Variance-based uncertainty relations

Details Variance-based uncertainty relations Variance-based uncertainty relations

2010-12-14

arxiv.org/abs/1012.3105v1

Physics

Quantum Physics

C191 course project at UC Berkeley

Scientific paper

It is hard to overestimate the fundamental importance of uncertainty relations in quantum mechanics. In this work, I propose state-independent variance-based uncertainty relations for arbitrary observables in both finite and infinite dimensional spaces. We recover the Heisenberg uncertainty principle as a special case. By studying examples, we find that the lower bounds provided by our new uncertainty relations are optimal or near-optimal. I illustrate the uses of our new uncertainty relations by showing that they eliminate one common obstacle in a sequence of well-known works in entanglement detection, and thus make these works much easier to access in applications.

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