Past exam of the computer science course of the University of Oxford / 2022 / Quantum information / 3 / a

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- Solution a

Solution

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

ρ \geq 0, Tr ρ = 1.

Here positive semidefinite includes being a Hermitian matrix, with

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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