Manuscript Em05-A@1 · Em05-A-v1.tex · definition · 9cac0def

Definition: Phase-corrected signed extractor

The complete signed extraction channel › Occupation ordering and the declared isometry · lines 305–326

Em05-A@1#def:extractor, Em05-A@1#eq:Vzero, Em05-A@1#eq:Vone

The map $V_{η} : C^{2} \to H_{R} \otimes H_{E}$ is

V_{η} ∣0 ⟩ V_{η} ∣1 ⟩ = ∣00 ⟩_{R} ∣00 ⟩_{E}, = η ∣11 ⟩_{R} ∣00 ⟩_{E} + η t ∣10 ⟩_{R} ∣01 ⟩_{E} - η t ∣01 ⟩_{R} ∣10 ⟩_{E} + t ∣00 ⟩_{R} ∣11 ⟩_{E} .

Define the accessible and complete complementary channels by

N_{η} (X) = Tr_{E} (V_{η} X V_{η}^{†}), C_{η} (X) = Tr_{R} (V_{η} X V_{η}^{†}) .

Displayed formulas in this passage

Em05-A@1#eq:Vzero · line 308
$V_{η} ∣0 ⟩ V_{η} ∣1 ⟩ = ∣00 ⟩_{R} ∣00 ⟩_{E}, = η ∣11 ⟩_{R} ∣00 ⟩_{E} + η t ∣10 ⟩_{R} ∣01 ⟩_{E} - η t ∣01 ⟩_{R} ∣10 ⟩_{E} + t ∣00 ⟩_{R} ∣11 ⟩_{E} .$
Em05-A@1#eq:Vone · line 308
$V_{η} ∣0 ⟩ V_{η} ∣1 ⟩ = ∣00 ⟩_{R} ∣00 ⟩_{E}, = η ∣11 ⟩_{R} ∣00 ⟩_{E} + η t ∣10 ⟩_{R} ∣01 ⟩_{E} - η t ∣01 ⟩_{R} ∣10 ⟩_{E} + t ∣00 ⟩_{R} ∣11 ⟩_{E} .$
unlabeled · line 321
$N_{η} (X) = Tr_{E} (V_{η} X V_{η}^{†}), C_{η} (X) = Tr_{R} (V_{η} X V_{η}^{†}) .$