14. Shantena Augusto Sabbadini, Persistence of Information in the Quantum Measurement Problem

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Volume 19: Pages 135-150, 2006

Persistence of Information in the Quantum Measurement Problem

Shantena Augusto Sabbadini

Pari Center for New Learning, Pari 58040 Italy

The quantum measurement problem has to do with the compatibility of two different prescriptions for the end state of a quantum measurement process: (1) a superposition representing an entangled state of object system and apparatus, and (2) a mixture of correlated states of object system and apparatus. The first prescription is a consequence of the linearity of time evolution in quantum mechanics; the second one (corresponding to what is usually called the “collapse of the wavefunction ”) is a basic feature of the axiomatic structure of the theory. This paper proves that the two prescriptions are exactly equivalent whenever information about the results of the measurement persists, i.e., whenever there is some kind of record or trace of the results (all the measurements we are ordinarily concerned with fulfill this requirement). Experimental evidence is cited suggesting that indeed we should expect the equivalence of prescriptions 1 and 2 to hold when and only when information about measurement results persists. Finally, the notion of an “element of reality”introduced by Einstein, Podolsky, and Rosen is discussed in the context of this description of the measurement process, and a brief remark is offered about the “classical” nature of the world we experience.

Keywords: appearance of a classical world, collapse of the wavefunction, decoherence, element of reality, entanglement, information, quantum beats, quantum eraser, quantum measurement, von Neumann chain

Received: July 18, 2005; Published online: December 15, 2008