Lectures on Quantum Measurement Theory: II

Lecture II: Modern approach: Quantum instruments, POVMs, measuring processes, intersubjectivity, and value reproducibility

The modern approach to quantum measurement theory is based on the "realizability theorem" stating that a measurement is physically realizable if and only if its statistical properties are represented by a completely positive instrument, and this is also equivalent to saying that the measurement can be described by an interaction with a measuring apparatus (Ozawa 1984, 2004).

The conventional analysis of a measuring process determines the post-measurement object state by applying the "projection postulate" to the meter measurement in the post-measurement state that "entangles" the object and the apparatus, but the above result has been established without assuming the projection postulate altogether; rather we use only the classical Bayesian probability update rule (Ozawa 1984).

We introduce the "intersubjectivity theorem" that states that, when multiple observers simultaneously and statistically correctly measure the same physical quantity, they obtain the same measurement value and the "value reproducibility theorem" that states that a statistically correct measurement correctly reproduces the value of the physical quantity immediately before the measurement (Ozawa 2025).

The above three theorems essentially solves the so-called measurement problem, since we eliminate the collapse of the wave function and we establish the reality of the the pre-measurement value of the measured observable to be copied to the meter value and to be recorded by the observer.