Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Generalized probabilistic theory
open-in-new
<p>A generalized probabilistic theory (GPT) is a general framework to describe the <a href="/facts/Operationalization/nm5Tff9F">operational</a> features of arbitrary <a href="/facts/Physical_theory/Cs2Y12rQ">physical theories</a>. A GPT must specify what kind of physical systems one can find in the lab, as well as rules to compute the outcome statistics of any experiment involving labeled preparations, transformations and measurements. The framework of GPTs has been used to define hypothetical non-quantum physical theories which nonetheless possess <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum theory</a>'s most remarkable features, such as <a href="/facts/Quantum_entanglement/afzslwN0">entanglement</a> or <a href="/facts/Quantum_teleportation/2lWvQA4F">teleportation</a>. Notably, a small set of physically motivated <a href="/facts/Axioms/mLjP14Mc">axioms</a> is enough to single out the GPT representation of quantum theory. </p><p>The mathematical formalism of GPTs has been developed since the 1950s and 1960s by many authors, and rediscovered independently several times. The earliest ideas are due to Segal and Mackey, although the first comprehensive and mathematically rigorous treatment can be traced back to the work of Ludwig, Dähn, and Stolz, all three based at the University of Marburg. While the formalism in these earlier works is less similar to the modern one, already in the early 1970s the ideas of the Marburg school had matured and the notation had developed towards the modern usage, thanks also to the independent contribution of Davies and Lewis. The books by Ludwig and the proceedings of a conference held in Marburg in 1973 offer a comprehensive account of these early developments. The term "generalized probabilistic theory" itself was coined by Jonathan Barrett in 2007, based on the version of the framework introduced by Lucien Hardy. </p><p>Note that some authors use the term <i>operational probabilistic theory</i> (OPT). OPTs are an alternative way to define hypothetical non-quantum physical theories, based on the language of <a href="/facts/Category_theory/6zS3DXPa">category theory</a>, in which one specify the axioms that should be satisfied by observations. </p>