Data on activation of the CHSH inequality

In Reference [1]  two states , are found such that an arbitrary number of copies of one state or the other cannot violate the CHSH inequality, however the composite state does violate it.

Here one can find all details of the matrices of the measurement operators and the density matrices of the states which result in the violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality. The optimal measurements correspond to {+1,-1} observables, they along with the density matrices are given in the computational basis. In order to obtain the violations reported in Ref.[1], it was enough to consider real valued matrices. The four different cases investigated numerically in this paper are listed below:

1.      The two-qubit states,are such states that neither nor gives rise to CHSH violation, however produces a CHSH violation of 2.023243. The matrices are given here and can also be downloaded as a mat-file. 

 

2.      The two-qutrit states,are such states that neither nor gives rise to CHSH violation, however produces a CHSH violation of 2.040167. The matrices given here and can also be downloaded as a mat-file. 

 

3.      The two-qutrit states,are such states that neither nor gives rise to (Collins-Gisin-Linden-Massar-Popescu) CGLMP violation, however produces a CGLMP violation of 2.030126. The matrices are given here and can also be downloaded as a mat-file.

 

4.      The symmetric two-ququart states,have the property that neither of them gives rise to CHSH violation, however produces a CHSH violation of 2.011591. The matrices can be found here and can also be downloaded as a mat-file. However, note the construction in Ref.[1] yielding the value of 2.0116216, which is slightly better than the previous value.

 

 

References

[1] M. Navascués and T. Vértesi: CHSH activation, arXiv:1010.5191 (2010) .