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Zbl 1180.81007
Khrennikov, Andrei
Von Neumann and Luders postulates and quantum information theory. (English)
[J] Int. J. Quantum Inf. 7, No. 7, 1303-1311 (2009). ISSN 0219-7499

Summary: This note is devoted to some foundational aspects of quantum mechanics (QM) related to quantum information (QI), especially quantum teleportation and ``one way quantum computing." We emphasize the role of the projection postulate (determining post-measurement states) in QI and the difference between its Lüders and von Neumann versions. As is well-known, these postulates differ in the case of observables with degenerate spectra. Such observables are important in operations with entangled states: any measurement on one subsystem is represented by an observable with degenerate spectrum in the Hilbert space of a composite system. Some QI schemes (e.g., quantum teleportation and ``one way quantum computing") are based on the use of Lüders postulate. The formal application of von Neumann postulate can block these QI schemes. In this note, we present a list of natural conditions under which von Neumann's description of measurements via refinement implies Lüders projection postulate.

MSC 2000:: *81P15 Quantum measurement theory
81P45
81P68 Quantum computation and quantum cryptography

Keywords: Lüders and von Neumann versions of the projection postulate; quantum teleportation; one way quantum computing; post measurement states; pure states; statistical mixtures

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Zentralblatt MATH Berlin [Germany]