 Solution

ID: past-exam-of-the-theoretical-physics-ii-course-of-the-university-of-cambridge/2019/4/e/iii/solution

1/2

S_{R} = - Tr (ρ_{R} ln ρ_{R}) = - 2 (\frac{1}{2} ln \frac{1}{2}) = ln 2.

This is one bit when base-two logarithms are used. It is the maximum entanglement entropy for a pair of two-dimensional systems, while the joint Von Neumann entropy of the singlet state remains zero.

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