"Uncertainty Principle" Extended to Include Biology

В. Г. Нестеренко

Ijaz Durrani

Roy B. Leipnik

R. N. Costa Filho, João Philipe Macedo Braga, Jorge H. de Lira +1 more

A translation operator acting in a space with a diagonal metric is introduced to describe the motion of a particle in a quantum system. We show that the momentum operator and, as a consequence, the uncertainty relation now depend on the metric. It is also shown that, for any metric expanded up to second order, this formalism naturally leads to an extended uncertainty principle (EUP) with a minimum momentum dispersion. The Ehrenfest theorem is modified to include an additional term related to a tidal force arriving from the space curvature introduced by the metric. For one-dimensional systems, we show how to map a harmonic potential to an effective potential in Euclidean space using different metrics.

Yan‐Han Yang, Xin-Zhu Liu, Xing-Zhou Zheng +6 more

Heisenberg's uncertainty principle, coherence, and Bell nonlocality have been individually examined through many experiments. In this Letter, we systematically characterize all of this quantumness in a unified manner. We first construct universal uncertainty relations to reveal intrinsic features of incompatible measurements, which include all the state-independent uncertainties as special cases. We further extend to witness both quantum coherence and Bell nonlocality. We finally perform experiments with unified two-photon states and validate the uncertainty principle, coherence, and Bell nonlocality within experimental error. Our methods for witnessing quantumness are valuable in characterizing quantum correlations in quantum information processing.