Tight N-observable uncertainty relations and their experimental demonstrations

Abstract

The uncertainty relation, as one of the fundamental principles of quantum physics, captures the incompatibility of noncommuting observables in the preparation of quantum states. In this work, we derive two strong and universal uncertainty relations for N ( N ≥ 2) observables with discrete and bounded spectra, one in multiplicative form and the other in additive form. To verify their validity, for illustration, we implement in the spin-1/2 system an experiment with single-photon measurement. The experimental results exhibit the validity and robustness of these uncertainty relations, and indicate the existence of stringent lower bounds.

Tighter uncertainty relations based on Wigner-Yanase skew information for observables and channels

“…Uncertainty relations for general multiple observables have been further studied either in product form [30,31] or sum form of variances [32][33][34][35][36].…”

Minimal Products of Coordinate and Momentum Uncertainties of High Orders: Significant and Weak High-Order Squeezing

“…Or, how to generalize our results to the case of mixed quantum states with the fixed value of quantum purity (see, e.g., studies [ 85 , 86 ] for the second-order uncertainty products)? It would be interesting to verify the new relations in experiments, for example, using the scheme of measuring high-order moments of canonical variables proposed in [ 87 ] (some experiments related to uncertainty relations for the second-order moments were performed in [ 88 ]; experimental verifications of the uncertainty relations for the angular momentum operator and other quantum systems in finite-dimensional Hilbert spaces were reported in [ 89 , 90 , 91 , 92 , 93 , 94 ]). Other interesting areas, where high-order uncertainty relations can be useful, include entanglement, steerability, and Bell nonlocality (see, e.g., studies [ 95 , 96 , 97 ]).…”

Experimental test of the majorization uncertainty relation with mixed states

“…Existing tests of the uncertainty relations mainly focus on the pure systems. The variance-based uncertainty relations have been tested with single quantum of SPDC photons [14][15][16][17][18] and nitrogen-vacancy (NV) center system [19]. The entropic uncertainty relation for multiple observables was also investigated in the NV center system [20].…”