判定多参数量子Fisher信息的可达性是NP-难的
Deciding the Attainability of the Multiparameter Quantum Fisher Information is NP-Hard
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中文总结 AI 辅助
本文证明判定多参数量子Fisher信息的可达性为NP-难问题，表明该长期难题源于根本计算障碍，除非P=NP，否则不存在高效充要判据。
中文摘要 AI 辅助
量子Fisher信息（QFI）为同时估计多个参数时可达的精度设定了基本界限。在某些情况下，各自最优测量之间的不相容性可能意味着由QFI设定的精度极限无法达到。在某些特殊情形下，包括纯态和满秩态，QFI设定的精度极限何时可被饱和的精确条件已知。然而，关于通过对量子态的单个副本进行测量时QFI可达性的一般条件长期以来一直未被找到。事实上，这最近被[P. Horodecki等人，PRX Quantum 3, 010101 (2022)]列为量子信息理论中的五个问题之一。在这项工作中，我们证明了即使对于受限的实值、常数秩量子模型，通过单个测量判定精确可达性是NP-难的。我们证明的源问题是判定给定二分密度矩阵是否可分的NP-难问题。我们的结果表明，长期难以获得QFI可达性的一般条件反映了根本的计算障碍，而不仅仅是现有数学技术的局限：除非P=NP，否则一般不存在可有效计算的充要判据。
英文摘要
The quantum Fisher information (QFI) sets a fundamental bound on the attainable precision when estimating multiple parameters simultaneously. Incompatibility among the individually optimal measurements can, in some cases, imply that the precision limit set by the QFI is not attainable. In certain special cases, including pure states and full-rank states, the exact conditions for when the precision limit set by the QFI can be saturated are known. However, general conditions for the attainability of the QFI with measurements on individual copies of the quantum state have long been sought. Indeed, this was recently stated as one of the five problems in quantum information theory highlighted by [P. Horodecki et al, PRX Quantum 3, 010101 (2022)]. In this work we prove that exact attainability with individual measurements is NP-hard to decide, even for a restricted set of real, constant-rank quantum models. The source problem for our proof is the NP-hard problem of deciding whether a given bipartite density matrix is separable or not. Our result shows that the longstanding difficulty in obtaining general conditions for QFI attainability reflects a fundamental computational obstruction, rather than merely a limitation of existing mathematical techniques: unless P=NP, no efficiently computable necessary-and-sufficient criterion can exist in general.
发表机构
- Joint Quantum Institute, NIST/University of Maryland（美国国家标准与技术研究院/马里兰大学联合量子研究所）
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（美国国家标准与技术研究院/马里兰大学量子信息与计算科学联合中心）
- Centre for Quantum Technologies (CQT), National University of Singapore（新加坡国立大学量子技术中心）
- Quantum Innovation Centre (Q.InC), Agency for Science, Technology and Research (A*STAR)（科学技术研究局量子创新中心）
- UMIACS, University of Maryland（马里兰大学计算机科学与信息系统多学科研究中心）
- Center for Quantum Software and Innovation, University of Technology Sydney（悉尼科技大学量子软件与创新中心）
- Department of Quantum Science and Technology, Research School of Physics, The Australian National University（澳大利亚国立大学物理研究学院量子科学与技术系）
- Axiomatic AI, Inc.（公理人工智能公司）
- Graduate School of Informatics and Engineering, The University of Electro-Communications（电气通信大学信息工程学研究生院）
机构由 AI 辅助整理，请以论文原文为准。
