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A remark on the uncertainty principle for Hilbertian basis

Jean Bourgain

Journal of Functional AnalysisJul 1, 198843 citations

The Uncertainty Principle Determines the Nonlocality of Quantum Mechanics

Jonathan Oppenheim, Stephanie Wehner

Two central concepts of quantum mechanics are Heisenberg's uncertainty principle and a subtle form of nonlocality that Einstein famously called "spooky action at a distance." These two fundamental features have thus far been distinct concepts. We show that they are inextricably and quantitatively linked: Quantum mechanics cannot be more nonlocal with measurements that respect the uncertainty principle. In fact, the link between uncertainty and nonlocality holds for all physical theories. More specifically, the degree of nonlocality of any theory is determined by two factors: the strength of the uncertainty principle and the strength of a property called "steering," which determines which states can be prepared at one location given a measurement at another.Two central concepts of quantum mechanics are Heisenberg's uncertainty principle and a subtle form of nonlocality that Einstein famously called "spooky action at a distance." These two fundamental features have thus far been distinct concepts. We show that they are inextricably and quantitatively linked: Quantum mechanics cannot be more nonlocal with measurements that respect the uncertainty principle. In fact, the link between uncertainty and nonlocality holds for all physical theories. More specifically, the degree of nonlocality of any theory is determined by two factors: the strength of the uncertainty principle and the strength of a property called "steering," which determines which states can be prepared at one location given a measurement at another.

arXiv:1004.2507ScienceNov 18, 2010366 citations

Does the uncertainty relation determine the quantum state?

Olga V. Man’ko, Vladimir I. Man’ko, Giuseppe Marmo +2 more

arXiv:quant-ph/0604044Physics Letters AMay 23, 200625 citations

Quantum entanglement with generalized uncertainty principle

DaeKil Park

We explore how the quantum entanglement is modified in the generalized uncertainty principle (GUP)-corrected quantum mechanics by introducing the coupled harmonic oscillator system. Constructing the ground state ρ0 and its reduced substate ρA=TrBρ0, we compute two entanglement measures of ρ0, i.e. EEoF(ρ0)=Svon(ρA) and Eγ(ρ0)=Sγ(ρA), where Svon and Sγ are the von Neumann and Rényi entropies, up to the first order of the GUP parameter α. It is shown that Eγ(ρ0) increases with increasing α when γ=2,3,⋯. The remarkable fact is that EEoF(ρ0) does not have first-order of α. Based on there results we conjecture that Eγ(ρ0) increases or decreases with increasing α when γ>1 or γ<1 respectively for nonnegative real γ.We explore how the quantum entanglement is modified in the generalized uncertainty principle (GUP)-corrected quantum mechanics by introducing the coupled harmonic oscillator system. Constructing the ground state ρ0 and its reduced substate ρA=TrBρ0, we compute two entanglement measures of ρ0, i.e. EEoF(ρ0)=Svon(ρA) and Eγ(ρ0)=Sγ(ρA), where Svon and Sγ are the von Neumann and Rényi entropies, up to the first order of the GUP parameter α. It is shown that Eγ(ρ0) increases with increasing α when γ=2,3,⋯. The remarkable fact is that EEoF(ρ0) does not have first-order of α. Based on there results we conjecture that Eγ(ρ0) increases or decreases with increasing α when γ>1 or γ<1 respectively for nonnegative real γ.

arXiv:2203.06557Nuclear Physics BMar 17, 20226 citations

Some remarks on the determination of quantum states by measurements

Werner Stulpe, Matthias Singer

Foundations of Physics LettersApr 1, 199019 citations

What We Can Say about the Uncertainty Relation in Quantum Measurement

Wonmin Son

Physics and High TechnologyMay 31, 20130 citations

Remarks on the fact that the uncertainty principle does not determine the quantum state

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