Lehr- und Forschungsgebiet
Mathematische Grundlagen der Informatik RWTH Aachen
Prof. Dr. E. Grädel, F. Abu-Zaid, S. Schalthöfer
SS 2015
Quantum Computing — Assignment 1 Due: Wednesday, 22.04., 14:15
Exercise 1 5 Points
Consider the polarisation experiment from the lecture, where, instead of 45◦, the filter in the middle polarises light with an angleα, for arbitraryα.
Specify how much light passes through the three filters depending on the angle α.
Exercise 2 15 Points
(a) Give a construction of an equation system EQ|ψifor each vector|ψi ∈H4, such that EQ|ψi is solvable if, and only if|ψi is not entangled.
(b) For each of the following states, prove or disprove that it is entangled.
Hint: The equation system may not be helpful in all cases. You can, for instance, consider the properties of tensor products.
(i) 12|00i+12|01i+√1
2|11i (ii) −16 +i
√ 2 3
|00i+1−
√ 2 6 +i1+
√ 2 6
|01i+1−
√ 2 6 +i1+
√ 2 6
|10i+ (i13)|11i (iii) 38|00i+
√ 7
8 |01i+34|10i+
√ 3 4 |11i
Exercise 3 10 Points
Show that, for each qubit|ψi=α|0i+β|1i, there are γ, ϑ, ϕ∈Rsuch that
|ψi=eiγ
cosϑ
2|0i+e−iϕsinϑ 2 |1i
.
Hint: Each complex numberz can be written as z=r·eiγ for somer, γ∈R.
http://logic.rwth-aachen.de/Teaching/QC-SS15/
