Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Institutions: National Institute of Standards and Technology, Joint Center for Quantum Information and Computer Science, Joint Quantum Institute, University of Maryland, College Park, Agency for Science, Technology and Research, Centre for Quantum Technologies, National University of Singapore, University of Technology Sydney, Australian National University, University of Electro-Communications
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, U.S. Department of Energy, National Research Foundation Singapore, Defense Advanced Research Projects Agency, Office of Science, Multidisciplinary University Research Initiative, Japan Society for the Promotion of Science, Office of Naval Research, Advanced Scientific Computing Research, Exploratory Research for Advanced Technology, Air Force Office of Scientific Research
OpenAlex ID: W7214923389