Four Postulates of Quantum Mechanics Are Three
Gabriele Carcassi, Lorenzo Maccone, C. Aidala
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 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.
Topics & Concepts
Tensor productTensor product of Hilbert spacesSIC-POVMHilbert spaceMathematicsCartesian tensorTensor (intrinsic definition)Interpretations of quantum mechanicsQuantum statistical mechanicsConsistent historiesQuantum mechanicsTheoretical physicsTensor contractionClassical mechanicsPure mathematicsPhysicsQuantumQuantum processQuantum dynamicsSupersymmetric quantum mechanicsTensor fieldTensor densityExact solutions in general relativityQuantum Mechanics and ApplicationsComputability, Logic, AI AlgorithmsLogic, programming, and type systems