A trapped-ion qubit is initialised imperfectly

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Quantum Information & Technology · Quantum information theory and communication

Quantum Information and Technology, Ch Entropy and compression

Problem

A trapped-ion qubit is initialised imperfectly, leaving it with a Bloch vector of magnitude r=0.6r = 0.6 pointing along +Z+Z, so its density operator is ρ=12(I+rZ).\rho = \frac{1}{2}(I + r Z). ((a)) Find the eigenvalues of ρ\rho. ((b)) Compute the von Neumann entropy S(ρ)S(\rho) in bits.

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