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 $N(N\ge 2)$ 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.

9 pages, 5 figures. Slightly extended

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• Optimized entropic uncertainty relations for multiple measurements
• Entropic uncertainty relations in Schwarzschild space-time
• Tighter sum uncertainty relations via variance and Wigner-Yanase skew information for N incompatible observables
• Experimental investigation of the uncertainty relations with coherent light
• Uncertainty relations for metric adjusted skew information and Cauchy-Schwarz inequality
• Stronger sum uncertainty relations for non-Hermitian operators
• Experimental test of the majorization uncertainty relation with mixed states
• Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems
• Identifying the $3$-qubit $W$ state with quantum uncertainty relation