摘要
Uncertainty and entanglement are both profound and key concepts in quantum theory. For three observables, recent works have revealed the tightest uncertainty constants for both product and summation forms. In this work, we give an alternative proof of the uncertainty relations, as well as a physical interpretation of the uncertainty constants. Our results show that such relations are intimately connected with the distinguishment between separable and entangled states. The uncertainty constant is a critical point whether such a condition of entanglement detection is valid.