Protecting weak measurements against systematic errors

Abstract

In this work, we consider the systematic error of quantum metrology by weak measurements under decoherence. We derive the systematic error of maximum likelihood estimation in general to the first-order approximation of a small deviation in the probability distribution, and study the robustness of standard weak measurement and postselected weak measurements against systematic errors. We show that, with a large weak value, the systematic error of a postselected weak measurement when the probe undergoes decoherence can be significantly lower than that of a standard weak measurement. This indicates the advantage of weak value amplification in improving the performance of parameter estimation. We illustrate the results by an exact numerical simulation of decoherence arising from a bosonic mode and compare it to the first-order analytical result we obtain.

9 pages, 3 figures. V2: close to the published version

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Cited by in corpus (16)

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• Error-Mitigated Quantum Metrology via Virtual Purification
• Properties and Applications of the Kirkwood-Dirac Distribution
• Enhanced weak-value amplification via photon recycling
• Weak-value-amplification analysis beyond the AAV limit of weak measurements
• Practical Advantages of Almost-Balanced-Weak-Values Metrological Techniques
• Difference Weak Measurement
• Noise suppression in inverse weak value based phase detection
• Enhancing interferometry using weak value amplification with real weak values
• Gravitational sensing with weak value based optical sensors
• Enhanced on-chip frequency measurement using weak value amplification
• Systematic errors in direct state measurements with quantum controlled measurements
• Quality analysis for precision metrology based on joint weak measurements without discarding readout data
• Multiparameter quantum metrology with postselection measurements