 Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2022/quantum-information/3/a/solution

The two conditions on a density matrix are positive semidefiniteness and unit trace:

ρ \geq 0, Tr ρ = 1.

v^{†} ρ v \geq 0

for every vector

v

. Equivalently, a density matrix is Hermitian with nonnegative eigenvalues summing to one.

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