arXiv subjects

Yonglong Li

Publications and source records attributed to Yonglong Li.

17 recordsLinked to original sources

arXiv2026

Binary Quantum Hypothesis Testing with a Rejection Option: The Exact Error-Exponent Trade-off

We characterize the exact error-exponent trade-off in binary quantum hypothesis testing with a rejection option for faithful states on a finite-dimensional Hilbert space. The probabilities of rejection under the two hypotheses are required to vanish exponentially, with exponents at least $K$ and $L$. We show that a quadruple $(a,b,K,L)$ of positive error and rejection exponents is achievable if and only if it satisfies three single-letter conditions: two conditions involve Petz--Rényi quantities and coincide with the converse bound conjectured to be tight by Ji and Regula; the third involves the $α$--$z$ Rényi quantities on the triangle $\max\{α,1-α\}\le z\le1$. The proof combines a sector decomposition inside Schur--Weyl blocks, an explicit one-shot measurement construction, and an exact minimax argument.

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arXiv2026

Convergence Analysis of the Quantum Blahut-Arimoto Algorithm and the Contraction Coefficient of Qubit Amplitude-Damping Channels

In this work, we investigate the convergence rate of the quantum Blahut-Arimoto (BA) algorithm proposed for computing the coherent information of less noisy quantum channels. Previous work established exponential convergence under certain restrictive assumptions on the channel. Using a Taylor expansion around a positive definite optimizer, we show that, for an injective degradable channel whose degrading channel has a relative-entropy contraction coefficient strictly less than one, the algorithm converges at an exponential rate after sufficiently many iterations. We further verify this condition for qubit amplitude-damping (AD) channels in the relevant parameter regime. In addition, by analyzing the Bogoliubov-Kubo-Mori (BKM) metric on the Bloch ball, we derive an explicit characterization of the relative-entropy contraction coefficient of qubit AD channels. The proposed approach is further extended to calculate the relative contraction coefficient and the relative expansion coefficient of two qubit AD channels.

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arXiv2026

Minimax Quantum State Tomography in a Known Trace-Distance Ball

We study quantum state tomography when the unknown state lies in a trace-distance ball of radius $R$ around a known reference state $ρ$. For arbitrary collective measurements, we determine the minimax expected risk and confidence radius up to universal constants, uniformly over the dimension, center spectrum, radius, and sample size. Write $Γ=d(\mathrm{Tr}\sqrtρ)^2+d^2R$. For $d\ge2$, $0 0$, the copy complexity is $Θ((Γ+\log(1/δ))/\varepsilon^2)$. For the lower bound we use a weighted trace-norm witness to retain all spectral scales in a square-root perturbation family. For the upper bound, we give a direct spectral and concentration analysis of a modified existing purification-based procedure.

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arXiv2026

Equality in the Bosonic Quantum Entropy Power Inequality

The bosonic quantum entropy power inequality bounds the entropy of a beam-splitter output in terms of the input entropies. We determine its complete equality class among independent inputs of finite mean photon number: for any number of modes and any transmissivity strictly between zero and one, equality in either the linear or the exponential form holds if and only if the inputs are Gaussian with the same covariance matrix, allowing arbitrary displacements. The main step shows that equality for one output forces the two outputs to be independent: a thermal auxiliary converts equality into preservation of mutual information by a fixed noisy channel, and a two-outcome instrument shows that preservation of mutual information requires a product state with the reference. The quantum Darmois--Skitovich theorem then gives Gaussianity, while a central-limit argument reduces exponential equality to linear equality.

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arXiv2025

Information-Theoretic Limits of Bistatic Integrated Sensing and Communication

Bistatic sensing refers to scenarios where the transmitter (illuminating the target) and the sensing receiver (estimating the target state) are physically separated, in contrast to monostatic sensing, where both functions are co-located. In practical settings, bistatic sensing may be required either due to inherent system constraints or as a means to mitigate the strong self-interference encountered in monostatic configurations. A key practical challenge in bistatic radio-frequency radar systems is the synchronization and calibration of the separate transmitter and sensing receiver. In this paper, we are not concerned with these signal processing aspects and take a complementary information-theoretic perspective on bistatic integrated sensing and communication (ISAC). Namely, we aim to characterize the capacity-distortion function-the fundamental tradeoff between communication capacity and sensing accuracy. We consider a general discrete channel model for a bistatic ISAC system and derive a multi-letter representation of its capacity-distortion function. Then, we establish single-letter upper and lower bounds and provide exact single-letter characterizations for degraded bistatic ISAC channels. Furthermore, we extend our analysis to a bistatic ISAC broadcast channel and derive the capacity-distortion region with a single-letter characterization in the degraded case. Numerical examples illustrate the theoretical results, highlighting the benefits of ISAC over separate communication and sensing, as well as the role of leveraging communication to assist sensing in bistatic systems.

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arXiv2025

On the Fundamental Limits of Integrated Sensing and Communications Under Logarithmic Loss

We study a unified information-theoretic framework for integrated sensing and communications (ISAC), applicable to both monostatic and bistatic sensing scenarios. Special attention is given to the case where the sensing receiver (Rx) is required to produce a "soft" estimate of the state sequence, with logarithmic loss serving as the performance metric. We derive lower and upper bounds on the capacity-distortion function, which delineates the fundamental tradeoff between communication rate and sensing distortion. These bounds coincide when the channel between the ISAC transmitter (Tx) and the communication Rx is degraded with respect to the channel between the ISAC Tx and the sensing Rx, or vice versa. Furthermore, we provide a complete characterization of the capacity-distortion function for an ISAC system that simultaneously transmits information over a binary-symmetric channel and senses additive Bernoulli states through another binary-symmetric channel. The Gaussian counterpart of this problem is also explored, which, together with a state-splitting trick, fully determines the capacity-distortion-power function under the squared error distortion measure.

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arXiv2022

Sequential Quantum Channel Discrimination

We consider the sequential quantum channel discrimination problem using adaptive and non-adaptive strategies. In this setting the number of uses of the underlying quantum channel is not fixed but a random variable that is either bounded in expectation or with high probability. We show that both types of error probabilities decrease to zero exponentially fast and, when using adaptive strategies, the rates are characterized by the measured relative entropy between two quantum channels, yielding a strictly larger region than that achievable by non-adaptive strategies. Allowing for quantum memory, we see that the optimal rates are given by the regularized channel relative entropy. Finally, we discuss achievable rates when allowing for repeated measurements via quantum instruments and conjecture that the achievable rate region is not larger than that achievable with POVMs by connecting the result to the strong converse for the quantum channel Stein's Lemma.

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arXiv2022

Renyi Entropy Rate of Stationary Ergodic Processes

In this paper, we examine the Renyi entropy rate of stationary ergodic processes. For a special class of stationary ergodic processes, we prove that the Renyi entropy rate always exists and can be polynomially approximated by its defining sequence; moreover, using the Markov approximation method, we show that the Renyi entropy rate can be exponentially approximated by that of the Markov approximating sequence, as the Markov order goes to infinity. For the general case, by constructing a counterexample, we disprove the conjecture that the Renyi entropy rate of a general stationary ergodic process always converges to its Shannon entropy rate as α goes to 1.

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arXiv2022

Asymptotic Nash Equilibrium for the $M$-ary Sequential Adversarial Hypothesis Testing Game

In this paper, we consider a novel $M$-ary sequential hypothesis testing problem in which an adversary is present and perturbs the distributions of the samples before the decision maker observes them. This problem is formulated as a sequential adversarial hypothesis testing game played between the decision maker and the adversary. This game is a zero-sum and strategic one. We assume the adversary is active under \emph{all} hypotheses and knows the underlying distribution of observed samples. We adopt this framework as it is the worst-case scenario from the perspective of the decision maker. The goal of the decision maker is to minimize the expectation of the stopping time to ensure that the test is as efficient as possible; the adversary's goal is, instead, to maximize the stopping time. We derive a pair of strategies under which the asymptotic Nash equilibrium of the game is attained. We also consider the case in which the adversary is not aware of the underlying hypothesis and hence is constrained to apply the same strategy regardless of which hypothesis is in effect. Numerical results corroborate our theoretical findings.

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arXiv2022

Rate-Constrained Shaping Codes for Finite-State Channels With Cost

Shaping codes are used to generate code sequences in which the symbols obey a prescribed probability distribution. They arise naturally in the context of source coding for noiseless channels with unequal symbol costs. Recently, shaping codes have been proposed to extend the lifetime of flash memory and reduce DNA synthesis time. In this paper, we study a general class of shaping codes for noiseless finite-state channels with cost and i.i.d. sources. We establish a relationship between the code rate and minimum average symbol cost. We then determine the rate that minimizes the average cost per source symbol (total cost). An equivalence is established between codes minimizing average symbol cost and codes minimizing total cost, and a separation theorem is proved, showing that optimal shaping can be achieved by a concatenation of optimal compression and optimal shaping for a uniform i.i.d. source.

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arXiv2022

Asymptotics of Sequential Composite Hypothesis Testing under Probabilistic Constraints

We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set $Γ$. We would like to design a test to decide which hypothesis is in effect. Under the constraints that the probabilities that the length of the test, a stopping time, exceeds $n$ are bounded by a certain threshold $ε$, we obtain certain fundamental limits on the asymptotic behavior of the sequential test as $n$ tends to infinity. Assuming that $Γ$ is a convex and compact set, we obtain the set of all first-order error exponents for the problem. We also prove a strong converse. Additionally, we obtain the set of second-order error exponents under the assumption that $\mathcal{X}$ is a finite alphabet. In the proof of second-order asymptotics, a main technical contribution is the derivation of a central limit-type result for a maximum of an uncountable set of log-likelihood ratios under suitable conditions. This result may be of independent interest. We also show that some important statistical models satisfy the conditions.

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arXiv2022

Optimal Adaptive Strategies for Sequential Quantum Hypothesis Testing

We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. In this setting, samples of an unknown state are requested sequentially and a decision to either continue or to accept one of the two hypotheses is made after each test. Under the constraint that the number of samples is bounded, either in expectation or with high probability, we exhibit adaptive strategies that minimize both types of misidentification errors. Namely, we show that these errors decrease exponentially (in the stopping time) with decay rates given by the measured relative entropies between the two states. Moreover, if we allow joint measurements on multiple samples, the rates are increased to the respective quantum relative entropies. We also fully characterize the achievable error exponents for non-adaptive strategies and provide numerical evidence showing that adaptive measurements are necessary to achieve our bounds under some additional assumptions.

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arXiv2020

On the Error Exponent of Approximate Sufficient Statistics for M-ary Hypothesis Testing

Consider the problem of detecting one of M i.i.d. Gaussian signals corrupted in white Gaussian noise. Conventionally, matched filters are used for detection. We first show that the outputs of the matched filter form a set of asymptotically optimal sufficient statistics in the sense of maximizing the error exponent of detecting the true signal. In practice, however, M may be large which motivates the design and analysis of a reduced set of N statistics which we term approximate sufficient statistics. Our construction of these statistics is based on a small set of filters that project the outputs of the matched filters onto a lower-dimensional vector using a sensing matrix. We consider a sequence of sensing matrices that has the desiderata of row orthonormality and low coherence. We analyze the performance of the resulting maximum likelihood (ML) detector, which leads to an achievable bound on the error exponent based on the approximate sufficient statistics; this bound recovers the original error exponent when N = M. We compare this to a bound that we obtain by analyzing a modified form of the Reduced Dimensionality Detector (RDD) proposed by Xie, Eldar, and Goldsmith [IEEE Trans. on Inform. Th., 59(6):3858-3874, 2013]. We show that by setting the sensing matrices to be column-normalized group Hadamard matrices, the exponents derived are ensemble-tight, i.e., our analysis is tight on the exponential scale given the sensing matrices and the decoding rule. Finally, we derive some properties of the exponents, showing, in particular, that they increase linearly in the compression ratio N/M.

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arXiv2020

Second-Order Asymptotics of Sequential Hypothesis Testing

We consider the classical sequential binary hypothesis testing problem in which there are two hypotheses governed respectively by distributions $P_0$ and $P_1$ and we would like to decide which hypothesis is true using a sequential test. It is known from the work of Wald and Wolfowitz that as the expectation of the length of the test grows, the optimal type-I and type-II error exponents approach the relative entropies $D(P_1\|P_0)$ and $D(P_0\|P_1)$. We refine this result by considering the optimal backoff---or second-order asymptotics---from the corner point of the achievable exponent region $(D(P_1\|P_0),D(P_0\|P_1))$ under two different constraints on the length of the test (or the sample size). First, we consider a probabilistic constraint in which the probability that the length of test exceeds a prescribed integer $n$ is less than a certain threshold $0<\varepsilon <1$. Second, the expectation of the sample size is bounded by $n$. In both cases, and under mild conditions, the second-order asymptotics is characterized exactly. Numerical examples are provided to illustrate our results.

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arXiv2019

On the Capacity of Channels with Deletions and States

We consider the class of channels formed from the concatenation of a deletion channel and a finite-state channel. For this class of channels, we show that the operational capacity is equal to the stationary capacity, which can be approached by a sequence of Markov processes with increasing Markovian orders. As a by-product, we show that the polar coding scheme constructed by Tal, Pfister, Fazeli and Vardy achieves the capacity of the deletion channel.

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arXiv2016

Asymptotics of Input-Constrained Erasure Channel Capacity

In this paper, we examine an input-constrained erasure channel and we characterize the asymptotics of its capacity when the erasure rate is low. More specifically, for a general memoryless erasure channel with its input supported on an irreducible finite-type constraint, we derive partial asymptotics of its capacity, using some series expansion type formulas of its mutual information rate; and for a binary erasure channel with its first-order Markovian input supported on the $(1, \infty)$-RLL constraint, based on the concavity of its mutual information rate with respect to some parameterization of the input, we numerically evaluate its first-order Markov capacity and further derive its full asymptotics. The asymptotics obtained in this paper, when compared with the recently derived feedback capacity for a binary erasure channel with the same input constraint, enable us to draw the conclusion that feedback may increase the capacity of an input-constrained channel, even if the channel is memoryless.

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arXiv2016

On the Capacity of Multilevel NAND Flash Memory Channels

In this paper, we initiate a first information-theoretic study on multilevel NAND flash memory channels with intercell interference. More specifically, for a multilevel NAND flash memory channel under mild assumptions, we first prove that such a channel is indecomposable and it features asymptotic equipartition property; we then further prove that stationary processes achieve its information capacity, and consequently, as its order tends to infinity, its Markov capacity converges to its information capacity; eventually, we establish that its operational capacity is equal to its information capacity. Our results suggest that it is highly plausible to apply the ideas and techniques in the computation of the capacity of finite-state channels, which are relatively better explored, to that of the capacity of multilevel NAND flash memory channels.

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