Damghan University PressJournal of Holography Applications in Physics2783-47783120230301Quantum Measuring Systems: Considerations from the Holographic Principle313830810.22128/jhap.2023.652.1039ENEijiKonishiGraduate School of Human and Environmental Studies, Kyoto University0000-0002-6539-144XJournal Article20230208In quantum mechanics without application of any superselection rule to the set of the observables, a closed quantum system temporally evolves unitarily, and this Lorentzian regime is characterized by von Neumann entropy of exactly zero.<br /> In the holographic theory in the classicalized ground state, we argue that the unitary real-time evolution of a non-relativistic free particle with complex-valued quantum probability amplitude in this Lorentzian regime can be temporally analytically continued to an imaginary-time classical stochastic process with real-valued conditional probability density in the Euclidean regime, where the von Neumann entropy of the classicalized hologram and the information of a particle trajectory acquired by the classicalized hologram are positive valued. This argument could shed light on the Euclidean regime of the holographic Universe.https://jhap.du.ac.ir/article_308_1ab04706d47f86b909059b11862bad3b.pdf