# Quantum mechanics without probability amplitudes

@article{Wootters1986QuantumMW, title={Quantum mechanics without probability amplitudes}, author={William K. Wootters}, journal={Foundations of Physics}, year={1986}, volume={16}, pages={391-405} }

First steps are taken toward a formulation of quantum mechanics which avoids the use of probability amplitudes and is expressed entirely in terms of observable probabilities. Quantum states are represented not by state vectors or density matrices but by “probability tables,” which contain only the probabilities of the outcomes of certain special measurements. The rule for computing transition probabilities, normally given by the squared modulus of the inner product of two state vectors, is re…

## 119 Citations

Probability Representation of Quantum States

- PhysicsEntropy
- 2021

The invertible map of density operators and wave functions onto the probability distributions describing the quantum states in quantum mechanics is constructed both for systems with continuous variables and systems with discrete variables by using the Born’s rule and recently suggested method of dequantizer–quantizer operators.

Conventional Quantum Statistics with a Probability Distribution Describing Quantum System States

- Physics
- 2020

The review of a new probability representation of quantum states is presented, where the states are described by conventional probability distribution functions. The invertible map of the probability…

Quantum theory of successive projective measurements

- Physics
- 2007

We show that a quantum state may be represented as the sum of a joint probability and a complex quantum modification term. The joint probability and the modification term can both be observed in…

A generic approach to the quantum mechanical transition probability

- MathematicsProceedings of the Royal Society A
- 2022

In quantum theory, the modulus-square of the inner product of two normalized Hilbert space elements is to be interpreted as the transition probability between the pure states represented by these…

A probabilistic approach to quantum mechanics based on ‘tomograms’

- Physics
- 2006

A tomographic approach to quantum states that leads to a probability representation of quantum states is discussed, which can be regarded as a classical-like formulation of quantum mechanics which avoids the counterintuitive concepts of wave function and density operator.

Correlations in a system of classical-like coins simulating spin-1/2 states in the probability representation of quantum mechanics

- PhysicsThe European Physical Journal D
- 2019

Abstract
An analog of classical “hidden variables” for qubit states is presented. The states of qubit (two-level atom, spin-1/2 particle) are mapped onto the states of three classical-like coins. The…

Information Invariance and Quantum Probabilities

- Mathematics
- 2009

We consider probabilistic theories in which the most elementary system, a two-dimensional system, contains one bit of information. The bit is assumed to be contained in any complete set of mutually…

Quantum theory within the probability calculus: a there-you-go theorem and partially exchangeable models

- Philosophy
- 2018

"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...]…

Some Theory and Applications of Probability in Quantum Mechanics

- Computer Science
- 2012

It is proved that quantum states are more difficult to estimate than their classical counterparts by finding optimal estimation strategies, requiring the solution to a difficult optimization problem, are difficult to implement in practise.

Quantum Mechanics Unscrambled

- Physics
- 2014

Is quantum mechanics about ‘states’? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to…

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