Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2304.12056

Quantum Broadcast Channel Simulation via Multipartite Convex Splitting

Hao–Chung Cheng, Gao Li, Mario Berta

Published Apr 24, 2023• 6 citations
arXivHTMLPDF

Abstract

We show that the communication cost of quantum broadcast channel simulation under free entanglement assistance between the sender and the receivers is asymptotically characterized by an efficiently computable single-letter formula in terms of the channel's multipartite mutual information. Our core contribution is a new one-shot achievability result for multipartite quantum state splitting via multipartite convex splitting. As part of this, we face a general instance of the quantum joint typicality problem with arbitrarily overlapping marginals. The crucial technical ingredient to sidestep this difficulty is a conceptually novel multipartite mean-zero decomposition lemma, together with employing recently introduced complex interpolation techniques for sandwiched Rényi divergences. Moreover, we establish an exponential convergence of the simulation error when the communication costs are within the interior of the capacity region. As the costs approach the boundary of the capacity region moderately quickly, we show that the error still vanishes asymptotically.

DOI
10.48550/arxiv.2304.12056

Related papers

Quantum Broadcast Channel Simulation via Multipartite Convex Splitting

Mario Berta, Hao–Chung Cheng, Li Gao

We show that the communication cost of quantum broadcast channel simulation under free entanglement assistance between the sender and the receivers is asymptotically characterized by an efficiently computable single-letter formula in terms of the channel's multipartite mutual information. Our core contribution is a new one-shot achievability result for multipartite quantum state splitting via multipartite convex splitting. As part of this, we face a general instance of the quantum joint typicality problem with arbitrarily overlapping marginals. The crucial technical ingredient to sidestep this difficulty is a conceptually novel multipartite mean-zero decomposition lemma, together with employing recently introduced complex interpolation techniques for sandwiched Rényi divergences. Moreover, we establish an exponential convergence of the simulation error when the communication costs are within the interior of the capacity region. As the costs approach the boundary of the capacity region moderately quickly, we show that the error still vanishes asymptotically.

Communications in Mathematical Physics•Jan 16, 2025•7 citations

Building Blocks for Communication Over Noisy Quantum Nerworks

Anurag Anshu, Rahul Jain, Naqueeb Ahmad Warsi

Capacity of a quantum channel characterizes the limits of reliable communication through a noisy quantum channel. This fundamental information theoretic question is very well studied specially in the setting of many independent uses of the channel. An important scenario, both from practical and conceptual point of view, is when the channel can be used only once. This is known as the one-shot channel coding problem. We provide a tight characterization of the one-shot entanglement assisted classical capacity of a quantum channel. We arrive at our result by introducing a simple decoding technique which we refer to as position-based decoding. We also consider two other important quantum network scenarios: quantum channel with a jammer and quantum broadcast channel. For these problems, we use the recently introduced convex split technique [1] in addition to position based decoding. Our approach exhibits that the simultaneous use of these two techniques provides a uniform and conceptually simple framework for designing communication protocols for quantum networks.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2018•0 citations

Building Blocks for Communication Over Noisy Quantum Networks

Anurag Anshu, Rahul Jain, Naqueeb Ahmad Warsi

A capacity of a quantum channel characterizes the limits of reliable communication through a noisy quantum channel. This fundamental information-theoretic question is very well studied specially in the setting of many independent uses of the channel. An important scenario, both from practical and conceptual point of view, is when the channel can be used only once. This is known as the one-shot channel coding problem. We provide a tight characterization of the one-shot entanglement-assisted classical capacity of a quantum channel. We arrive at our result by introducing a simple decoding technique which we refer to as position-based decoding. We also consider two other important quantum network scenarios: quantum channel with a jammer and quantum broadcast channel. For these problems, we use the recently introduced convex split technique in addition to position-based decoding. Our approach exhibits that the simultaneous use of these two techniques provides a uniform and conceptually simple framework for designing communication protocols for quantum networks.

arXiv:1702.01940•IEEE Transactions on Information Theory•Jun 28, 2018•90 citations

Entanglement-assisted private communication over quantum broadcast channels

Haoyu Qi, Kunal Sharma, Mark M. Wilde

Abstract We consider entanglement-assisted (EA) private communication over a quantum broadcast channel, in which there is a single sender and multiple receivers. We divide the receivers into two sets: the decoding set and the malicious set. The decoding set and the malicious set can either be disjoint or can have a finite intersection. For simplicity, we say that a single party Bob has access to the decoding set and another party Eve has access to the malicious set, and both Eve and Bob have access to the pre-shared entanglement with Alice. The goal of the task is for Alice to communicate classical information reliably to Bob and securely against Eve, and Bob can take advantage of pre-shared entanglement with Alice. In this framework, we establish a lower bound on the one-shot EA private capacity. When there exists a quantum channel mapping the state of the decoding set to the state of the malicious set, such a broadcast channel is said to be degraded. We establish an upper bound on the one-shot EA private capacity in terms of smoothed min- and max-entropies for such channels. In the limit of a large number of independent channel uses, we prove that the EA private capacity of a degraded quantum broadcast channel is given by a single-letter formula. Finally, we consider two specific examples of degraded broadcast channels and find their capacities. In the first example, we consider the scenario in which one part of Bob’s laboratory is compromised by Eve. We show that the capacity for this protocol is given by the conditional quantum mutual information of a quantum broadcast channel, and so we thus provide an operational interpretation to the dynamic counterpart of the conditional quantum mutual information. In the second example, Eve and Bob have access to mutually exclusive sets of outputs of a broadcast channel.

arXiv:1803.03976•Journal of Physics A Mathematical and Theoretical•Jul 26, 2018•29 citations

Tight Analysis of Convex Splitting with Applications in Quantum Information Theory

Hao–Chung Cheng, Li Gao

Convex splitting is a powerful technique in quantum information theory that applies to proving the achievability of numerous information-processing protocols. In this paper, we establish a one-shot error exponent and a one-shot strong converse for convex splitting with trace distance as the error criterion. Our result exhibits the following features. Firstly, the derived error exponent is given in terms of a generalized sandwiched Rényi mutual information which is additive for product states. Hence, our bound directly applies to the n-fold product scenario for any blocklength. Secondly, the one-shot error bound is meaningful in the sense that the error exponent is all positive on the achievable rate region. This leads to new one-shot exponent results in various tasks in quantum information theory. Conversely, we prove a one-shot strong converse to demonstrate that the convex splitting error converges to one exponentially fast at rates outside the achievable rate region. We also establish an optimal one-shot characterization of the sample complexity for convex splitting, which yields matched second-order asymptotics, showing the tightness of our result. This then leads to a stronger one-shot analysis in quantum information theory.Our technique is to introduce a unified functional analytic approach using Kosaki’s noncommutative weighted Lpnorm. Our results then follow from tight analysis based on such a norm framework.The full version of the manuscript can be found at [arXiv:2304.12055] [1].

IEEE International Symposium on Information Theory (ISIT)•Jun 25, 2023•6 citations

One-shot inner bounds for quantum multiple-access one-time pad

CHENG Feiran, LIU Xiaoming, Zhengjun Xi

We consider the one-shot coding of multiple access channels one-time pad. Suppose that the senders and the receiver share an entangled state in the multi-party systems. Using the position-based coding, each sender encodes the classical messages on their systems, then they transmit their systems over the ideal quantum channels. The receiver applies a decoding operator to all the systems in order to figure out which message was transmitted with respect to the quantum joint typicality lemma. We provide the upper bound of the information leakage by the convex split lemma. Combining quantum max-information with quantum hypothesis testing mutual information, we give the inner bound of the achievable rate.

Zhongguo kexue. Wulixue Lixue Tianwenxue•Feb 27, 2025•0 citations
We show that the communication cost of quantum broadcast channel simulation under free entanglement assistance between the sender and the receivers is asymptotically characterized by an efficiently computable single-letter formula in terms of the channel's multipartite mutual information. Our core contribution is a new one-shot achievability result for multipartite quantum state splitting via multipartite convex splitting. As part of this, we face a general instance of the quantum joint typicality problem with arbitrarily overlapping marginals. The crucial technical ingredient to sidestep this difficulty is a conceptually novel multipartite mean-zero decomposition lemma, together with employing recently introduced complex interpolation techniques for sandwiched Rényi divergences. Moreover, we establish an exponential convergence of the simulation error when the communication costs are within the interior of the capacity region. As the costs approach the boundary of the capacity region moderately quickly, we show that the error still vanishes asymptotically.
We show that the communication cost of quantum broadcast channel simulation under free entanglement assistance between the sender and the receivers is asymptotically characterized by an efficiently computable single-letter formula in terms of the channel's multipartite mutual information. Our core contribution is a new one-shot achievability result for multipartite quantum state splitting via multipartite convex splitting. As part of this, we face a general instance of the quantum joint typicality problem with arbitrarily overlapping marginals. The crucial technical ingredient to sidestep this difficulty is a conceptually novel multipartite mean-zero decomposition lemma, together with employing recently introduced complex interpolation techniques for sandwiched Rényi divergences. Moreover, we establish an exponential convergence of the simulation error when the communication costs are within the interior of the capacity region. As the costs approach the boundary of the capacity region moderately quickly, we show that the error still vanishes asymptotically.
Capacity of a quantum channel characterizes the limits of reliable communication through a noisy quantum channel. This fundamental information theoretic question is very well studied specially in the setting of many independent uses of the channel. An important scenario, both from practical and conceptual point of view, is when the channel can be used only once. This is known as the one-shot channel coding problem. We provide a tight characterization of the one-shot entanglement assisted classical capacity of a quantum channel. We arrive at our result by introducing a simple decoding technique which we refer to as position-based decoding. We also consider two other important quantum network scenarios: quantum channel with a jammer and quantum broadcast channel. For these problems, we use the recently introduced convex split technique [1] in addition to position based decoding. Our approach exhibits that the simultaneous use of these two techniques provides a uniform and conceptually simple framework for designing communication protocols for quantum networks.
A capacity of a quantum channel characterizes the limits of reliable communication through a noisy quantum channel. This fundamental information-theoretic question is very well studied specially in the setting of many independent uses of the channel. An important scenario, both from practical and conceptual point of view, is when the channel can be used only once. This is known as the one-shot channel coding problem. We provide a tight characterization of the one-shot entanglement-assisted classical capacity of a quantum channel. We arrive at our result by introducing a simple decoding technique which we refer to as position-based decoding. We also consider two other important quantum network scenarios: quantum channel with a jammer and quantum broadcast channel. For these problems, we use the recently introduced convex split technique in addition to position-based decoding. Our approach exhibits that the simultaneous use of these two techniques provides a uniform and conceptually simple framework for designing communication protocols for quantum networks.
Abstract We consider entanglement-assisted (EA) private communication over a quantum broadcast channel, in which there is a single sender and multiple receivers. We divide the receivers into two sets: the decoding set and the malicious set. The decoding set and the malicious set can either be disjoint or can have a finite intersection. For simplicity, we say that a single party Bob has access to the decoding set and another party Eve has access to the malicious set, and both Eve and Bob have access to the pre-shared entanglement with Alice. The goal of the task is for Alice to communicate classical information reliably to Bob and securely against Eve, and Bob can take advantage of pre-shared entanglement with Alice. In this framework, we establish a lower bound on the one-shot EA private capacity. When there exists a quantum channel mapping the state of the decoding set to the state of the malicious set, such a broadcast channel is said to be degraded. We establish an upper bound on the one-shot EA private capacity in terms of smoothed min- and max-entropies for such channels. In the limit of a large number of independent channel uses, we prove that the EA private capacity of a degraded quantum broadcast channel is given by a single-letter formula. Finally, we consider two specific examples of degraded broadcast channels and find their capacities. In the first example, we consider the scenario in which one part of Bob’s laboratory is compromised by Eve. We show that the capacity for this protocol is given by the conditional quantum mutual information of a quantum broadcast channel, and so we thus provide an operational interpretation to the dynamic counterpart of the conditional quantum mutual information. In the second example, Eve and Bob have access to mutually exclusive sets of outputs of a broadcast channel.
Convex splitting is a powerful technique in quantum information theory that applies to proving the achievability of numerous information-processing protocols. In this paper, we establish a one-shot error exponent and a one-shot strong converse for convex splitting with trace distance as the error criterion. Our result exhibits the following features. Firstly, the derived error exponent is given in terms of a generalized sandwiched Rényi mutual information which is additive for product states. Hence, our bound directly applies to the n-fold product scenario for any blocklength. Secondly, the one-shot error bound is meaningful in the sense that the error exponent is all positive on the achievable rate region. This leads to new one-shot exponent results in various tasks in quantum information theory. Conversely, we prove a one-shot strong converse to demonstrate that the convex splitting error converges to one exponentially fast at rates outside the achievable rate region. We also establish an optimal one-shot characterization of the sample complexity for convex splitting, which yields matched second-order asymptotics, showing the tightness of our result. This then leads to a stronger one-shot analysis in quantum information theory.Our technique is to introduce a unified functional analytic approach using Kosaki’s noncommutative weighted Lpnorm. Our results then follow from tight analysis based on such a norm framework.The full version of the manuscript can be found at [arXiv:2304.12055] [1].
We consider the one-shot coding of multiple access channels one-time pad. Suppose that the senders and the receiver share an entangled state in the multi-party systems. Using the position-based coding, each sender encodes the classical messages on their systems, then they transmit their systems over the ideal quantum channels. The receiver applies a decoding operator to all the systems in order to figure out which message was transmitted with respect to the quantum joint typicality lemma. We provide the upper bound of the information leakage by the convex split lemma. Combining quantum max-information with quantum hypothesis testing mutual information, we give the inner bound of the achievable rate.