Few years ago I have proposed a different definition of the quantum measurement; however, it does not relate to the relativity theory. My point is explained in details in linked conference presentation.
Abstract. Two states of the observed subsystem (say "2") are said to be equivalent, if they imply the same reduced state of the observing subsystem (say "1"), via the suitable partial trace. The result of the observation (of "2" by "1") is any equivalence class of the (non-reduced) states of "2". If the system is driven by a Hamiltonian built of a finite sum of multipliers in the product form, then the maximal available in subsystem "1" information about the state of "2" is the diagonal of its density matrix. For non-commuting factors, the result of observations is shown more informative. Intermediate quantum observations are illustrated by three-partite systems with product Hamiltonians, without any direct interaction between the observed and the observing subsystems. A rigorously calculated examples show that the subsystems cannot see each other if suitable factors of their interactions with the third party commute.
I would be grateful for any comment. Joachim
Conference Paper Quantum Systems' Measurement through Product Hamiltonians
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