The four postulates of quantum mechanics are three

Abstract

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 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 paper reduces by one the number of postulates necessary to quantum mechanics.

4 pages+supplementary information. Final version accepted for publication on Phys. Rev. Lett

References in corpus (13)

• Quantum Darwinism
• Quantum tensor product structures are observable-induced
• Virtual Quantum Subsystems
• Uncertainty Relations for Noise and Disturbance in Generalized Quantum Measurements
• Quantum from principles
• Introduction to the book "Quantum Theory: Informational Foundations and Foils"
• Quasi-quantization: classical statistical theories with an epistemic restriction
• The completeness of quantum theory for predicting measurement outcomes
• The measurement postulates of quantum mechanics are operationally redundant
• Classical interventions in quantum systems. II. Relativistic invariance
• Hilbert space structure in quantum gravity: an algebraic perspective
• Generalized Gibbs Ensembles in Discrete Quantum Gravity
• On the notion of composite system

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• On the state space structure of tripartite quantum systems