The Generalized Uncertainty Principle

Abstract

The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact belongs to the leading order approximation of a generalized uncertainty relation. That is, the leading order linear dependence of observables gives the Heisenberg type of uncertainty relations, while higher order nonlinear dependence may reveal more different and interesting correlation properties. Applications of the generalized uncertainty relation and the high order nonlinear dependence between observables in quantum information science are also discussed.

26 pages, 3 figures; published in Ann. Phys. (Berlin)

References in corpus (3)

• Stronger uncertainty relations for the sum of variances
• Grothendieck's constant and local models for noisy entangled quantum states
• Improved tripartite uncertainty relation with quantum memory

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• Decomposition of tracial positive maps and applications in quantum information
• Uncertainty from the Aharonov-Vaidman Identity
• An Effective Way of Characterizing the Quantum Nonlocality
• Feasibility analysis of a proposed test of quantum gravity via novel optical magnetometry in xenon