The density matrix of a pure quantum state ly) is defined as p = 1)land the density matrix of the collection of pure states ) with the corresponding probabilities p, is defined as p = Σ. Ρ|Ψ;}ψι|. (a) Find a density matrix of 4) =(100) + |11)) and show that this density matrix corresponds a pure state (by using the purity). (b) Find a density matrix composed of quantum states ₁) = (100) + |11)), 2)=(101) +110)) with corresponding probabilities P₁ = P₂ = 1/2. Show that the density matrix is in a mixed state.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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The density matrix of a pure quantum state ) is defined as p = 1)land the density matrix of the
collection of pure states ) with the corresponding probabilities p, is defined as
ρ = Σ; pi|Ψ}(Ψ.|.
(a) Find a density matrix of 4) = (100) + |11)) and show that this density matrix corresponds a
pure state (by using the purity).
(b) Find a density matrix composed of quantum states ₁) = (100) + 111)),
142)=(101) + |10)) with corresponding probabilities p₁ = P2 = 1/2.
Show that the density matrix is in a mixed state.
Transcribed Image Text:The density matrix of a pure quantum state ) is defined as p = 1)land the density matrix of the collection of pure states ) with the corresponding probabilities p, is defined as ρ = Σ; pi|Ψ}(Ψ.|. (a) Find a density matrix of 4) = (100) + |11)) and show that this density matrix corresponds a pure state (by using the purity). (b) Find a density matrix composed of quantum states ₁) = (100) + 111)), 142)=(101) + |10)) with corresponding probabilities p₁ = P2 = 1/2. Show that the density matrix is in a mixed state.
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