Einstein, Podolsky, and Rosen (EPR) pointed out that quantum theory (QT) is not a "complete" theory[1]. Well-known Bell[2] and Clauser-Horne-Shimony-Holt[3] inequalities showed inconsistency between the local realism and QT, and Bell[4] and Kochen-Specker[5] discussed the inconsistency between noncontextual realism and QT.
In this project, our goal is a demonstration of such a violation on a quantum computer.
Description
There is a tutorial that introduces Bell-CHSH inequality.
Various methods are known for the violation of the local hidden variable model (e.g. Svetlichny's inequality, Mermin-Klyshko inequalities, or google "Bell-like inequalities"...).
On the other hand, for contextuality, the Bell-Kochen-Spaecker scenario cannot be tested directly.
Some noncontextual inequalities were proposed to verify contextuality in quantum theory [6, 7].
You can choose such inequality and implement a violation of it on a quantum computer.
Quantification of entanglement can be also a good project. For example, we compute some entanglement measure on a quantum computer. (if you are interested)
Reference
[1] A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935)
[2] J. S. Bell, Physics. 1, 3 (1964)
[3] J.F. Clauser, M.A. Horne, A. Shimony, R.A. Holt, Phys. Rev. Lett. 23 15 (1969)
[4] J. S. Bell, Rev. Mod. Phys. 38, 447 (1966)
[5] S. Kochen, E. Specker, J. Math. Mech. 17, 59 (1968)
[6] A. A. Klyachko, M. A. Can, S. Binicioğlu, and A. S. Shumovsky, Phys. Rev. Lett. 101, 020403 (2008).
[7] A. K. Pan, M. Sumanth, and P. K. Panigrahi, Phys. Rev. A 87, 014104 (2013).
Abstract
Einstein, Podolsky, and Rosen (EPR) pointed out that quantum theory (QT) is not a "complete" theory[1]. Well-known Bell[2] and Clauser-Horne-Shimony-Holt[3] inequalities showed inconsistency between the local realism and QT, and Bell[4] and Kochen-Specker[5] discussed the inconsistency between noncontextual realism and QT. In this project, our goal is a demonstration of such a violation on a quantum computer.
Description
There is a tutorial that introduces Bell-CHSH inequality. Various methods are known for the violation of the local hidden variable model (e.g. Svetlichny's inequality, Mermin-Klyshko inequalities, or google "Bell-like inequalities"...).
On the other hand, for contextuality, the Bell-Kochen-Spaecker scenario cannot be tested directly. Some noncontextual inequalities were proposed to verify contextuality in quantum theory [6, 7].
You can choose such inequality and implement a violation of it on a quantum computer.
Quantification of entanglement can be also a good project. For example, we compute some entanglement measure on a quantum computer. (if you are interested)
Reference
[1] A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935) [2] J. S. Bell, Physics. 1, 3 (1964) [3] J.F. Clauser, M.A. Horne, A. Shimony, R.A. Holt, Phys. Rev. Lett. 23 15 (1969) [4] J. S. Bell, Rev. Mod. Phys. 38, 447 (1966) [5] S. Kochen, E. Specker, J. Math. Mech. 17, 59 (1968) [6] A. A. Klyachko, M. A. Can, S. Binicioğlu, and A. S. Shumovsky, Phys. Rev. Lett. 101, 020403 (2008). [7] A. K. Pan, M. Sumanth, and P. K. Panigrahi, Phys. Rev. A 87, 014104 (2013).
Members
@slackhandleemail:example@example.comDeliverable
Jupyter notebook
GitHub repo