Weak values are universal in von Neumann measurements

Area of Science:

• Quantum mechanics
• Quantum information theory

Background:

• The prevailing understanding links quantum weak values exclusively to weak measurements.
• This connection has limited the exploration of weak values in broader quantum measurement contexts.

Purpose of the Study:

• To challenge the notion that quantum weak values are solely applicable to weak measurements.
• To establish a framework for understanding weak values in the context of strong measurements.

Main Methods:

• Utilizing the transverse position of a beam as a detector for conditioned von Neumann measurements.
• Employing the Wigner distribution of the initial detector state to derive compact weak value expressions.
• Analyzing detector position and momentum averages through generalized weak values.

Main Results:

• Demonstrated that detector position and momentum averages are fully described by the real parts of three generalized weak values, irrespective of coupling strength or initial states.
• Established that higher-order detector moments also exhibit weak value expansions.
• Derived compact expressions for weak values within the reduced system Hilbert space.

Conclusions:

• Quantum weak values are applicable beyond weak measurements, extending to strong measurement regimes.
• The developed framework provides a unified approach to describing measurement outcomes using weak values.
• The findings offer new perspectives on quantum measurement theory and its applications.