Stronger Schrödinger-like uncertainty relations

Abstract

Uncertainty relation is one of the fundamental building blocks of quantum theory. Nevertheless, the traditional uncertainty relations do not fully capture the concept of incompatible observables. Here we present a stronger Schrödinger-like uncertainty relation, which is stronger than the relation recently derived by L. Maccone and A. K. Pati [Phys. Rev. Lett. 113 (2014) 260401]. Furthermore, we give an additive uncertainty relation which holds for three incompatible observables, which is stronger than the relation newly obtained by S. Kechrimparis and S. Weigert [Phys. Rev. A 90 (2014) 062118] and the simple extension of the Schrödinger uncertainty relation.

Experimental investigation of multi-observable uncertainty relations

“…With the qubit-system experiments, the results verify the validity of these uncertainty relations, and the superiority of our proposed uncertainty relations [17,33] is also exhibited.…”

“…After these, more state-dependent [15][16][17][18][19][20] and state-independent [21][22][23][24][25][26] lower bounds of uncertainty relations were also obtained. The generalization and improvement mainly focused on the uncertainty relation capable of dealing with more than two incompatible observables, i.e., the Heisenberg-type uncertainty relation for three canonical observables [27], uncertainty relations for angular momentum [28], and arbitrary incompatible observables [17]. There are also uncertainty relations with even more incompatible observables formulated in products [29,30] or sums [31][32][33] of variances.…”

A Stronger Multi-observable Uncertainty Relation

“…which is equal to the relation (7). It is easy to see that the right-hand side of (16) is greater than the right-hand side of (14). Hence, the relation (7) is stronger than the relation (11).…”

Tight N-observable uncertainty relations and their experimental demonstrations

“…In the literature, there exists another kind of uncertainty relation in summed form for S i (i = 1, 2, 3) 41 , a special case of (26) in the reference 18 , which has been testified in an experiment with a negatively charged nitrogen-vacancy centre in diamond,…”