Optimal joint measurements of complementary observables by a single trapped ion

Abstract

The uncertainty relations, pioneered by Werner Heisenberg nearly 90 years ago, set a fundamental limitation on the joint measurability of complementary observables. This limitation has long been a subject of debate, which has been reignited recently due to new proposed forms of measurement uncertainty relations. The present work is associated with a new error trade-off relation for compatible observables approximating two incompatible observables, in keeping with the spirit of Heisenberg's original ideas of 1927. We report the first \textsl{direct} test and confirmation of the tight bounds prescribed by such an error trade-off relation, based on an experimental realisation of optimal joint measurements of complementary observables using a single ultracold ${}^{40}C{a}^{+}$ ion trapped in a harmonic potential. Our work provides a prototypical determination of ultimate joint measurement error bounds with potential applications in quantum information science for high-precision measurement and information security.

arXiv comment14 pages

References in corpus (30)

• Quantum entanglement
• Quantum-enhanced measurements: beating the standard quantum limit
• Entanglement detection
• The Uncertainty Principle in the Presence of Quantum Memory
• Heisenberg's Uncertainty Principle
• Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement
• Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
• The uncertainty principle determines the non-locality of quantum mechanics
• Violation of Heisenberg's Measurement-Disturbance Relationship by Weak Measurements
• Experimental demonstration of a universally valid error-disturbance uncertainty relation in spin-measurements
• Uncertainty Relations for Noise and Disturbance in Generalized Quantum Measurements
• Proof of Heisenberg's error-disturbance relation
• Quantum root-mean-square error and measurement uncertainty relations
• Measurements incompatible in Quantum Theory cannot be measured jointly in any other local theory
• One-to-one mapping between steering and joint measurability problems
• How well can one jointly measure two incompatible observables on a given quantum state?
• Prior information: how to circumvent the standard joint-measurement uncertainty relation
• Experimental Test of Error-Disturbance Uncertainty Relations by Weak Measurement
• Joint quantum measurements with minimum uncertainty
• Heisenberg uncertainty for qubit measurements
• Uncertainty Relations for Joint Measurements of Noncommuting Observables
• Violation of Heisenberg's error-disturbance uncertainty relation in neutron spin measurements
• Measuring measurement--disturbance relationships with weak values
• Experimental test of universal complementarity relations
• Experimental test of Heisenberg's measurement uncertainty relation based on statistical distances
• The Link between Entropic Uncertainty and Nonlocality
• Correcting detection error in quantum computation and state engineering through data processing
• A universally valid Heisenberg uncertainty relation
• Direct tests of measurement uncertainty relations: what it takes
• Optimal joint measurement of two observables of a qubit

Cited by in corpus (4)

• Measurement uncertainty relations: characterising optimal error bounds for qubits
• Experimental test of error-disturbance uncertainty relation with continuous variables
• Single-qubit measurement of Heisenberg uncertainty lower bounds for three incompatible observables
• Optimal simultaneous measurements of incompatible observables of a single photon