Equivalence theorem of uncertainty relations

Abstract

We present an equivalence theorem to unify the two classes of uncertainty relations, i.e., the variance-based ones and the entropic forms, which shows that the entropy of an operator in a quantum system can be built from the variances of a set of commutative operators. That means an uncertainty relation in the language of entropy may be mapped onto a variance-based one, and vice versa. Employing the equivalence theorem, alternative formulations of entropic uncertainty relations stronger than existing ones in the literature are obtained for qubit system, and variance based uncertainty relations for spin systems are reached from the corresponding entropic uncertainty relations.

18 pages, 1 figure; published in J. Phys. A: Math. Theor

References in corpus (6)

• Entanglement detection
• Entropic Uncertainty Relations and their Applications
• The uncertainty principle determines the non-locality of quantum mechanics
• Stronger uncertainty relations for the sum of variances
• Improved bounds in entropic uncertainty relations
• Connection between Measurement Disturbance Relation and Multipartite Quantum Correlation