Entropic uncertainty relations in multidimensional position and momentum spaces

2011/01/31 by Yichen Huang · 2 citations
Computer Science · Decision Sciences · Mathematics · Physics and Astronomy · #Algebra over a field #Applied mathematics #Commutator #Conjecture #Economics #Entropic uncertainty #Financial economics #Mathematical economics #Mathematics #Momentum (technical analysis) #Physics #Position (finance) #Probabilistic and Robust Engineering Design #Pure mathematics #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Statistical physics #Uncertainty principle #Variance (accounting) #quant-ph

paper · pdf · doi:10.1103/physreva.83.052124

published as Physical Review A 83, 052124 (2011) · v2: close to the published version

openalex publication_date 2011/05/24 · openalex created_date 2016/06/24 · arxiv created 2021/07/30 · arxiv updated 2021/08/02 · openalex updated_date 2026/08/05

Abstract

Commutator-based entropic uncertainty relations in multidimensional position and momentum spaces are derived, twofold generalizing previous entropic uncertainty relations for one-mode states. They provide optimal lower bounds and imply the multidimensional variance-based uncertainty principle. The article concludes with an open conjecture.

Citations

• Entanglement criteria via concave-function uncertainty relations
• A Mathematical Theory of Communication
• The Uncertainty Principle
• Linear Transformations in Hilbert Space
• Inequalities in Fourier Analysis
• Inseparability Criterion for Continuous Variable Systems
• The Fractional Order Fourier Transform and its Application to Quantum Mechanics
• Peres-Horodecki Separability Criterion for Continuous Variable Systems
• Quantum entanglement
• Entanglement detection

Cited by

• Entropic uncertainty relations and their applications
• Fractional Fourier transform [wikipedia]

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