No measurement is possible without any theory. With respect to a theory under consideration one has to distinguish between direct and indirect measurements. Direct measurements are defined by pre-theories, i.e. without the theory under consideration. The direct measurements for quantum theory are given by measurable processes on macroscopic devices. It is demonstrated how indirect measurements in quantum mechanics can be reduced to direct measurements. A theory of the measuring device is in this context not possible by quantum mechanics alone, but by a more comprehensive theory of macrosystems.No measurement is possible without any theory. With respect to a theory under consideration one has to distinguish between direct and indirect measurements. Direct measurements are defined by pre-theories, i.e. without the theory under consideration. The direct measurements for quantum theory are given by measurable processes on macroscopic devices. It is demonstrated how indirect measurements in quantum mechanics can be reduced to direct measurements. A theory of the measuring device is in this context not possible by quantum mechanics alone, but by a more comprehensive theory of macrosystems.

MetrologiaJan 1, 19869 citations

Does a classical probability space for two-dimensional quantum measurement theory exist?

Koji Nagata, Tadao Nakamura

Recently, a new measurement theory based on the truth values is proposed \cite{NN1}. The results of measurements are either 0 or 1. The measurement theory accepts a hidden variables model for a single Pauli observable. Therefore we can introduce a classical probability space for the measurement theory in this case. On the other hand, we discuss the fact that the projective measurement theory (the results of measurements are either $+1$ or $-1$ ) does not meet a hidden variables model for a single Pauli observable. Hence we cannot introduce a classical probability space for the projective measurement theory in this case. Our discussion provides new insight to formulate quantum measurement theory, by using the measurement theory based on the truth values.Recently, a new measurement theory based on the truth values is proposed \cite{NN1}. The results of measurements are either 0 or 1. The measurement theory accepts a hidden variables model for a single Pauli observable. Therefore we can introduce a classical probability space for the measurement theory in this case. On the other hand, we discuss the fact that the projective measurement theory (the results of measurements are either $+1$ or $-1$) does not meet a hidden variables model for a single Pauli observable. Hence we cannot introduce a classical probability space for the projective measurement theory in this case. Our discussion provides new insight to formulate quantum measurement theory, by using the measurement theory based on the truth values.

Jun 1, 20160 citations

Measurement Theory

Paul Busch, PEKKA J. LAHTI

Compendium of Quantum PhysicsJan 1, 20093 citations

Measurement theory for physics

John F. Cyranski

Foundations of PhysicsOct 1, 19797 citations

Why measurements are made of effects

Tobias Fritz

Both in quantum theory and in general probabilistic theories, measurements with $n$ outcomes are modelled as $n$ -tuples of \emph{effects} summing up to the unit effect. Why is this the case, and can this assumption be meaningfully relaxed? Here we develop \emph{generalized measurement theories (GMTs)} as a mathematical framework for physical theories that is complementary to general probabilistic theories, and where this kind of question can be made precise and answered. We then give a definition of \emph{probabilistic state} on a GMT, prove that measurements are made of effects in every GMT in which the probabilistic states separate the measurements, and also argue that this separation condition is physically well-motivated. Finally, we also discuss when a GMT should be considered classical and characterize GMTs corresponding to Boolean algebras as those that are strongly classical and projective.Both in quantum theory and in general probabilistic theories, measurements with $n$ outcomes are modelled as $n$-tuples of \emph{effects} summing up to the unit effect. Why is this the case, and can this assumption be meaningfully relaxed? Here we develop \emph{generalized measurement theories (GMTs)} as a mathematical framework for physical theories that is complementary to general probabilistic theories, and where this kind of question can be made precise and answered. We then give a definition of \emph{probabilistic state} on a GMT, prove that measurements are made of effects in every GMT in which the probabilistic states separate the measurements, and also argue that this separation condition is physically well-motivated. Finally, we also discuss when a GMT should be considered classical and characterize GMTs corresponding to Boolean algebras as those that are strongly classical and projective.

quant-pharXiv:2602.18898Feb 24, 20260 citations

+1

-1

) does not meet a hidden variables model for a single Pauli observable. Hence we cannot introduce a classical probability space for the projective measurement theory in this case. Our discussion provides new insight to formulate quantum measurement theory, by using the measurement theory based on the truth values.

Both in quantum theory and in general probabilistic theories, measurements with

n

outcomes are modelled as

n

-tuples of \emph{effects} summing up to the unit effect. Why is this the case, and can this assumption be meaningfully relaxed? Here we develop \emph{generalized measurement theories (GMTs)} as a mathematical framework for physical theories that is complementary to general probabilistic theories, and where this kind of question can be made precise and answered. We then give a definition of \emph{probabilistic state} on a GMT, prove that measurements are made of effects in every GMT in which the probabilistic states separate the measurements, and also argue that this separation condition is physically well-motivated. Finally, we also discuss when a GMT should be considered classical and characterize GMTs corresponding to Boolean algebras as those that are strongly classical and projective.