The error exponent of fixed-length lossy source coding was established by Marton. Ahlswede showed that this exponent can be discontinuous at a rate $R$, depending on the source distribution $P$ and the distortion measure $d(x,y)$. The reason for the discontinuity in the error exponent is that there exists a distortion measure $d(x,y)$ and a distortion level $Delta$ such that the rate-distortion function $R(Delta|P)$ is neither concave nor quasi-concave with respect to $P$. Arimoto's algorithm for computing the error exponent in lossy source coding is based on Blahut's parametric representation of the error exponent. However, Blahut's parametric representation is a lower convex envelope of Marton's exponent, and the two do not generally agree. A major contribution of this paper is to provide a parametric representation that perfectly matches the inverse function of Marton's exponent, thereby preventing the problems arising from the above-mentioned non-concavity of $R(Delta|P)$. For fixed parameters, an optimal distribution can be obtained using Arimoto's algorithm. By performing a nonconvex optimization over the parameters, the inverse function of Marton's exponent is obtained.
{"title":"Computation of the optimal error exponent function for fixed-length lossy source coding in discrete memoryless sources","authors":"Yutaka Jitsumatsu","doi":"arxiv-2312.03784","DOIUrl":"https://doi.org/arxiv-2312.03784","url":null,"abstract":"The error exponent of fixed-length lossy source coding was established by\u0000Marton. Ahlswede showed that this exponent can be discontinuous at a rate $R$,\u0000depending on the source distribution $P$ and the distortion measure $d(x,y)$.\u0000The reason for the discontinuity in the error exponent is that there exists a\u0000distortion measure $d(x,y)$ and a distortion level $Delta$ such that the\u0000rate-distortion function $R(Delta|P)$ is neither concave nor quasi-concave\u0000with respect to $P$. Arimoto's algorithm for computing the error exponent in\u0000lossy source coding is based on Blahut's parametric representation of the error\u0000exponent. However, Blahut's parametric representation is a lower convex\u0000envelope of Marton's exponent, and the two do not generally agree. A major\u0000contribution of this paper is to provide a parametric representation that\u0000perfectly matches the inverse function of Marton's exponent, thereby preventing\u0000the problems arising from the above-mentioned non-concavity of $R(Delta|P)$.\u0000For fixed parameters, an optimal distribution can be obtained using Arimoto's\u0000algorithm. By performing a nonconvex optimization over the parameters, the\u0000inverse function of Marton's exponent is obtained.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"228 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138553955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lucas Monteiro Paes, Ananda Theertha Suresh, Alex Beutel, Flavio P. Calmon, Ahmad Beirami
Machine learning (ML) models used in prediction and classification tasks may display performance disparities across population groups determined by sensitive attributes (e.g., race, sex, age). We consider the problem of evaluating the performance of a fixed ML model across population groups defined by multiple sensitive attributes (e.g., race and sex and age). Here, the sample complexity for estimating the worst-case performance gap across groups (e.g., the largest difference in error rates) increases exponentially with the number of group-denoting sensitive attributes. To address this issue, we propose an approach to test for performance disparities based on Conditional Value-at-Risk (CVaR). By allowing a small probabilistic slack on the groups over which a model has approximately equal performance, we show that the sample complexity required for discovering performance violations is reduced exponentially to be at most upper bounded by the square root of the number of groups. As a byproduct of our analysis, when the groups are weighted by a specific prior distribution, we show that R'enyi entropy of order $2/3$ of the prior distribution captures the sample complexity of the proposed CVaR test algorithm. Finally, we also show that there exists a non-i.i.d. data collection strategy that results in a sample complexity independent of the number of groups.
{"title":"Multi-Group Fairness Evaluation via Conditional Value-at-Risk Testing","authors":"Lucas Monteiro Paes, Ananda Theertha Suresh, Alex Beutel, Flavio P. Calmon, Ahmad Beirami","doi":"arxiv-2312.03867","DOIUrl":"https://doi.org/arxiv-2312.03867","url":null,"abstract":"Machine learning (ML) models used in prediction and classification tasks may\u0000display performance disparities across population groups determined by\u0000sensitive attributes (e.g., race, sex, age). We consider the problem of\u0000evaluating the performance of a fixed ML model across population groups defined\u0000by multiple sensitive attributes (e.g., race and sex and age). Here, the sample\u0000complexity for estimating the worst-case performance gap across groups (e.g.,\u0000the largest difference in error rates) increases exponentially with the number\u0000of group-denoting sensitive attributes. To address this issue, we propose an\u0000approach to test for performance disparities based on Conditional Value-at-Risk\u0000(CVaR). By allowing a small probabilistic slack on the groups over which a\u0000model has approximately equal performance, we show that the sample complexity\u0000required for discovering performance violations is reduced exponentially to be\u0000at most upper bounded by the square root of the number of groups. As a\u0000byproduct of our analysis, when the groups are weighted by a specific prior\u0000distribution, we show that R'enyi entropy of order $2/3$ of the prior\u0000distribution captures the sample complexity of the proposed CVaR test\u0000algorithm. Finally, we also show that there exists a non-i.i.d. data collection\u0000strategy that results in a sample complexity independent of the number of\u0000groups.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"103 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138553758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Michael Baur, Benedikt Böck, Nurettin Turan, Wolfgang Utschick
This work utilizes a variational autoencoder for channel estimation and evaluates it on real-world measurements. The estimator is trained solely on noisy channel observations and parameterizes an approximation to the mean squared error-optimal estimator by learning observation-dependent conditional first and second moments. The proposed estimator significantly outperforms related state-of-the-art estimators on real-world measurements. We investigate the effect of pre-training with synthetic data and find that the proposed estimator exhibits comparable results to the related estimators if trained on synthetic data and evaluated on the measurement data. Furthermore, pre-training on synthetic data also helps to reduce the required measurement training dataset size.
{"title":"Variational Autoencoder for Channel Estimation: Real-World Measurement Insights","authors":"Michael Baur, Benedikt Böck, Nurettin Turan, Wolfgang Utschick","doi":"arxiv-2312.03450","DOIUrl":"https://doi.org/arxiv-2312.03450","url":null,"abstract":"This work utilizes a variational autoencoder for channel estimation and\u0000evaluates it on real-world measurements. The estimator is trained solely on\u0000noisy channel observations and parameterizes an approximation to the mean\u0000squared error-optimal estimator by learning observation-dependent conditional\u0000first and second moments. The proposed estimator significantly outperforms\u0000related state-of-the-art estimators on real-world measurements. We investigate\u0000the effect of pre-training with synthetic data and find that the proposed\u0000estimator exhibits comparable results to the related estimators if trained on\u0000synthetic data and evaluated on the measurement data. Furthermore, pre-training\u0000on synthetic data also helps to reduce the required measurement training\u0000dataset size.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138547779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Israel Leyva-Mayorga, Jose Manuel Gimenez-Guzman, Lorenzo Valentini, Petar Popovski
Since the advent of ultra-reliable and low-latency communications (URLLC), the requirements of low-latency applications tend to be completely characterized by a single pre-defined latency-reliability target. That is, operation is optimal whenever the pre-defined latency threshold is met but the system is assumed to be in error when the latency threshold is violated. This vision is severely limited and does not capture the real requirements of most applications, where multiple latency thresholds can be defined, together with incentives or rewards associated with meeting each of them. Such formulation is a generalization of the single-threshold case popularized by URLLC and, in the asymptotic case, approximates to defining a cost for each point in the support of the latency distribution. In this paper, we explore the implications of defining multiple latency targets on the design of access protocols and on the optimization of repetition-based access strategies in orthogonal and non-orthogonal multiple access scenarios with users that present heterogeneous traffic characteristics and requirements. We observe that the access strategies of the users can be effectively adapted to the requirements of the application by carefully defining the latency targets and the associated rewards.
{"title":"Heterogeneous radio access with multiple latency targets","authors":"Israel Leyva-Mayorga, Jose Manuel Gimenez-Guzman, Lorenzo Valentini, Petar Popovski","doi":"arxiv-2312.03131","DOIUrl":"https://doi.org/arxiv-2312.03131","url":null,"abstract":"Since the advent of ultra-reliable and low-latency communications (URLLC),\u0000the requirements of low-latency applications tend to be completely\u0000characterized by a single pre-defined latency-reliability target. That is,\u0000operation is optimal whenever the pre-defined latency threshold is met but the\u0000system is assumed to be in error when the latency threshold is violated. This\u0000vision is severely limited and does not capture the real requirements of most\u0000applications, where multiple latency thresholds can be defined, together with\u0000incentives or rewards associated with meeting each of them. Such formulation is\u0000a generalization of the single-threshold case popularized by URLLC and, in the\u0000asymptotic case, approximates to defining a cost for each point in the support\u0000of the latency distribution. In this paper, we explore the implications of\u0000defining multiple latency targets on the design of access protocols and on the\u0000optimization of repetition-based access strategies in orthogonal and\u0000non-orthogonal multiple access scenarios with users that present heterogeneous\u0000traffic characteristics and requirements. We observe that the access strategies\u0000of the users can be effectively adapted to the requirements of the application\u0000by carefully defining the latency targets and the associated rewards.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"62 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138547785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mohammad NaseriTehrani, MohammadJavad Salehi, Antti Tölli
A practical and scalable multicast beamformer design in multi-input multi-output~(MIMO) coded caching~(CC) systems is introduced in this paper. The proposed approach allows multicast transmission to multiple groups with partially overlapping user sets using receiver dimensions to distinguish between different group-specific streams. Additionally, it provides flexibility in accommodating various parameter configurations of the MIMO-CC setup and overcomes practical limitations, such as the requirement to use successive interference cancellation~(SIC) at the receiver, while achieving the same degrees-of-freedom~(DoF). To evaluate the proposed scheme, we define the symmetric rate as the sum rate of the partially overlapping streams received per user, comprising a linear multistream multicast transmission vector and the linear minimum mean square error~(LMMSE) receiver. The resulting non-convex symmetric rate maximization problem is solved using alternative optimization and successive convex approximation~(SCA). Moreover, a fast iterative Lagrangian-based algorithm is developed, significantly reducing the computational overhead compared to previous designs. The effectiveness of our proposed method is demonstrated by extensive simulations.
{"title":"Low-complexity Linear Multicast Beamforming for Cache-aided MIMO Communications","authors":"Mohammad NaseriTehrani, MohammadJavad Salehi, Antti Tölli","doi":"arxiv-2312.02839","DOIUrl":"https://doi.org/arxiv-2312.02839","url":null,"abstract":"A practical and scalable multicast beamformer design in multi-input\u0000multi-output~(MIMO) coded caching~(CC) systems is introduced in this paper. The\u0000proposed approach allows multicast transmission to multiple groups with\u0000partially overlapping user sets using receiver dimensions to distinguish\u0000between different group-specific streams. Additionally, it provides flexibility\u0000in accommodating various parameter configurations of the MIMO-CC setup and\u0000overcomes practical limitations, such as the requirement to use successive\u0000interference cancellation~(SIC) at the receiver, while achieving the same\u0000degrees-of-freedom~(DoF). To evaluate the proposed scheme, we define the\u0000symmetric rate as the sum rate of the partially overlapping streams received\u0000per user, comprising a linear multistream multicast transmission vector and the\u0000linear minimum mean square error~(LMMSE) receiver. The resulting non-convex\u0000symmetric rate maximization problem is solved using alternative optimization\u0000and successive convex approximation~(SCA). Moreover, a fast iterative\u0000Lagrangian-based algorithm is developed, significantly reducing the\u0000computational overhead compared to previous designs. The effectiveness of our\u0000proposed method is demonstrated by extensive simulations.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138547522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sebastian Cammerer, Fayçal Aït Aoudia, Jakob Hoydis, Andreas Oeldemann, Andreas Roessler, Timo Mayer, Alexander Keller
We introduce a neural network (NN)-based multiuser multiple-input multiple-output (MU-MIMO) receiver with 5G New Radio (5G NR) physical uplink shared channel (PUSCH) compatibility. The NN architecture is based on convolution layers to exploit the time and frequency correlation of the channel and a graph neural network (GNN) to handle multiple users. The proposed architecture adapts to an arbitrary number of sub-carriers and supports a varying number of multiple-input multiple-output (MIMO) layers and users without the need for any retraining. The receiver operates on an entire 5G NR slot, i.e., processes the entire received orthogonal frequency division multiplexing (OFDM) time-frequency resource grid by jointly performing channel estimation, equalization, and demapping. The proposed architecture operates less than 1 dB away from a baseline using linear minimum mean square error (LMMSE) channel estimation with K-best detection but benefits from a significantly lower computational complexity. We show the importance of a carefully designed training process such that the trained receiver is universal for a wide range of different unseen channel conditions. Finally, we demonstrate the results of a hardware-in-the-loop verification based on 3GPP compliant conformance test scenarios.
{"title":"A Neural Receiver for 5G NR Multi-user MIMO","authors":"Sebastian Cammerer, Fayçal Aït Aoudia, Jakob Hoydis, Andreas Oeldemann, Andreas Roessler, Timo Mayer, Alexander Keller","doi":"arxiv-2312.02601","DOIUrl":"https://doi.org/arxiv-2312.02601","url":null,"abstract":"We introduce a neural network (NN)-based multiuser multiple-input\u0000multiple-output (MU-MIMO) receiver with 5G New Radio (5G NR) physical uplink\u0000shared channel (PUSCH) compatibility. The NN architecture is based on\u0000convolution layers to exploit the time and frequency correlation of the channel\u0000and a graph neural network (GNN) to handle multiple users. The proposed\u0000architecture adapts to an arbitrary number of sub-carriers and supports a\u0000varying number of multiple-input multiple-output (MIMO) layers and users\u0000without the need for any retraining. The receiver operates on an entire 5G NR\u0000slot, i.e., processes the entire received orthogonal frequency division\u0000multiplexing (OFDM) time-frequency resource grid by jointly performing channel\u0000estimation, equalization, and demapping. The proposed architecture operates\u0000less than 1 dB away from a baseline using linear minimum mean square error\u0000(LMMSE) channel estimation with K-best detection but benefits from a\u0000significantly lower computational complexity. We show the importance of a\u0000carefully designed training process such that the trained receiver is universal\u0000for a wide range of different unseen channel conditions. Finally, we\u0000demonstrate the results of a hardware-in-the-loop verification based on 3GPP\u0000compliant conformance test scenarios.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138547523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In Vehicle-to-Everything (V2X) systems, reliable and secure information exchange plays a pivotal role in road safety and traffic management. Due to the open nature of the wireless medium and the constant or intermittent mobility of vehicles, the security of transmissions in V2X is more challenging compared to traditional wireless networks. Physical layer security (PLS) leverages the inherent randomness of wireless communication channels to ensure the confidentiality and security of information transmission. Current PLS schemes in integrated communications and sensing (ISAC) enabled V2X systems is to utilize communication interference to significantly impact the eavesdropping channel more than the legitimate channel. However, in an ISAC-enabled V2X system, it is crucial to prioritize and address the issue of interference coupling as it significantly impacts the confidentiality and security of information exchange. This goes beyond simply relying on the communication interference. Until now, no discussions or studies on integrating security with ISAC (Seucue-ISAC) in ISAC-enabled V2X systems, specifically regarding the exploitation of sensing interference or coupling interference. In this article, we provide a comprehensive review on PLS metrics and security threats encountered in V2X communication. And then, we discuss and analyze four popular PLS techniques and the main challenges associated with their implementation in ISAC-enabled V2X systems. Finally, we share our vision for PLS studies in ISAC-based V2X systems to promote Secure-ISAC.
{"title":"Secure-ISAC: Secure V2X Communication: An Integrated Sensing and Communication Perspective","authors":"Kan Yu, Zhiyong Feng, Dong Li, Jiguo Yu","doi":"arxiv-2312.01720","DOIUrl":"https://doi.org/arxiv-2312.01720","url":null,"abstract":"In Vehicle-to-Everything (V2X) systems, reliable and secure information\u0000exchange plays a pivotal role in road safety and traffic management. Due to the\u0000open nature of the wireless medium and the constant or intermittent mobility of\u0000vehicles, the security of transmissions in V2X is more challenging compared to\u0000traditional wireless networks. Physical layer security (PLS) leverages the\u0000inherent randomness of wireless communication channels to ensure the\u0000confidentiality and security of information transmission. Current PLS schemes\u0000in integrated communications and sensing (ISAC) enabled V2X systems is to\u0000utilize communication interference to significantly impact the eavesdropping\u0000channel more than the legitimate channel. However, in an ISAC-enabled V2X\u0000system, it is crucial to prioritize and address the issue of interference\u0000coupling as it significantly impacts the confidentiality and security of\u0000information exchange. This goes beyond simply relying on the communication\u0000interference. Until now, no discussions or studies on integrating security with\u0000ISAC (Seucue-ISAC) in ISAC-enabled V2X systems, specifically regarding the\u0000exploitation of sensing interference or coupling interference. In this article,\u0000we provide a comprehensive review on PLS metrics and security threats\u0000encountered in V2X communication. And then, we discuss and analyze four popular\u0000PLS techniques and the main challenges associated with their implementation in\u0000ISAC-enabled V2X systems. Finally, we share our vision for PLS studies in\u0000ISAC-based V2X systems to promote Secure-ISAC.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138535886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lorenzo Miretti, Renato L. G. Cavalcante, Sławomir Stańczak
This study presents novel applications of fixed-point methods to solve previously open joint power control and beamforming design problems in modern large-scale MIMO systems, e.g., based on the cell-free massive MIMO and XL-MIMO concepts. In particular, motivated by the need for scalable system architectures, we revisit the classical sum power minimization and max-min fair design criteria by considering long-term power control and beamforming design based on channel statistics and possibly limited channel state information (CSI) sharing across distributed processing units. This approach is believed to mitigate the severe scalability issues of competing short-term optimal algorithms in the literature, which must be executed for every channel realization by a central controller endowed with global CSI, hence imposing very demanding requirements in terms of computation and interconnection capabilities. The obtained optimal algorithms are then illustrated and compared against existing short-term and long-term approaches via numerical simulations in a cell-free massive MIMO setup.
{"title":"Fixed-point methods for long-term power control and beamforming design in large-scale MIMO","authors":"Lorenzo Miretti, Renato L. G. Cavalcante, Sławomir Stańczak","doi":"arxiv-2312.02080","DOIUrl":"https://doi.org/arxiv-2312.02080","url":null,"abstract":"This study presents novel applications of fixed-point methods to solve\u0000previously open joint power control and beamforming design problems in modern\u0000large-scale MIMO systems, e.g., based on the cell-free massive MIMO and XL-MIMO\u0000concepts. In particular, motivated by the need for scalable system\u0000architectures, we revisit the classical sum power minimization and max-min fair\u0000design criteria by considering long-term power control and beamforming design\u0000based on channel statistics and possibly limited channel state information\u0000(CSI) sharing across distributed processing units. This approach is believed to\u0000mitigate the severe scalability issues of competing short-term optimal\u0000algorithms in the literature, which must be executed for every channel\u0000realization by a central controller endowed with global CSI, hence imposing\u0000very demanding requirements in terms of computation and interconnection\u0000capabilities. The obtained optimal algorithms are then illustrated and compared\u0000against existing short-term and long-term approaches via numerical simulations\u0000in a cell-free massive MIMO setup.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138535888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yu-Ao Chen, Chengkai Zhu, Keming He, Mingrui Jing, Xin Wang
Quantum Markov chains generalize classical Markov chains for random variables to the quantum realm and exhibit unique inherent properties, making them an important feature in quantum information theory. In this work, we propose the concept of virtual quantum Markov chains (VQMCs), focusing on scenarios where subsystems retain classical information about global systems from measurement statistics. As a generalization of quantum Markov chains, VQMCs characterize states where arbitrary global shadow information can be recovered from subsystems through local quantum operations and measurements. We present an algebraic characterization for virtual quantum Markov chains and show that the virtual quantum recovery is fully determined by the block matrices of a quantum state on its subsystems. Notably, we find a distinction between two classes of tripartite entanglement by showing that the W state is a VQMC while the GHZ state is not. Furthermore, we establish semidefinite programs to determine the optimal sampling overhead and the robustness of virtual quantum Markov chains. We demonstrate the optimal sampling overhead is additive, indicating no free lunch to further reduce the sampling cost of recovery from parallel calls of the VQMC states. Our findings elucidate distinctions between quantum Markov chains and virtual quantum Markov chains, extending our understanding of quantum recovery to scenarios prioritizing classical information from measurement statistics.
{"title":"Virtual Quantum Markov Chains","authors":"Yu-Ao Chen, Chengkai Zhu, Keming He, Mingrui Jing, Xin Wang","doi":"arxiv-2312.02031","DOIUrl":"https://doi.org/arxiv-2312.02031","url":null,"abstract":"Quantum Markov chains generalize classical Markov chains for random variables\u0000to the quantum realm and exhibit unique inherent properties, making them an\u0000important feature in quantum information theory. In this work, we propose the\u0000concept of virtual quantum Markov chains (VQMCs), focusing on scenarios where\u0000subsystems retain classical information about global systems from measurement\u0000statistics. As a generalization of quantum Markov chains, VQMCs characterize\u0000states where arbitrary global shadow information can be recovered from\u0000subsystems through local quantum operations and measurements. We present an\u0000algebraic characterization for virtual quantum Markov chains and show that the\u0000virtual quantum recovery is fully determined by the block matrices of a quantum\u0000state on its subsystems. Notably, we find a distinction between two classes of\u0000tripartite entanglement by showing that the W state is a VQMC while the GHZ\u0000state is not. Furthermore, we establish semidefinite programs to determine the\u0000optimal sampling overhead and the robustness of virtual quantum Markov chains.\u0000We demonstrate the optimal sampling overhead is additive, indicating no free\u0000lunch to further reduce the sampling cost of recovery from parallel calls of\u0000the VQMC states. Our findings elucidate distinctions between quantum Markov\u0000chains and virtual quantum Markov chains, extending our understanding of\u0000quantum recovery to scenarios prioritizing classical information from\u0000measurement statistics.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"83 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138535818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we generalize the completely monotone conjecture from Shannon entropy to the R'enyi entropy. We confirm this conjecture for the order of derivative up to $3$, when the order of R'enyi entropy is in certain regimes. We also investigate concavity of R'enyi entropy power and the completely monotone conjecture for Tsallis entropy. We observe that the completely monotone conjecture is true for Tsallis entropy of order $2$. Our proofs in this paper are based on the techniques of integration-by-parts and sum-of-squares.
{"title":"On the Completely Monotone Conjecture for Rényi Entropy","authors":"Hao Wu, Lei Yu, Laigang Guo","doi":"arxiv-2312.01819","DOIUrl":"https://doi.org/arxiv-2312.01819","url":null,"abstract":"In this paper, we generalize the completely monotone conjecture from Shannon\u0000entropy to the R'enyi entropy. We confirm this conjecture for the order of\u0000derivative up to $3$, when the order of R'enyi entropy is in certain regimes.\u0000We also investigate concavity of R'enyi entropy power and the completely\u0000monotone conjecture for Tsallis entropy. We observe that the completely\u0000monotone conjecture is true for Tsallis entropy of order $2$. Our proofs in\u0000this paper are based on the techniques of integration-by-parts and\u0000sum-of-squares.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138535887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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