A derivation of quantum theory from physical requirements

By L. Masanes, Markus P. Mueller. 2010

407 citations recorded by the source corpus.

Quantum theory (QT) is usually formulated in terms of abstract mathematical postulates involving Hilbert spaces, state vectors and unitary operators. In this paper, we show that the full formalism of QT can instead be derived from five simple physical requirements, based on elementary assumptions regarding preparations, transformations and measurements. This is very similar to the usual formulation of special relativity, where two simple physical requirements—the principles of relativity and light speed invariance—are used to derive the mathematical structure of Minkowski space–time. Our derivation provides insights into the physical origin of the structure of quantum state spaces (including a group-theoretic explanation of the Bloch ball and its three dimensionality) and suggests several natural possibilities to construct consistent modifications of QT.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9bda426f1aab980c94e3a61d9703d66089ea66ca

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. Lucien Hardy
2. Fabio Costa
3. Č. Brukner
4. Ognyan Oreshkov
5. Tobias Fritz

In Atomic and Molecular Physics, and Optics

1. Lucien Hardy
2. Ognyan Oreshkov
3. Č. Brukner
4. Markus P. Mueller
5. Tobias Fritz
6. Fabio Costa
7. Howard Barnum
8. Cozmin Ududec

In Statistical and Nonlinear Physics

1. Ognyan Oreshkov
2. Lucien Hardy
3. Č. Brukner
4. Fabio Costa
5. Tobias Fritz
6. Antonio Acín
7. Christina Giarmatzi

Citations in the corpus

• Quantum correlations with no causal order (2011, methodology): “The process described by equation (7) can be exploited for the task described above in the following way.”
• Reformulating and Reconstructing Quantum Theory (2011, methodology): “Work by Masanes and Müller [55] suggests this counterexample can be eliminated.”
• TSIRELSON'S PROBLEM AND KIRCHBERG'S CONJECTURE (2010, background): “is applies for example to categorical quantum mechanics [Coe10] and to certain approaches of reconstructing quantum mechanics from certain axioms on the probabilistic structure of the theory [Har01], [MM11]. So from our point of view, the tensor product operation should not be a fundamental structur”
• Algorithmic Pseudorandomness in Quantum Setups. (2014, background): “Its foundations, intensely debated in the early days of the theory [1, 2], remain an active area of research with many recent insightful results, such as the possibility to derive quantum theory from physical axioms [3], proving the completeness of quantum theory [4], or establishing that quantum st”
• Higher-order interference and single-system postulates characterizing quantum theory (2014, background): “These range from studies of the information processing capabilities of theories similar to quantum theory [10, 15, 35–37], to reconstructions of the formalism from information-theoretic principles [42, 43, 48, 50, 51, 71], to no-go theorems regarding interpretations and generalizations of the formal”