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Abstract
Measurements are crucial in quantum mechanics, for fundamental research as well as for applicative fields like quantum metrology, quantum-enhanced measurements and other quantum technologies. In the recent years, weak-interaction-based protocols like Weak Measurements and Protective Measurements have been experimentally realized, showing peculiar features leading to surprising advantages in several different applications. In this work we analyze the validity range for such measurement protocols, that is, how the interaction strength affects the weak value extraction, by measuring different polarization weak values on heralded single photons. We show that, even in the weak interaction regime, the coupling intensity limits the range of weak values achievable, setting a threshold on the signal amplification effect exploited in many weak measurement based experiments.
Highlights
WMs can give rise to anomalous values, whose real part is regarded as a conditional average of the observable in the zero-disturbance limit[9], while the imaginary one is related to the disturbance of the measuring pointer during the measurement[10]
Both of these protocols require a von Neumann interaction with a very weak coupling between the observable to be measured and the pointer observable, rising the issue of when the regime of weak interaction approximation can be considered valid[49,50]. This is of the utmost relevance specially when dealing with anomalous weak values, for which the weakness of the von Neumann interaction is crucial for the reliability of the measurement, giving rise to a signal amplification effect already demonstrated in several experiments[6,26,27,28,29,30,31]
We show how the von Neumann coupling intensity intrinsically provides some boundaries on the range of weak values that one is able to determine without abandoning the weak interaction approximation, setting, as a consequence, a threshold on the signal amplification effect mentioned above
Summary
Measurements are crucial in quantum mechanics, for fundamental research as well as for applicative fields like quantum metrology, quantum-enhanced measurements and other quantum technologies. A very controversial and debated topic from the foundational perspective[38,39,40,41,42,43,44,45,46,47,48], PMs have demonstrated unprecedented measurement capability, allowing to extract the quantum expectation value of an observable in a single measurement on a single (protected) particle[8], a task usually forbidden in quantum mechanics Both of these protocols require a von Neumann interaction with a very weak coupling between the observable to be measured and the pointer observable, rising the issue of when the regime of weak interaction approximation can be considered valid[49,50]. We show how the von Neumann coupling intensity intrinsically provides some boundaries on the range of weak values that one is able to determine without abandoning the weak interaction approximation, setting, as a consequence, a threshold on the signal amplification effect mentioned above
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