Improving the Precision of Weak Measurements by Postselection Measurement

Area of Science:

• Quantum Measurement
• Quantum Information Science
• Precision Measurement

Background:

• Postselected weak measurement is a protocol for amplifying weak physical effects.
• Recent controversy exists regarding the precision advantages of postselected weak measurement.
• Retaining failed postselections can increase Fisher information, but the benefit of postselection itself needs clarification.

Purpose of the Study:

• To clarify the precision advantage of postselected weak measurement itself.
• To investigate two estimation strategies: averaging measurement results and maximum likelihood estimation.

Main Methods:

• Analysis of averaging measurement results for postselected weak measurements.
• Analysis of maximum likelihood estimation for postselected weak measurements.
• Comparison with standard weak measurements using coherent and squeezed coherent states.

Main Results:

• Squeezed coherent states in postselected weak measurements yield higher signal-to-noise ratios than standard measurements.
• Standard coherent states do not provide an advantage with postselection, indicating the need for nonclassicality.
• Quantum Fisher information is generally larger for postselected weak measurements compared to standard ones, even without failed events.

Conclusions:

• Postselected weak measurements can offer enhanced precision, particularly when pointer states exhibit nonclassicality.
• The advantage of postselection in weak measurements is linked to the nonclassical properties of the pointer states.
• Maximum likelihood estimation shows a general quantum Fisher information advantage for postselected weak measurements, which can be optimized by system state selection.