User talk:Aschimmo/sandbox/Quantum Contextuality Sandbox

Quantum Contextuality is a foundational concept in quantum mechanics stating that the outcome one gets in a measurement is dependent upon what other measurements one is trying to make. More formally, the measurement result of a quantum observable is dependent upon which other commuting observables are within the same measurement set.

Contextuality was first proposed in the Bell-Kochen-Specker theorem, which revealed that hidden variables and non-contextuality are incompatible with quantum mechanics[1]. That is, the state of a quantum system cannot be described either deterministically or independent of the experimental setup. Since then, contextuality has developed under several mathematical frameworks, including the Sheaf Theoretic, Spekkens' operational contextuality, and the graph theoretic. The Sheaf Theoretic proposed by Samson Abramsky and Adam Brandenburger employs sheaf theory to generalize contextuality to all forms of measurement, not just measurements in quantum mechanics[2]. Meanwhile, Spekkens defines and expands upon contextuality as it applies to quantum information and experimentation[3], and the graph theoretic explains contextuality using the mathematical formalism present in graph theory[4]. There also exists contextuality by default[5], which applies the principles of contextuality to psychology and sociology[6].

Recently, Quantum contextuality has been explored as a potential means for quantum computing. In 2013, Robert Raussendorf showed that in general, under the Sheaf Theoretic framework, a proof for quantum contextuality (such as the Kochen-Specker theorem) can be used to perform measurement-based quantum computations[7]. Then in 2014, Mark Howard, et. al. showed that under the graph-theoretic framework, universal quantum computing could be made possible by applying contextuality to magic state distillation[8]. In both cases, contextuality has a potential advantage over other quantum computational techniques since contextuality itself can be thought of as a theory of information that is built directly into quantum mechanics. Comparatively, more traditional quantum phenomena such as entanglement and interference use delicate physical states which are incredibly susceptible to noise and very difficult to manipulate experimentally. How does contextuality avoid these issues?

'''I would suggest trying to expand upon the different frameworks if at all possible. It seems that the current explanations don't really say much other than that the frameworks have been applied to quantum contextuality. Likewise, I feel that the idea of contextuality by default being useful in psychology and sociology should be explained a little more. How/why does applying these principles to psychology and sociology help those fields?'''

Jleamer1 (talk) 02:42, 26 November 2018 (UTC)

http://iopscience.iop.org/article/10.1088/1367-2630/17/2/023037 — Preceding unsigned comment added by Aschimmo (talk • contribs) 01:02, 28 November 2018 (UTC)

The explanations seem well enough, better than what was there before. However, the article would benefit from subsections for the frameworks used, such as the Sheaf Theoretic framework and especially for the graph-theoretic framework.

It would also be really interesting to see an extra paragraph or subsection on the applications to psychology.

Arinconl (talk) 00:38, 8 December 2018 (UTC)