Multi-observable Uncertainty Equality based on the sum of standard deviations in the qubit system

Abstract

We construct a multi-observable uncertainty equality as well as an inequality based on the sum of standard deviations in the qubit system. The obtained equality indicates that the uncertainty relation can be expressed more accurately, and also can be used to detect the mixedness of the system. Meanwhile, the new uncertainty inequality can provide a tighter lower bound, and the tightness can be maintained at a high level even in an open system. Furthermore, the deficiency of the uncertainty relation, that the lower bound of the product form uncertainty relations can be null even for two incompatible observables, can be completely fixed by the new uncertainty relation.

References in corpus (5)

• The uncertainty principle determines the non-locality of quantum mechanics
• Stronger uncertainty relations for the sum of variances
• Quantum-memory-assisted entropic uncertainty principle under noise
• Detecting mixedness of qutrit systems using the uncertainty relation
• Implications and applications of the variance-based uncertainty equalities