Experimental Test of Tight State-Independent Preparation Uncertainty Relations for Qubits

Abstract

The well-known Robertson-Schroedinger uncertainty relations miss an irreducible lower bound. This is widely attributed to the lower bound's state-dependence. Therefore, Abbott \emph{et al.} introduced a general approach to derive tight state-independent uncertainty relations for qubit measurements [Mathematics 4, 8 (2016)]. The relations are expressed in two measures of uncertainty, which are standard deviation and entropy, both functions of the expectation value. Here, we present a neutron optical test of the tight state-independent preparation uncertainty relations for non-commuting Pauli spin observables with mixed spin states. The final results, obtained in a polarimetric experiment, reproduce the theoretical predictions evidently for arbitrary initial states of variable degree of polarization.

8 pages, 8 figures

References in corpus (4)

• Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory
• Improved bounds in entropic uncertainty relations
• State-independent Uncertainty Relations and Entanglement Detection in Noisy Systems
• Error-Disturbance Trade-off in Sequential Quantum Measurements

Cited by in corpus (5)

• Tests of Fundamental Quantum Mechanics and Dark Interactions with Low Energy Neutrons -- Extended Version
• Uncertainty regions of observables and state-independent uncertainty relations
• Fundamental Neutron Physics: a White Paper on Progress and Prospects in the US
• Probability density functions of quantum mechanical observable uncertainties
• Experimental test of the majorization uncertainty relation with mixed states