Converse bounds for quantum hypothesis exclusion: A divergence-radius approach
Cornell University(康奈尔大学);Indian Institute of Technology (Indian School of Mines)(印度理工学院(印度矿业学院));HUN-REN Alfréd Rényi Institute of Mathematics(匈牙利研究与教育网络阿尔弗雷德·雷尼数学研究所);Budapest University of Technology and Economics(布达佩斯技术与经济大学)
Kaiyuan Ji, Hemant K. Mishra, Milán Mosonyi, Mark M. Wilde
备注:
7 pages, 1 figure
发表信息:
2025 IEEE International Symposium on Information Theory (ISIT), Ann Arbor, MI, USA, 2025, pp. 1-6
假设排除是一项信息论任务,实验者旨在从有限个已知候选假设中排除一个错误假设,当且仅当被排除的假设是真实情况时发生错误。对于量子态排除和量子信道排除任务——其中假设分别由量子态和量子信道表示——当前作者在最近的工作[Ji et al., arXiv:2407.13728 (2024)]中建立了渐近错误指数的可计算上界,其推导基于非渐近分析。在本篇作为先前工作姊妹篇的论文中,我们为量子态和信道排除的渐近错误指数提供了相同的上界,但使用了与先前工作不同的概念性方法。具体地,我们将非对称二元假设检验的强逆结果应用于区分任意一个“虚拟”假设与每个相关候选假设。通过几何启发式论证,这导致了以散度半径表示的所需上界。
英文摘要:
Hypothesis exclusion is an information-theoretic task in which an experimenter aims at ruling out a false hypothesis from a finite set of known candidates, and an error occurs if and only if the hypothesis being ruled out is the ground truth. For the tasks of quantum state exclusion and quantum channel exclusion -- where hypotheses are represented by quantum states and quantum channels, respectively -- efficiently computable upper bounds on the asymptotic error exponents were established in a recent work of the current authors [Ji et al., arXiv:2407.13728 (2024)], where the derivation was based on nonasymptotic analysis. In this companion paper of our previous work, we provide alternative proofs for the same upper bounds on the asymptotic error exponents of quantum state and channel exclusion, but using a conceptually different approach from the one adopted in the previous work. Specifically, we apply strong converse results for asymmetric binary hypothesis testing to distinguishing an arbitrary ``dummy'' hypothesis from each of the concerned candidates. This leads to the desired upper bounds in terms of divergence radii via a geometrically inspired argument.
Barycentric bounds on the error exponents of quantum hypothesis exclusion
Cornell University(康奈尔大学);Indian Institute of Technology (Indian School of Mines) Dhanbad(印度理工学院(印度矿业学院)丹巴德分校);HUN-REN Alfréd Rényi Institute of Mathematics(匈牙利研究与教育网络阿尔弗雷德·雷尼数学研究所);Budapest University of Technology and Economics(布达佩斯技术与经济大学)
Strong converse exponent for classical-quantum channel coding
我们确定了经典量子信道编码的确切强逆指数,对于每一个速率以上的Holevo容量。我们的指数形式是Arimoto的精确模拟,作为参数α>1的Renyi容量的变换给出。重要的是要注意,与经典情况不同,有许多不等价的方法来定义状态的Renyi散度,从而定义通道的Renyi容量。我们的指数是根据与最近在[Müller-Lennert,Dupuis,Szehr,Fehr and Tomamichel,J. Math.Phys.54,122203,(2013)]和[Wilde,Winter,Yang,Commun. 331,(2014)]。我们的结果增加了越来越多的证据表明,这个新的版本是强逆问题的目的的自然定义。
Continuity of Regularized Channel Rényi Divergences
Zyphra;QICI Quantum Information and Computation Initiative, School of Computing and Data Science, The University of Hong Kong(量子信息与计算倡议,计算与数据科学学院,香港大学)
Quantum Channel Stein's Lemma with an Exponential Strong Converse
Institute of Software, Chinese Academy of Sciences(中国科学院软件研究所);University of Chinese Academy of Sciences(中国科学院大学);Department of Computer Science and Technology, Tsinghua University(清华大学计算机科学与技术系)
Universality Sacrifices Reliability in Classical-Quantum Channel Coding
The University of Tokyo(东京大学);RIKEN Center for Quantum Computing (RQC)(理化学研究所量子计算中心);The Chinese University of Hong Kong, Shenzhen(香港中文大学(深圳));International Quantum Academy(国际量子学院);Nagoya University(名古屋大学);National Taiwan University(台湾大学);National Center for Theoretical Sciences, Taiwan(台湾理论科学中心);Hon Hai (Foxconn) Quantum Computing Center(鸿海(富士康)量子计算中心)
RIKEN Hakubi Research Team, RIKEN Pioneering Research Institute (PRI) and RIKEN Center for Quantum Computing (RQC)(RIKEN 博慧研究团队、RIKEN 先锋研究所(PRI)和 RIKEN 量子计算中心);Department of Electrical and Computer Engineering, National University of Singapore(新加坡国立大学电气与计算机工程系);Centre for Quantum Technologies, National University of Singapore(新加坡国立大学量子技术中心)
Quantum Channel Stein Theorem beyond Definite Causal Order
QudeLeap Research, Shanghai 200030, China(科跃研究);Thrust of Artificial Intelligence, Information Hub,The Hong Kong University of Science and Technology (Guangzhou), Guangzhou 511453, China(香港科技大学(广州)人工智能 thrust 信息枢纽)
The Chinese University of Hong Kong, Shenzhen(香港中文大学(深圳));RWTH Aachen University(亚琛工业大学);City University of Hong Kong (Dongguan)(香港城市大学(东莞));National Taiwan University(台湾大学);National Center for Theoretical Sciences(国家理论科学中心);Hon Hai (Foxconn) Quantum Computing Center(鸿海(富士康)量子计算中心);Wuhan University(武汉大学);Wuhan Institute of Quantum Science and Technology(武汉量子技术研究院);International Quantum Academy(国际量子学院);Nagoya University(名古屋大学)
On the near-optimality of one-shot classical communication over quantum channels
本文研究了在几种网络场景中,经典信息通过量子信道的一次性传输问题。我们考虑了点到点量子信道、量子多址信道、有态量子信道和量子广播信道的纠缠辅助和无辅助情况。我们表明,可以使用先前工作中引入的基于位置的解码策略[Anshu,Jain和Warsi,2017]来近似最优地表征可以在这些场景中传输的通信量。在这个过程中,我们提供了一个简短而基本的证明,证明了纠缠辅助的量子信道编码在量子假设检验发散方面的逆(在[Matthews and Wehner,2014]中获得)。我们的证明具有额外的效用,它自然地扩展到上面提到的各种网络场景。此外,我们的可并行性结果都不需要同时解码策略,这是量子香农理论中一个重要的开放问题。