Manuscript Em05-B@1 · Em05-B-v1.tex · definition · 6c050f5b

Definition: Phase-corrected signed extractor

The complete signed extraction channel · lines 427–448

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

Define $V_{η} : C^{2} \to H_{R} \otimes H_{E}$ by

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} .

The accessible and complete complementary channels are

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-B@1#eq:Vzero · line 430
$V_{η} ∣0 ⟩ V_{η} ∣1 ⟩ = ∣00 ⟩_{R} ∣00 ⟩_{E}, = η ∣11 ⟩_{R} ∣00 ⟩_{E} + η t ∣10 ⟩_{R} ∣01 ⟩_{E} - η t ∣01 ⟩_{R} ∣10 ⟩_{E} + t ∣00 ⟩_{R} ∣11 ⟩_{E} .$
Em05-B@1#eq:Vone · line 430
$V_{η} ∣0 ⟩ V_{η} ∣1 ⟩ = ∣00 ⟩_{R} ∣00 ⟩_{E}, = η ∣11 ⟩_{R} ∣00 ⟩_{E} + η t ∣10 ⟩_{R} ∣01 ⟩_{E} - η t ∣01 ⟩_{R} ∣10 ⟩_{E} + t ∣00 ⟩_{R} ∣11 ⟩_{E} .$
unlabeled · line 443
$N_{η} (X) = Tr_{E} (V_{η} X V_{η}^{†}), C_{η} (X) = Tr_{R} (V_{η} X V_{η}^{†}) .$