An entropic uncertainty principle for positive operator valued measures

DOI10.1007/s11005-011-0543-4zbMath1264.47024arXiv1109.5889OpenAlexW3103699422MaRDI QIDQ454337

Michel Rumin

Publication date: 1 October 2012

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.5889

zbMATH Keywords

entropyhomogeneous spacesuncertainty principlelog-Sobolev inequalitypositive operator valued measure (POVM)

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06) Measures of information, entropy (94A17)

Related Items

Quantum-memory-assisted entropic uncertainty relation in the Heisenberg XXZ spin chain model with external magnetic fields and Dzyaloshinski-Moriya interaction ⋮ Position-momentum uncertainty relations in the presence of quantum memory ⋮ Extended quantum conditional entropy and quantum uncertainty inequalities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Balanced distribution-energy inequalities and related entropy bounds
• On the equality in Jensen's inequality for operator convex functions
• A Schwarz inequality for positive linear maps on C\(^*\)-algebras
• Diamagnetic behavior of sums of Dirichlet eigenvalues
• Estimates for sums of eigenvalues for domains in homogeneous spaces
• Lieb--Thirring type inequalities and Gagliardo--Nirenberg inequalities for systems