e metric to compute the order-$\alpha$ Augustin information, a widely used quantity for characterizing exponential error behaviors in information theory. We prove that the algorithm converges to the optimum at a rate of $\mathcal{O}(1 / T)$. As far as we know, this is the first algorithm with a non-asymptotic optimization error guarantee for all positive orders. Numerical experimental results demonstrate the empirical efficiency of the algorithm. Our result is based on a novel hybrid analysis of Riemannian gradient descent for functions that are geodesically convex in a Riemannian metric and geodesically smooth in another.

cs.IT↗

arXiv2023

Adaptive Circuit Learning of Born Machine: Towards Realization of Amplitude Embedding and Quantum Data Loading

Quantum data loading plays a central role in quantum algorithms and quantum information processing. Many quantum algorithms hinge on the ability to prepare arbitrary superposition states as a subroutine, with claims of exponential speedups often predicated on access to an efficient data-loading oracle. In practice, constructing a circuit to prepare a generic $n$-qubit quantum state typically demands computational efforts scaling as $\mathcal{O}(2^n)$, posing a significant challenge for quantum algorithms to outperform their classical counterparts. To address this critical issue, various hybrid quantum-classical approaches have been proposed. However, many of these solutions favor simplistic circuit architectures, which are susceptible to substantial optimization challenges. In this study, we harness quantum circuits as Born machines to generate probability distributions. Drawing inspiration from methods used to investigate electronic structures in quantum chemistry and condensed matter physics, we propose a framework called Adaptive Circuit Learning of Born Machine, which dynamically expands the ansatz circuit. Our algorithm is designed to selectively integrate two-qubit entangled gates that best capture the intricate entanglement present within the target state. Empirical experiments underscore the efficacy of our approach in encoding real-world data through amplitude embedding, demonstrating not only compliance with but also enhancement over the performance benchmarks set by prior research.

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arXiv2023

Fast Minimization of Expected Logarithmic Loss via Stochastic Dual Averaging

Consider the problem of minimizing an expected logarithmic loss over either the probability simplex or the set of quantum density matrices. This problem includes tasks such as solving the Poisson inverse problem, computing the maximum-likelihood estimate for quantum state tomography, and approximating positive semi-definite matrix permanents with the currently tightest approximation ratio. Although the optimization problem is convex, standard iteration complexity guarantees for first-order methods do not directly apply due to the absence of Lipschitz continuity and smoothness in the loss function. In this work, we propose a stochastic first-order algorithm named $B$-sample stochastic dual averaging with the logarithmic barrier. For the Poisson inverse problem, our algorithm attains an $\varepsilon$-optimal solution in $\smash{\tilde{O}}(d^2/\varepsilon^2)$ time, matching the state of the art, where $d$ denotes the dimension. When computing the maximum-likelihood estimate for quantum state tomography, our algorithm yields an $\varepsilon$-optimal solution in $\smash{\tilde{O}}(d^3/\varepsilon^2)$ time. This improves on the time complexities of existing stochastic first-order methods by a factor of $d^{\omega-2}$ and those of batch methods by a factor of $d^2$, where $\omega$ denotes the matrix multiplication exponent. Numerical experiments demonstrate that empirically, our algorithm outperforms existing methods with explicit complexity guarantees.

math.OC↗

arXiv2023

Privacy Amplification Against Quantum Side Information Via Regular Random Binning

We consider privacy amplification against quantum side information by using regular random binning as an effective extractor. For constant-type sources, we obtain error exponent and strong converse bounds in terms of the so-called quantum Augustin information. Via type decomposition, we then recover the error exponent for independent and identically distributed sources proved by Dupuis [arXiv:2105.05342]. As an application, we obtain an achievable secrecy exponent for classical-quantum wiretap channel coding in terms of the Augustin information, which solves an open problem in [IEEE Trans.~Inf.~Theory, 65(12):7985, 2019]. Our approach is to establish an operational equivalence between privacy amplification and quantum soft covering; this may be of independent interest.

quant-ph↗

arXiv2023

The Mutual Information In The Vicinity of Capacity-Achieving Input Distributions

The mutual information is bounded from above by a decreasing affine function of the square of the distance between the input distribution and the set of all capacity-achieving input distributions $\Pi_{\mathcal{A}}$, on small enough neighborhoods of $\Pi_{\mathcal{A}}$, using an identity due to Tops{\o}e and the Pinsker's inequality, assuming that the input set of the channel is finite and the constraint set $\mathcal{A}$ is polyhedral, i.e., can be described by (possibly multiple but) finitely many linear constraints. Counterexamples demonstrating nonexistence of such a quadratic bound are provided for the case of infinitely many linear constraints and the case of infinite input sets. Using Taylor's theorem with the remainder term, rather than the Pinsker's inequality and invoking Moreau's decomposition theorem the exact characterization of the slowest decrease of the mutual information with the distance to $\Pi_{\mathcal{A}}$ is determined on small neighborhoods of $\Pi_{\mathcal{A}}$. Corresponding results for classical-quantum channels are established under separable output Hilbert space assumption for the quadratic bound and under finite-dimensional output Hilbert space assumption for the exact characterization. Implications of these observations for the channel coding problem and applications of the proof techniques to related problems are discussed.

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