A source prepares a spin- particle either in the state (Bloch vector along ) or in…

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 source prepares a spin-12\tfrac12 particle either in the state ∣0⟩|0\rangle (Bloch vector along +Z+Z) or in the state ∣ψ⟩=cos⁡60∘∣0⟩+sin⁡60∘∣1⟩|\psi\rangle = \cos60^\circ|0\rangle + \sin60^\circ|1\rangle (Bloch vector at polar angle 120∘120^\circ from +Z+Z), each with probability 12\tfrac12. The resulting state is ρ=12∣0⟩⟨0∣+12∣ψ⟩⟨ψ∣.\rho = \tfrac12|0\rangle\langle0| + \tfrac12|\psi\rangle\langle\psi|. ((a)) Find the eigenvalues of ρ\rho. ((b)) Compute S(ρ)S(\rho) in bits and compare it with the 11 bit needed to record which state was prepared.

Related theory

Browse the problem library