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arXiv · 1705.01385

Optimal joint measurements of complementary observables by a single trapped ion

T. P. Xiong·L. L. Yan·Z. H. Ma·F. Zhou·L. Chen·W. L. Yang·M. Feng·P. Busch
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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 $^{40}Ca^{+}$ 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.

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T. P. Xiong, L. L. Yan, Z. H. Ma, F. Zhou, L. Chen, W. L. Yang, M. Feng, P. Busch. 2017-05-03. Optimal joint measurements of complementary observables by a single trapped ion. https://doi.org/10.1088/1367-2630%2Faa70a5

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