Four Postulates of Quantum Mechanics Are Three

The tensor product postulate of quantum mechanics states that the Hilbert space of a composite system is the tensor product of the components' Hilbert spaces. All current formalizations of quantum mechanics that do not contain this postulate contain some equivalent postulate or assumption (some...

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Bibliographic Details
Published in:Physical review letters 2021-03, Vol.126 (11), p.110402-110402, Article 110402
Main Authors: Carcassi, Gabriele, Maccone, Lorenzo, Aidala, Christine A
Format: Article
Language:English
Subjects:
Hilbert space
Mathematical analysis
Quantum mechanics
Quantum physics
Tensors
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Summary:The tensor product postulate of quantum mechanics states that the Hilbert space of a composite system is the tensor product of the components' Hilbert spaces. All current formalizations of quantum mechanics that do not contain this postulate contain some equivalent postulate or assumption (sometimes hidden). Here we give a natural definition of a composite system as a set containing the component systems and show how one can logically derive the tensor product rule from the state postulate and from the measurement postulate. In other words, our Letter reduces by one the number of postulates necessary to quantum mechanics.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.126.110402