Conditional probabilities of measurements, quantum time and the Wigner's friend case

Martino Trassinelli (1, 2)

1 INSP - Institut des Nanosciences de Paris
2 INSP-E10 - Agrégats et surfaces sous excitations intenses

Considering a minimal number of assumptions and in the context of the timeless formalism, conditional probabilities are derived for subsequent measurements in the non-relativistic regime. Only unitary transformations are considered with detection processes described by generalized measurements (POVM). One-time conditional probabilities are unambiguously derived via the Gleason-Bush theorem, including for puzzling cases like the Wigner's friend scenario where their form underlines the relativity aspect of measurements. No paradoxical situations emerge and the roles of Wigner and the friend are completely interchangeable. Wigner can be seen by his friend as being in a superposition but, at the same time, the friend acts as a which-path detector destroying the coherence of the measured state.

Domaines: Physique Quantique [quant-ph]

Martino Trassinelli. Conditional probabilities of measurements, quantum time and the Wigner's friend case. 2021. ⟨hal-03179772v3⟩