Spekkens Toy Model - Elementary Systems - Transformations


The only transformations on the ontic state of the system which respect the knowledge balance principle are permutations of the four ontic states. These map valid epistemic states to other valid epistemic states, for instance

Failed to parse (Cannot store math image on filesystem.): ((12)(34)) (1 lor 2) to 1 lor 2

Failed to parse (Cannot store math image on filesystem.): ((12)(34)) (1 lor 3) to 2 lor 4

Failed to parse (Cannot store math image on filesystem.): ((12)(3)(4)) (1 lor 3) to 2 lor 3.

Considering again the analogy between the epistemic states of this model and the qubit states on the Bloch Sphere, these transformations consist of the typical allowed permutations of the six analogous states, as well as a set of permutations that are forbidden in the continuous qubit model. These are transformations such as (12)(3)(4) which correspond to antiunitary maps on Hilbert space. These are not allowed in a continuous model, however in this discrete system they arise as natural transformations. There is however an analogy to a characteristically quantum phenomenon, that no allowed transformation functions as a universal state inverter. In this case, this means that there is no single transformation S with the properties

Failed to parse (Cannot store math image on filesystem.): S(1 lor 2) to 3 lor 4 qquad S(3 lor 4) to 1 lor 2

Failed to parse (Cannot store math image on filesystem.): S(1 lor 3) to 2 lor 4 qquad S(2 lor 4) to 1 lor 3

Failed to parse (Cannot store math image on filesystem.): S(1 lor 4) to 2 lor 3 qquad S(2 lor 3) to 1 lor 4.

Read more about this topic:  Spekkens Toy Model, Elementary Systems

Other articles related to "transformation, transformations":

Social Transformation
... One definition of Social transformation is the process by which an individual alters the socially ascribed social status of their parents into a socially achieved status for themselves ... refers to large scale social change as in cultural reforms or transformations ... which occur from the parents' to the children's generation, social transformation focuses on how an individual can alter the class culture to which they feel aligned ...
Coord - Transformations
... A coordinate transformation is a conversion from one system to another, to describe the same space ... bijection from the space to itself two coordinate transformations can be associated such that the new coordinates of the image of each point are the same as the old coordinates of the original point (the ...
Spin (physics) - Mathematical Formulation of Spin - Spin and Lorentz Transformations
... approach to determine the behavior of spin under general Lorentz transformations, but we would immediately discover a major obstacle ... Unlike SO(3), the group of Lorentz transformations SO(3,1) is non-compact and therefore does not have any faithful, unitary, finite-dimensional representations ... These spinors transform under Lorentz transformations according to the law where are gamma matrices and is an antisymmetric 4x4 matrix parametrizing the ...
Lie Sphere Geometry in The Plane - Lie Transformations
... Any element of the group O(3,2) of orthogonal transformations of R3,2 maps any null one dimensional subspaces of R3,2 to another such subspace ... These transformations of cycles are called "Lie transformations" ... In particular, points are not preserved by general Lie transformations ...
Spatial ETL - Transform - Common Geometric Transformations
... Spatial transformations the ability to model spatial interactions and calculate spatial predicates Topological transformations the ability to create topological relationships between ...