Environment-assisted two-state pure-state transformation

There are a unitary

U

and normalized environment states

∣ ⟨ ϕ_{0} ∣ ϕ_{1} ⟩ ∣ \leq ∣ ⟨ ψ_{0} ∣ ψ_{1} ⟩ ∣.

satisfying

U ∣ ϕ_{i} ⟩ ∣0 ⟩ = ∣ ψ_{i} ⟩ ∣ e_{i} ⟩, i = 0, 1,

exactly when

∣ ⟨ ϕ_{0} ∣ ϕ_{1} ⟩ ∣ \leq ∣ ⟨ ψ_{0} ∣ ψ_{1} ⟩ ∣.

Necessity follows from preservation of inner products. For sufficiency, choose

⟨ e_{0} ∣ e_{1} ⟩

to make the input and output inner products equal; equal two-vector Gram matrices define an isometry that extends to a unitary.

 Ancestors (4)

 Incoming links (1)

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 1 / 10D / c / Solution

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version