Uncertainty relation revisited from quantum estimation theory

2010/10/31 by Yu Watanabe, Takahiro Sagawa, Masahito Ueda · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Computer science #Hilbert space #Mathematics #Observable #Open quantum system #POVM #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum operation #Quantum state #Relation (database) #SIC-POVM #Statistical physics #Theoretical physics #Uncertainty principle #quant-ph

paper · pdf · doi:10.1103/physreva.84.042121

manuscript including 4 pages and 2 figures

arxiv created 2011/04/06 · openalex publication_date 2011/10/28 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We use quantum estimation theory to formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two noncommuting observables satisfy Heisenberg-type uncertainty relation, find the achievable bound, and propose a strategy to achieve it.

Citations

• A generalized inverse for matrices
• The Uncertainty Principle
• Quantum detection and estimation theory
• �ber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik
• Complementarity and uncertainty in Mach–Zehnder interferometry and beyond
• Can Quantum-Mechanical Description of Physical Reality be Considered Complete?

Cited by

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• Colloquium: Quantum root-mean-square error and measurement uncertainty relations
• Hardy's paradox and measurement-disturbance relations
• Effects of partial measurements on quantum resources and quantum Fisher information of a teleported state in a relativistic scenario