IEEE Transactions on Information Theory最新文献

{"title":"Matrix Majorization in Large Samples With Varying Support Restrictions","authors":"Frits Verhagen;Marco Tomamichel;Erkka Haapasalo","doi":"10.1109/TIT.2025.3585062","DOIUrl":"https://doi.org/10.1109/TIT.2025.3585062","url":null,"abstract":"We say that a matrix <italic>P</i> with non-negative entries majorizes another such matrix <italic>Q</i> if there is a stochastic matrix <italic>T</i> such that <inline-formula> <tex-math>$Q=TP$ </tex-math></inline-formula>. We study matrix majorization in large samples and in the catalytic regime in the case where the columns of the matrices need not have equal support, as has been assumed in earlier works. We focus on two cases: either there are no support restrictions (except for requiring a non-empty intersection for the supports) or the final column dominates the others. Using real-algebraic methods, we identify sufficient and almost necessary conditions for majorization in large samples or when using catalytic states under these support conditions. These conditions are given in terms of multivariate divergences that generalize the Rényi divergences. We notice that varying support conditions dramatically affect the relevant set of divergences. Our results find an application in the theory of catalytic state transformation in quantum thermodynamics.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"6517-6545"},"PeriodicalIF":2.9,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal Tomography of Quantum Markov Chains via Continuity of Petz Recovery States","authors":"Li Gao;Nengkun Yu","doi":"10.1109/TIT.2025.3584694","DOIUrl":"https://doi.org/10.1109/TIT.2025.3584694","url":null,"abstract":"In this work, we show that the Petz recovered state &lt;inline-formula&gt; &lt;tex-math&gt;$rho _{BC}^{1/2}(rho _{B}^{-1/2}rho _{AB}rho _{B}^{-1/2}otimes I_{C})rho _{BC}^{1/2}$ &lt;/tex-math&gt;&lt;/inline-formula&gt; is continuous regarding its marginals &lt;inline-formula&gt; &lt;tex-math&gt;$rho _{AB}$ &lt;/tex-math&gt;&lt;/inline-formula&gt; and &lt;inline-formula&gt; &lt;tex-math&gt;$rho _{BC}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;. In terms of infidelity &lt;inline-formula&gt; &lt;tex-math&gt;$1-F(rho,sigma)=1-mathop {mathrm {tr}}nolimits |sqrt {rho }sqrt {sigma }|$ &lt;/tex-math&gt;&lt;/inline-formula&gt; and trace norm &lt;inline-formula&gt; &lt;tex-math&gt;$parallel ! rho -sigma ! parallel _{1}=mathop {mathrm {tr}}nolimits (|rho -sigma |)$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, we obtain the following dimension-independent estimate: &lt;inline-formula&gt; &lt;tex-math&gt;$1-F(rho _{AB},sigma _{AB}) le delta hspace {.1cm}, 1-F(rho _{BC},sigma _{BC}) le delta hspace {.1cm}Longrightarrow 1-F(rho _{ABC},sigma _{ABC})le 18delta, parallel ! rho _{AB}-sigma _{AB} ! parallel _{1} le varepsilon hspace {.1cm}, parallel ! rho _{BC}-sigma _{BC} ! parallel _{1} le varepsilon hspace {.1cm}Longrightarrow parallel ! rho _{ABC}-sigma _{ABC} ! parallel _{}le varepsilon +4varepsilon ^{frac {1}{2}}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;. As applications, we obtain the following applications in tomography of quantum Markov chains: 1) The sample complexity of quantum Markov chain tomography, i.e., how many copies of an unknown quantum Markov chain are necessary and sufficient to determine the state, is &lt;inline-formula&gt; &lt;tex-math&gt;$tilde {Theta }left ({{frac {(d_{A}^{2}+d_{C}^{2})d_{B}^{2}}{delta }}}right)$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, and &lt;inline-formula&gt; &lt;tex-math&gt;$tilde {Theta }left ({{frac {(d_{A}^{2}+d_{C}^{2})d_{B}^{2}}{epsilon ^{2}}}}right)$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, where &lt;inline-formula&gt; &lt;tex-math&gt;$delta $ &lt;/tex-math&gt;&lt;/inline-formula&gt; denotes infidelity error and &lt;inline-formula&gt; &lt;tex-math&gt;$epsilon $ &lt;/tex-math&gt;&lt;/inline-formula&gt; denotes trace distance. 2) The sample complexity of quantum Markov chain certification, i.e., to certify whether a tripartite state equals a given quantum Markov chain &lt;inline-formula&gt; &lt;tex-math&gt;$sigma _{ABC}$ &lt;/tex-math&gt;&lt;/inline-formula&gt; or at least &lt;inline-formula&gt; &lt;tex-math&gt;$delta $ &lt;/tex-math&gt;&lt;/inline-formula&gt;-far from &lt;inline-formula&gt; &lt;tex-math&gt;$sigma _{ABC}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, is &lt;inline-formula&gt; &lt;tex-math&gt;${Theta }left ({{frac {(d_{A}+d_{C})d_{B}}{delta }}}right)$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, and &lt;inline-formula&gt; &lt;tex-math&gt;${Theta }left ({{frac {(d_{A}+d_{C})d_{B}}{epsilon ^{2}}}}right)$ &lt;/tex-math&gt;&lt;/inline-formula&gt;. 3) &lt;inline-formula&gt; &lt;tex-math&gt;$tilde {O}left ({{frac {min {d_{A}d_{B}^{3}d_{C}^{3},d_{A}^{3}d_{B}^{3}d_{C}}}{epsilon ^{2}}}}right)$ &lt;/tex-math&gt;&lt;/inline-formula&gt; copies of sample are sufficient to certify whether &lt;inline-formula&gt; &lt;tex-math&gt;$rho _{ABC}$ &lt;/tex-math&gt;&lt;/inline-formula&gt; is a quantum Markov chain or &lt;inline-formula&gt; &lt;tex-math&gt;$epsilon $ &lt;/tex-math&gt;&lt;/inline-formula&gt;-far from its Petz recovered state in trace distanc","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"7016-7028"},"PeriodicalIF":2.9,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hidden Markov Models and the Bayes Filter in Categorical Probability","authors":"Tobias Fritz;Andreas Klingler;Drew McNeely;Areeb Shah Mohammed;Yuwen Wang","doi":"10.1109/TIT.2025.3584695","DOIUrl":"https://doi.org/10.1109/TIT.2025.3584695","url":null,"abstract":"We use Markov categories to generalize the basic theory of Markov chains and hidden Markov models to an abstract setting. This comprises characterizations of hidden Markov models in terms of conditional independences and algorithms for Bayesian filtering and smoothing applicable in all Markov categories with conditionals. When instantiated in appropriate Markov categories, these algorithms specialize to existing ones such as the Kalman filter, forward-backward algorithm, and the Rauch-Tung–Striebel smoother. We also prove that the sequence of outputs of our abstract Bayes filter is itself a Markov chain with a concrete formula for its transition maps. There are two main features of this categorical framework. The first is its abstract generality, as manifested in our unified account of hidden Markov models and algorithms for filtering and smoothing in discrete probability, Gaussian probability, measure-theoretic probability, possibilistic nondeterminism and others at the same time. The second feature is the intuitive visual representation of information flow in terms of string diagrams.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"7052-7075"},"PeriodicalIF":2.9,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Quantum Repeater Network Saturates the Entanglement Distribution Asymptotically","authors":"Nengkun Yu","doi":"10.1109/TIT.2025.3584199","DOIUrl":"https://doi.org/10.1109/TIT.2025.3584199","url":null,"abstract":"Efficient and reliable entanglement distribution forms the core of quantum network architecture. The Quantum Max-Flow concept defines the upper boundary for efficiently transmitting entanglement within quantum tensor networks (Calegari, Freedman, and Walker, Journal of the American Mathematical Society, 2010). Despite the general invalidity of the Quantum analog of the Max-Flow Min-Cut theorem, this paper introduces a precise Quantum Max-Flow Min-Cut Theorem tailored to quantum tensor networks enhanced by ancilla entanglement. Specifically, our research establishes infinite ‘n’ values for any quantum tensor network, where the Quantum Max-Flow matches the Quantum Min-Cut by attaching a maximally entangled state with dimension ‘n’ to each edge. Our protocol exclusively relies on quantum teleportation and guarantees unambiguous success. This work highlights the potential of quantum repeaters, enabled by ancilla entanglement, to efficiently distribute entanglement throughout quantum networks.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 8","pages":"6155-6164"},"PeriodicalIF":2.2,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144695644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Additivity of Quantum Capacities in Simple Non-Degradable Quantum Channels","authors":"Graeme Smith;Peixue Wu","doi":"10.1109/TIT.2025.3583936","DOIUrl":"https://doi.org/10.1109/TIT.2025.3583936","url":null,"abstract":"Quantum channel capacities give the fundamental performance limits for information flow over a communication channel. However, the prevalence of superadditivity is a major obstacle to understanding capacities, both quantitatively and conceptually. In contrast, examples exhibiting additivity, though relatively rare, offer crucial insights into the origins of nonadditivity and form the basis of our strongest upper bounds on capacity. Degradable channels, whose coherent information is provably additive, stand out as among the few classes of channels for which the quantum capacity is exactly computable. In this paper, we introduce two families of non-degradable channels whose coherent information remains additive, making their quantum capacities tractable. First, we demonstrate that channels capable of “outperforming” their environment, under conditions weaker than degradability, can exhibit either strong or weak additivity of coherent information. Second, we explore a complementary construction that modifies a channel to preserve coherent information additivity while destroying the “outperforming” property. We analyze how structural constraints guarantee strong and weak additivity and investigate how relaxing these constraints leads to the failure of strong additivity, with weak additivity potentially persisting.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 8","pages":"6134-6154"},"PeriodicalIF":2.2,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144695504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Capacity of Resistive Random-Access Memory Channel: Upper Bound and Achievable Rate Under Suboptimal Decodings","authors":"Guanghui Song;Qi Cao;Ying Li;Zhaoji Zhang;Kui Cai","doi":"10.1109/TIT.2025.3583423","DOIUrl":"https://doi.org/10.1109/TIT.2025.3583423","url":null,"abstract":"The achievable rate of code over resistive random-access memory (ReRAM) channel with finite selector failures was published in our recent work. The rate was derived under the assumption of independent and identically distributed (i.i.d.) input. In this work, focusing on the ReRAM channel with a single selector failure in the memory array, we derive an upper bound on achievable rate under arbitrary input distribution. This upper bound is within 0.02 bits from the achievable rate of i.i.d. input, indicating that i.i.d. is very close to optimal for large memory arrays. Moreover, we analyze the achievable rate of random code over ReRAM channel with suboptimal decodings where the decoder ignores the channel correlation. Our result indicates that in this case the achievable rate is limited by the capacity of a memoryless channel. We reveal both weak and strong asymptotic properties of ReRAM channel to prove this. The proof can be directly extended to the case of ReRAM with an arbitrary number of selector failures in the memory array.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"6641-6656"},"PeriodicalIF":2.9,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Capacity of Correlated Phase-Noise Channels: An Electro-Optic Frequency Comb Example","authors":"Mohammad Farsi;Hamdi Joudeh;Gabriele Liga;Alex Alvarado;Magnus Karlsson;Erik Agrell","doi":"10.1109/TIT.2025.3583548","DOIUrl":"https://doi.org/10.1109/TIT.2025.3583548","url":null,"abstract":"The capacity of a discrete-time channel with correlated phase noises is investigated. In particular, the electro-optic frequency comb system is considered, where the phase noise of each subchannel is a combination of two independent Wiener phase-noise sources. Capacity upper and lower bounds are derived for this channel and are compared with lower bounds obtained by numerically evaluating the achievable information rates using quadrature amplitude modulation constellations. Capacity upper and lower bounds are provided for the high signal-to-noise ratio (SNR) regime. The multiplexing gain (pre-log) is shown to be <inline-formula> <tex-math>$M-1$ </tex-math></inline-formula>, where <italic>M</i> represents the number of subchannels. A constant gap between the asymptotic upper and lower bounds is observed, which depends on the number of subchannels <italic>M</i>. For the specific case of <inline-formula> <tex-math>$M=2$ </tex-math></inline-formula>, capacity is characterized up to a term that vanishes as the SNR grows large.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"6912-6931"},"PeriodicalIF":2.9,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Topological Invariants for Linear Codes and APN Functions","authors":"Zijian Zhou;Kangquan Li;Yue Zhou","doi":"10.1109/TIT.2025.3583010","DOIUrl":"https://doi.org/10.1109/TIT.2025.3583010","url":null,"abstract":"In this paper, we try to apply methods from topological data analysis (TDA) to study geometric properties invariant under code equivalence transformation, especially for the linear codes associated with almost perfect nonlinear (APN) functions which offer optimal resistance to differential attacks and are very important in the design of block ciphers in cryptography. By employing persistent homology from TDA and tools from graph theory, we present new CCZ-invariants for APN functions. Some of them are computationally efficient and sufficient to distinguish many known APN functions, including <inline-formula> <tex-math>$x^{3}$ </tex-math></inline-formula> and <inline-formula> <tex-math>$x^{9}$ </tex-math></inline-formula> (resp. <inline-formula> <tex-math>$x^{33}$ </tex-math></inline-formula>) over <inline-formula> <tex-math>$mathbb {F}_{2^{7}}$ </tex-math></inline-formula> (resp. <inline-formula> <tex-math>$mathbb {F}_{2^{9}}$ </tex-math></inline-formula>) for which previously known invariants fail to do so.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"6771-6784"},"PeriodicalIF":2.9,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sequential Outlier Hypothesis Testing Under Universality Constraints","authors":"Jun Diao;Lin Zhou","doi":"10.1109/TIT.2025.3583065","DOIUrl":"https://doi.org/10.1109/TIT.2025.3583065","url":null,"abstract":"We revisit sequential outlier hypothesis testing and derive bounds on achievable exponents when both the nominal and anomalous distributions are <italic>unknown</i>. The task of outlier hypothesis testing is to identify the set of outliers that are generated from an anomalous distribution among all observed sequences where the rest majority are generated from a nominal distribution. In the sequential setting, one obtains a symbol from each sequence per unit time until a reliable decision could be made. For the case with exactly one outlier, our exponent bounds are tight, providing exact large deviations characterization of sequential tests and strengthening a previous result of Li et al. (2017). In particular, the average sample size of our sequential test is bounded universally under any pair of nominal and anomalous distributions and our sequential test achieves larger Bayesian exponent than the fixed-length test, which could not be guaranteed by the sequential test of Li et al. (2017). For the case with at most one outlier, we propose a threshold-based test that has bounded expected stopping time under mild conditions and we bound the exponential decay rate of error probabilities, a.k.a., error exponents, under each non-null hypothesis and the null hypothesis. Our sequential test resolves the tradeoff among the exponential decay rates of misclassification, false reject and false alarm probabilities for the fixed-length test of Zhou et al. (2022). Finally, with a further step towards practical applications, we generalize our results to the cases of multiple outliers and show that there is a penalty in the error exponents when the number of outliers is unknown.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"6602-6625"},"PeriodicalIF":2.9,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Existence of Plotkin-Optimal Linear Codes Over ℤ4","authors":"Hopein Christofen Tang","doi":"10.1109/TIT.2025.3582936","DOIUrl":"https://doi.org/10.1109/TIT.2025.3582936","url":null,"abstract":"We generalize the Plotkin-type Lee distance bound for linear codes over <inline-formula> <tex-math>$mathbb {Z}_{4}$ </tex-math></inline-formula> to several new and stronger bounds. We apply these bounds to determine all possible integers <italic>n</i> such that Plotkin-optimal linear codes over <inline-formula> <tex-math>$mathbb {Z}_{4}$ </tex-math></inline-formula> of length <italic>n</i> and type <inline-formula> <tex-math>$4^{k_{1}}2^{k_{2}}$ </tex-math></inline-formula> exist for any given non-negative integers <inline-formula> <tex-math>$k_{1}$ </tex-math></inline-formula> and <inline-formula> <tex-math>$k_{2}$ </tex-math></inline-formula>. We furthermore provide construction methods for Plotkin-optimal linear codes over <inline-formula> <tex-math>$mathbb {Z}_{4}$ </tex-math></inline-formula> for each possible length mentioned above. Our results are in large part established by considering column multiplicities of generator matrices.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"6712-6726"},"PeriodicalIF":2.9,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}