Pub Date : 2025-01-14DOI: 10.1109/TIT.2025.3529680
Neophytos Charalambides;Hessam Mahdavifar;Alfred O. Hero
This paper addresses the gradient coding and coded matrix multiplication problems in distributed optimization and coded computing. We present a computationally efficient coding method which overcomes the drawbacks of the Fractional Repetition Coding gradient coding method proposed by Tandon et al., and can also be leveraged by coded computing networks whose servers are of heterogeneous nature. Specifically, we propose a construction for fractional repetition gradient coding; while ensuring that the generator matrix remains close to perfectly balanced for any set of coding parameters, as well as a low complexity decoding step. The proposed binary encoding avoids operations over the real and complex numbers which inherently introduce numerical and rounding errors, thereby enabling accurate distributed encodings of the partial gradients. We then make connections between gradient coding and coded matrix multiplication. Specifically, we show that any gradient coding scheme can be extended to coded matrix multiplication. Furthermore, we show how the proposed binary gradient coding scheme can be used to construct two different coded matrix multiplication schemes, each achieving different trade-offs.
{"title":"Generalized Fractional Repetition Codes for Binary Coded Computations","authors":"Neophytos Charalambides;Hessam Mahdavifar;Alfred O. Hero","doi":"10.1109/TIT.2025.3529680","DOIUrl":"https://doi.org/10.1109/TIT.2025.3529680","url":null,"abstract":"This paper addresses the gradient coding and coded matrix multiplication problems in distributed optimization and coded computing. We present a computationally efficient coding method which overcomes the drawbacks of the Fractional Repetition Coding gradient coding method proposed by Tandon et al., and can also be leveraged by coded computing networks whose servers are of heterogeneous nature. Specifically, we propose a construction for fractional repetition gradient coding; while ensuring that the generator matrix remains close to perfectly balanced for any set of coding parameters, as well as a low complexity decoding step. The proposed binary encoding avoids operations over the real and complex numbers which inherently introduce numerical and rounding errors, thereby enabling accurate distributed encodings of the partial gradients. We then make connections between gradient coding and coded matrix multiplication. Specifically, we show that any gradient coding scheme can be extended to coded matrix multiplication. Furthermore, we show how the proposed binary gradient coding scheme can be used to construct two different coded matrix multiplication schemes, each achieving different trade-offs.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"2170-2194"},"PeriodicalIF":2.2,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455190","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}
This paper studies an internet of things (IoT) network where a fusion center relies on multi-view and correlated information generated by multiple sources to monitor various regions. Each region possesses hard age of correlated information (AoCI) constraints for information update, and accordingly we propose a scheduling policy to satisfy such needs and minimize the required wireless resources. We first approximate the problem to a dual bin-packing problem. Secondly, efficient scheduling policies are identified when the age constraints possess special mathematical properties, where the number of channels at most required is analyzed. Optimality conditions of the proposed policies are presented. For general constraints, a two-step grouping algorithm for multi-view (TGAM) is proposed to establish scheduling policies. Under TGAM, the constraints are mapped into a combination of the special constraints. To quickly identify an optimized mapping from a vast solution space, TGAM heuristically groups the regions according to their constraints and then searches for the optimal mapping for each group. Numerical results demonstrate that, compared to a derived lower bound, the proposed TGAM requires only 1.07% more channels. Additionally, the number of regions that can be served by TGAM is significantly larger than the state-of-the art algorithm, given the number of channels.
{"title":"Grouping-Based Cyclic Scheduling Under Age of Correlated Information Constraints","authors":"Lehan Wang;Jingzhou Sun;Yuxuan Sun;Sheng Zhou;Zhisheng Niu;Miao Jiang;Lu Geng","doi":"10.1109/TIT.2025.3529497","DOIUrl":"https://doi.org/10.1109/TIT.2025.3529497","url":null,"abstract":"This paper studies an internet of things (IoT) network where a fusion center relies on multi-view and correlated information generated by multiple sources to monitor various regions. Each region possesses hard age of correlated information (AoCI) constraints for information update, and accordingly we propose a scheduling policy to satisfy such needs and minimize the required wireless resources. We first approximate the problem to a dual bin-packing problem. Secondly, efficient scheduling policies are identified when the age constraints possess special mathematical properties, where the number of channels at most required is analyzed. Optimality conditions of the proposed policies are presented. For general constraints, a two-step grouping algorithm for multi-view (TGAM) is proposed to establish scheduling policies. Under TGAM, the constraints are mapped into a combination of the special constraints. To quickly identify an optimized mapping from a vast solution space, TGAM heuristically groups the regions according to their constraints and then searches for the optimal mapping for each group. Numerical results demonstrate that, compared to a derived lower bound, the proposed TGAM requires only 1.07% more channels. Additionally, the number of regions that can be served by TGAM is significantly larger than the state-of-the art algorithm, given the number of channels.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"2218-2244"},"PeriodicalIF":2.2,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455238","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}
Pub Date : 2025-01-13DOI: 10.1109/TIT.2025.3528655
Recep Can Yavas;Yuqi Huang;Vincent Y. F. Tan;Jonathan Scarlett
We develop a general framework for clustering and distribution matching problems with bandit feedback. We consider a K-armed bandit model where some subset of K arms is partitioned into M groups. Within each group, the random variable associated to each arm follows the same distribution on a finite alphabet. At each time step, the decision maker pulls an arm and observes its outcome from the random variable associated to that arm. Subsequent arm pulls depend on the history of arm pulls and their outcomes. The decision maker has no knowledge of the distributions of the arms or the underlying partitions. The task is to devise an online algorithm to learn the underlying partition of arms with the least number of arm pulls on average and with an error probability not exceeding a pre-determined value $delta $ . Several existing problems fall under our general framework, including finding M pairs of arms, odd arm identification, and N-ary clustering of K arms belong to our general framework. We derive a non-asymptotic lower bound on the average number of arm pulls for any online algorithm with an error probability not exceeding $delta $ . Furthermore, we develop a computationally-efficient online algorithm based on the Track-and-Stop method and Frank-Wolfe algorithm, and show that the average number of arm pulls of our algorithm asymptotically matches that of the lower bound. Our refined analysis also uncovers a novel bound on the speed at which the average number of arm pulls of our algorithm converges to the fundamental limit as $delta $ vanishes.
{"title":"A General Framework for Clustering and Distribution Matching With Bandit Feedback","authors":"Recep Can Yavas;Yuqi Huang;Vincent Y. F. Tan;Jonathan Scarlett","doi":"10.1109/TIT.2025.3528655","DOIUrl":"https://doi.org/10.1109/TIT.2025.3528655","url":null,"abstract":"We develop a general framework for clustering and distribution matching problems with bandit feedback. We consider a K-armed bandit model where some subset of K arms is partitioned into M groups. Within each group, the random variable associated to each arm follows the same distribution on a finite alphabet. At each time step, the decision maker pulls an arm and observes its outcome from the random variable associated to that arm. Subsequent arm pulls depend on the history of arm pulls and their outcomes. The decision maker has no knowledge of the distributions of the arms or the underlying partitions. The task is to devise an online algorithm to learn the underlying partition of arms with the least number of arm pulls on average and with an error probability not exceeding a pre-determined value <inline-formula> <tex-math>$delta $ </tex-math></inline-formula>. Several existing problems fall under our general framework, including finding M pairs of arms, odd arm identification, and N-ary clustering of K arms belong to our general framework. We derive a non-asymptotic lower bound on the average number of arm pulls for any online algorithm with an error probability not exceeding <inline-formula> <tex-math>$delta $ </tex-math></inline-formula>. Furthermore, we develop a computationally-efficient online algorithm based on the Track-and-Stop method and Frank-Wolfe algorithm, and show that the average number of arm pulls of our algorithm asymptotically matches that of the lower bound. Our refined analysis also uncovers a novel bound on the speed at which the average number of arm pulls of our algorithm converges to the fundamental limit as <inline-formula> <tex-math>$delta $ </tex-math></inline-formula> vanishes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"2116-2139"},"PeriodicalIF":2.2,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455308","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}
Pub Date : 2025-01-10DOI: 10.1109/TIT.2025.3528340
Biao Chen;Joshua Kortje
This paper proposes two linear projection methods for supervised dimension reduction using only first- and second-order statistics. The methods, each catering to a different parameter regime, are derived under the general Gaussian model by maximizing the Kullback-Leibler divergence between the two classes in the projected sample for a binary classification problem. They subsume existing linear projection approaches developed under simplifying assumptions of Gaussian distributions, such as these distributions might share an equal mean or covariance matrix. As a by-product, we establish that the multi-class linear discriminant analysis, a celebrated method for classification and supervised dimension reduction, is provably optimal for maximizing pairwise Kullback-Leibler divergence when the Gaussian populations share an identical covariance matrix. For the case when the Gaussian distributions share an equal mean, we establish conditions under which the optimal subspace remains invariant regardless of how the Kullback-Leibler divergence is defined, despite the asymmetry of the divergence measure itself. Such conditions encompass the classical case of signal plus noise, where both signal and noise have zero mean and arbitrary covariance matrices. Experiments are conducted to validate the proposed solutions, demonstrate their superior performance over existing alternatives, and illustrate the procedure for selecting the appropriate linear projection solution.
{"title":"Divergence Maximizing Linear Projection for Supervised Dimension Reduction","authors":"Biao Chen;Joshua Kortje","doi":"10.1109/TIT.2025.3528340","DOIUrl":"https://doi.org/10.1109/TIT.2025.3528340","url":null,"abstract":"This paper proposes two linear projection methods for supervised dimension reduction using only first- and second-order statistics. The methods, each catering to a different parameter regime, are derived under the general Gaussian model by maximizing the Kullback-Leibler divergence between the two classes in the projected sample for a binary classification problem. They subsume existing linear projection approaches developed under simplifying assumptions of Gaussian distributions, such as these distributions might share an equal mean or covariance matrix. As a by-product, we establish that the multi-class linear discriminant analysis, a celebrated method for classification and supervised dimension reduction, is provably optimal for maximizing pairwise Kullback-Leibler divergence when the Gaussian populations share an identical covariance matrix. For the case when the Gaussian distributions share an equal mean, we establish conditions under which the optimal subspace remains invariant regardless of how the Kullback-Leibler divergence is defined, despite the asymmetry of the divergence measure itself. Such conditions encompass the classical case of signal plus noise, where both signal and noise have zero mean and arbitrary covariance matrices. Experiments are conducted to validate the proposed solutions, demonstrate their superior performance over existing alternatives, and illustrate the procedure for selecting the appropriate linear projection solution.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"2104-2115"},"PeriodicalIF":2.2,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455192","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}
A conflict-avoiding code (CAC) is a deterministic transmission scheme for asynchronous multiple access without feedback. When the number of simultaneously active users is less than or equal to w, a CAC of length L with weight w can provide a hard guarantee that each active user has at least one successful transmission within every consecutive L slots. In this paper, we generalize some previously known constructions of constant-weight CACs, and then derive several classes of optimal CACs by the help of Kneser’s Theorem and some techniques in Additive Combinatorics. Another spotlight of this paper is to relax the identical-weight constraint in prior studies to study mixed-weight CACs for the first time, for the purpose of increasing the throughput and reducing the access delay of some potential users with higher priority. As applications of those obtained optimal CACs, we derive some classes of optimal mixed-weight CACs.
{"title":"Optimal Constant-Weight and Mixed-Weight Conflict-Avoiding Codes","authors":"Yuan-Hsun Lo;Tsai-Lien Wong;Kangkang Xu;Yijin Zhang","doi":"10.1109/TIT.2025.3528132","DOIUrl":"https://doi.org/10.1109/TIT.2025.3528132","url":null,"abstract":"A conflict-avoiding code (CAC) is a deterministic transmission scheme for asynchronous multiple access without feedback. When the number of simultaneously active users is less than or equal to w, a CAC of length L with weight w can provide a hard guarantee that each active user has at least one successful transmission within every consecutive L slots. In this paper, we generalize some previously known constructions of constant-weight CACs, and then derive several classes of optimal CACs by the help of Kneser’s Theorem and some techniques in Additive Combinatorics. Another spotlight of this paper is to relax the identical-weight constraint in prior studies to study mixed-weight CACs for the first time, for the purpose of increasing the throughput and reducing the access delay of some potential users with higher priority. As applications of those obtained optimal CACs, we derive some classes of optimal mixed-weight CACs.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"2257-2270"},"PeriodicalIF":2.2,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455271","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}
Pub Date : 2025-01-10DOI: 10.1109/TIT.2025.3528083
Yuhan Wang;Youlong Wu
Coded distributed computing can reduce the communication load for distributed computing systems by introducing redundant computation and creating multicasting opportunities. However, the existing schemes require delicate data placement and output function assignment, which is not feasible when distributed nodes fetch data without the orchestration of a central server. In this paper, we consider the general systems where the data placement and output function assignment are arbitrary but pre-set. We propose two coded computing schemes, One-shot Coded Transmission (OSCT) and Few-shot Coded Transmission (FSCT), to reduce the communication load. Both schemes first group the nodes into clusters and divide the transmission of each cluster into multiple rounds, and then design coded transmission in each round to maximize the multicast gain. The key difference between OSCT and FSCT is that the former uses a one-shot transmission where each encoded message can be decoded independently by the intended nodes, while the latter allows each node to jointly decode multiple received symbols to achieve potentially larger multicast gains. Furthermore, based on the lower bound proposed by Yu et al., we derive sufficient conditions for the optimality of OSCT and FSCT, respectively. This not only recovers the existing optimality results but also includes some cases where our schemes are optimal while others are not.
{"title":"Coded Distributed Computing With Pre-Set Data Placement and Output Functions Assignment","authors":"Yuhan Wang;Youlong Wu","doi":"10.1109/TIT.2025.3528083","DOIUrl":"https://doi.org/10.1109/TIT.2025.3528083","url":null,"abstract":"Coded distributed computing can reduce the communication load for distributed computing systems by introducing redundant computation and creating multicasting opportunities. However, the existing schemes require delicate data placement and output function assignment, which is not feasible when distributed nodes fetch data without the orchestration of a central server. In this paper, we consider the general systems where the data placement and output function assignment are arbitrary but pre-set. We propose two coded computing schemes, One-shot Coded Transmission (OSCT) and Few-shot Coded Transmission (FSCT), to reduce the communication load. Both schemes first group the nodes into clusters and divide the transmission of each cluster into multiple rounds, and then design coded transmission in each round to maximize the multicast gain. The key difference between OSCT and FSCT is that the former uses a one-shot transmission where each encoded message can be decoded independently by the intended nodes, while the latter allows each node to jointly decode multiple received symbols to achieve potentially larger multicast gains. Furthermore, based on the lower bound proposed by Yu et al., we derive sufficient conditions for the optimality of OSCT and FSCT, respectively. This not only recovers the existing optimality results but also includes some cases where our schemes are optimal while others are not.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"2195-2217"},"PeriodicalIF":2.2,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455237","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}
Quasi complementary sequence sets (QCSSs) are important in modern communication systems as they are capable of supporting more users, which is desired in applications like MC-CDMA nowadays. In this paper, we first derive a tighter bound on the maximum aperiodic correlation among all constituent complementary sequence sets in QCSSs. By proposing a new combinatorial structure called quasi-Florentine rectangles, we obtain a new construction of QCSSs with large set sizes. Using Butson-type Hadamard matrices and quasi-Florentine rectangles, we propose another construction which can construct QCSSs with flexible parameters over any given alphabet size, including small alphabets. All the proposed sequences are optimal with respect to the newly proposed bound. Also, through some of the constructions, the column sequence PMEPR of the proposed QCSSs are upper bounded by 2.
{"title":"Quasi Complementary Sequence Sets: New Bounds and Optimal Constructions via Quasi-Florentine Rectangles","authors":"Avik Ranjan Adhikary;Hui Zhang;Zhengchun Zhou;Qi Wang;Sihem Mesnager","doi":"10.1109/TIT.2025.3528056","DOIUrl":"https://doi.org/10.1109/TIT.2025.3528056","url":null,"abstract":"Quasi complementary sequence sets (QCSSs) are important in modern communication systems as they are capable of supporting more users, which is desired in applications like MC-CDMA nowadays. In this paper, we first derive a tighter bound on the maximum aperiodic correlation among all constituent complementary sequence sets in QCSSs. By proposing a new combinatorial structure called quasi-Florentine rectangles, we obtain a new construction of QCSSs with large set sizes. Using Butson-type Hadamard matrices and quasi-Florentine rectangles, we propose another construction which can construct QCSSs with flexible parameters over any given alphabet size, including small alphabets. All the proposed sequences are optimal with respect to the newly proposed bound. Also, through some of the constructions, the column sequence PMEPR of the proposed QCSSs are upper bounded by 2.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"2271-2291"},"PeriodicalIF":2.2,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455277","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}
Pub Date : 2025-01-10DOI: 10.1109/TIT.2025.3528241
Boaz Shuval;Ido Tal
A transform that is universally polarizing over a set of channels with memory is presented. Memory may be present in both the input to the channel and the channel itself. Both the encoder and the decoder are aware of the input distribution, which is fixed. However, only the decoder is aware of the actual channel being used. The transform can be used to design a universal code for this scenario. The code is to have vanishing error probability when used over any channel in the set, and achieve the infimal information rate over the set. The setting considered is, in fact, more general: we consider a set of processes with memory. Universal polarization is established for the case where each process in the set: 1) has memory in the form of an underlying hidden Markov state sequence that is aperiodic and irreducible; and 2) satisfies a ‘forgetfulness’ property. Forgetfulness, which we believe to be of independent interest, occurs when two hidden Markov states become approximately independent of each other given a sufficiently long sequence of observations between them. We show that aperiodicity and irreducibility of the underlying Markov chain is not sufficient for forgetfulness, and develop a sufficient condition for a hidden Markov process to be forgetful.
{"title":"Universal Polarization for Processes With Memory","authors":"Boaz Shuval;Ido Tal","doi":"10.1109/TIT.2025.3528241","DOIUrl":"https://doi.org/10.1109/TIT.2025.3528241","url":null,"abstract":"A transform that is universally polarizing over a set of channels with memory is presented. Memory may be present in both the input to the channel and the channel itself. Both the encoder and the decoder are aware of the input distribution, which is fixed. However, only the decoder is aware of the actual channel being used. The transform can be used to design a universal code for this scenario. The code is to have vanishing error probability when used over any channel in the set, and achieve the infimal information rate over the set. The setting considered is, in fact, more general: we consider a set of processes with memory. Universal polarization is established for the case where each process in the set: 1) has memory in the form of an underlying hidden Markov state sequence that is aperiodic and irreducible; and 2) satisfies a ‘forgetfulness’ property. Forgetfulness, which we believe to be of independent interest, occurs when two hidden Markov states become approximately independent of each other given a sufficiently long sequence of observations between them. We show that aperiodicity and irreducibility of the underlying Markov chain is not sufficient for forgetfulness, and develop a sufficient condition for a hidden Markov process to be forgetful.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"1705-1757"},"PeriodicalIF":2.2,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465616","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}
Pub Date : 2025-01-09DOI: 10.1109/TIT.2025.3527858
Mario Berta;Ludovico Lami;Marco Tomamichel
We show that Frenkel’s integral representation of the quantum relative entropy provides a natural framework to derive continuity bounds for quantum information measures. Our main general result is a dimension-independent semi-continuity relation for the quantum relative entropy with respect to the first argument. Using it, we obtain a number of results: 1) a tight continuity relation for the conditional entropy in the case where the two states have equal marginals on the conditioning system, resolving a conjecture by Wilde in this special case; 2) a stronger version of the Fannes-Audenaert inequality on quantum entropy; 3) better estimates on the quantum capacity of approximately degradable channels; 4) an improved continuity relation for the entanglement cost; 5) general upper bounds on asymptotic transformation rates in infinite-dimensional entanglement theory; and 6) a proof of a conjecture due to Christandl, Ferrara, and Lancien on the continuity of ‘filtered’ relative entropy distances.
{"title":"Continuity of Entropies via Integral Representations","authors":"Mario Berta;Ludovico Lami;Marco Tomamichel","doi":"10.1109/TIT.2025.3527858","DOIUrl":"https://doi.org/10.1109/TIT.2025.3527858","url":null,"abstract":"We show that Frenkel’s integral representation of the quantum relative entropy provides a natural framework to derive continuity bounds for quantum information measures. Our main general result is a dimension-independent semi-continuity relation for the quantum relative entropy with respect to the first argument. Using it, we obtain a number of results: 1) a tight continuity relation for the conditional entropy in the case where the two states have equal marginals on the conditioning system, resolving a conjecture by Wilde in this special case; 2) a stronger version of the Fannes-Audenaert inequality on quantum entropy; 3) better estimates on the quantum capacity of approximately degradable channels; 4) an improved continuity relation for the entanglement cost; 5) general upper bounds on asymptotic transformation rates in infinite-dimensional entanglement theory; and 6) a proof of a conjecture due to Christandl, Ferrara, and Lancien on the continuity of ‘filtered’ relative entropy distances.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"1896-1908"},"PeriodicalIF":2.2,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455297","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}
Pub Date : 2025-01-09DOI: 10.1109/TIT.2025.3526419
Alexander Streltsov
A key problem in quantum information science is to determine optimal protocols for the interconversion of entangled states shared between remote parties. While for two parties a large number of results in this direction is available, the multipartite setting still remains a major challenge. In this article, this problem is addressed by extending the resource theory of entanglement for multipartite systems beyond the standard framework of local operations and classical communication. Specifically, we consider transformations capable of introducing a small, controllable increase of entanglement of a state, with the requirement that the increase can be made arbitrarily small. We demonstrate that in this adjusted framework, the transformation rates between multipartite states are fundamentally dictated by the bipartite entanglement entropies of the respective quantum states. Remarkably, this approach allows the reduction of tripartite entanglement to its bipartite analog, indicating that every pure tripartite state can be reversibly synthesized from a suitable number of singlets distributed between pairs of parties.
{"title":"Multipartite Entanglement Theory With Entanglement-Nonincreasing Operations","authors":"Alexander Streltsov","doi":"10.1109/TIT.2025.3526419","DOIUrl":"https://doi.org/10.1109/TIT.2025.3526419","url":null,"abstract":"A key problem in quantum information science is to determine optimal protocols for the interconversion of entangled states shared between remote parties. While for two parties a large number of results in this direction is available, the multipartite setting still remains a major challenge. In this article, this problem is addressed by extending the resource theory of entanglement for multipartite systems beyond the standard framework of local operations and classical communication. Specifically, we consider transformations capable of introducing a small, controllable increase of entanglement of a state, with the requirement that the increase can be made arbitrarily small. We demonstrate that in this adjusted framework, the transformation rates between multipartite states are fundamentally dictated by the bipartite entanglement entropies of the respective quantum states. Remarkably, this approach allows the reduction of tripartite entanglement to its bipartite analog, indicating that every pure tripartite state can be reversibly synthesized from a suitable number of singlets distributed between pairs of parties.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"1841-1850"},"PeriodicalIF":2.2,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465590","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}
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