Consistency and Linearity in Quantum Theory
Ariel Caticha
Abstract
Quantum theory is formulated as the uniquely consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if the amplitude of a quantum process can be computed in two different ways, the two answers must agree. The constraint is expressed in the form of functional equations the solution of which leads to the usual sum and product rules for amplitudes. An immediate consequence is that the Schrodinger equation must be linear: non-linear variants of quantum mechanics violate the requirement of consistency. PACS: 03.65.Bz, 03.65.Ca.
Create a lesson
Related papers
An entangling Hubbard quasiparticle collider on a digital quantum processor
Chan Bin Bark, Hanbyul Kim, Yoonil Koo et al.
A Warped Born Rule Turns an Observer into a Maxwell's Demon
Olumakinde Ogunnaike
A scalable sample-based quantum diagonalization solver for general Pauli-sum Hamiltonians
Yutaro Iiyama
Quantum Query Complexity of Maximum Degree and its Generalizations
Amin Shiraz Gilani, Nikhil S. Mande, Subhasree Patro et al.
Maximally antiflat fixed-particle-number fermionic states
Rahul Gupta, Arya Haghighian, James D. Whitfield
An Annealing-based Quantum Neural Network with Discrete Wavelet Transforms for Enhanced Air Pollution Nowcasting
Otto Menegasso Pires, André Saimon, Daniela Herrmann et al.