Experimental Demonstration of Uncertainty Relations for the Triple Components of Angular Momentum

Abstract

The uncertainty principle is considered to be one of the most striking features in quantum mechanics. In the textbook literature, uncertainty relations usually refer to the preparation uncertainty which imposes a limitation on the spread of measurement outcomes for a pair of non-commuting observables. In this work, we study the preparation uncertainty for the angular momentum, especially in the spin-1/2 representation. We derive uncertainty relations encompassing the triple components of angular momentum, and show that compared with the relations involving only two components, a triple constant $2/\sqrt{3}$ often arises. Intriguingly, this constant is the same for the position and momentum case. Experimental verification is carried out on a single spin in diamond, and the results confirm the triple constant in a wide range of experimental parameters.

References in corpus (14)

• High-fidelity projective readout of a solid-state spin quantum register
• Heisenberg's Uncertainty Principle
• Dynamic polarization of single nuclear spins by optical pumping of NV color centers in diamond at room temperature
• Decoherence-protected quantum gates for a hybrid solid-state spin register
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• Formulation of the uncertainty relations in terms of the Renyi entropies
• Single Spin Magnetic Resonance
• Sum Uncertainty Relation in Quantum Theory
• Rényi entropy uncertainty relation for successive projective measurements
• Higher entropic uncertainty relations for anti-commuting observables
• Heisenberg Uncertainty Relation for Three Canonical Observables
• Sum uncertainty relations based on Wigner-Yanase skew information
• Variance-based uncertainty relations for incompatible observables
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Cited by in corpus (25)

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• Uncertainty Relations Based on Modified Wigner-Yanase-Dyson Skew Information
• State independent uncertainty relations from eigenvalue minimization
• Tighter sum uncertainty relations via variance and Wigner-Yanase skew information for N incompatible observables
• Optimal approximations of available states and a triple uncertainty relation
• Complete Optimal Convex Approximations of Qubit States under $B_2$ Distance
• Uncertainty relation based on Wigner-Yanase-Dyson skew information with quantum memory
• Quantum, noncommutative and MOND corrections to the entropic law of gravitation
• Experimental investigation of the uncertainty relations with coherent light
• Optical signatures of Mott-superfluid transition in nitrogen-vacancy centers coupled to photonic crystal cavities
• Parameterized Multi-observable Sum Uncertainty Relations
• Optimizing incompatible triple quantum measurements
• Strong Majorization Uncertainty Relations: Theory and Experiment
• A note on Wigner-Yanase skew information-based uncertainty of quantum channels
• Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems
• Experimental test of the majorization uncertainty relation with mixed states
• A Note on Hierarchy of Quantum Measurement Incompatibilities
• Quantum speed limit time in a magnetic resonance
• Uncertainty relations in the product form
• Single-qubit measurement of Heisenberg uncertainty lower bounds for three incompatible observables
• Observing tight triple uncertainty relations in two-qubit systems
• Identifying the $3$-qubit $W$ state with quantum uncertainty relation
• Quantum Uncertainty and Entropy