2014/07/31 by Spiros Kechrimparis, Stefan Weigert · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Computer science #Heisenberg picture #Mathematics #Momentum (technical analysis) #Noncommutative and Quantum Gravity Theories #Observable #Physics #Position (finance) #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum state #Relation (database) #Statistical physics #Theoretical physics #Uncertainty principle #quant-ph
paper · pdf · doi:10.1103/physreva.90.062118
published as Phys. Rev. A 90, 062118 (2014) · 5 pages, 2 figures. Material rearranged to match published version
openalex publication_date 2014/12/15 · arxiv created 2014/12/23 · arxiv updated 2014/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Uncertainty relations provide fundamental limits on what can be said about the properties of quantum systems. For a quantum particle, the commutation relation of position and momentum observables entails Heisenberg's uncertainty relation. A third observable is presented which satisfies canonical commutation relations with both position and momentum. The resulting triple of pairwise canonical observables gives rise to a Heisenberg uncertainty relation for the product of three standard deviations. We derive the smallest possible value of this bound and determine the specific squeezed state which saturates the triple uncertainty relation. Quantum optical experiments are proposed to verify our findings.