Manuscript En01-A@1 · En01-A.tex · section · 558b972b

Three different recording interfaces

Recorded circuits and the two statistical models › Three different recording interfaces · lines 790–826

En01-A@1#eq:coherentcopy, En01-A@1#eq:destructive, En01-A@1#eq:nondestructive

For a measured factor $S$ , an untouched factor $B$ , and a computational basis ${∣ z ⟩_{S}}$ , coherent recording is the isometry

V (∣ z ⟩_{S} \otimes ∣ b ⟩_{B}) = ∣ z ⟩_{S} \otimes ∣ z ⟩_{A} \otimes ∣ b ⟩_{B} .

It retains $S$ and a quantum carrier $A$ . It does not make $A$ a classical register in the sense of a joint block-diagonal output state.

By contrast, destructive readout is the channel

M_{S} (Y) = z \sum ∣ z ⟩ ⟨ z ∣_{R} \otimes (⟨ z ∣_{S} \otimes 1_{B}) Y (∣ z ⟩_{S} \otimes 1_{B}),

whose output does not contain $S$ .

A represented nondestructive projective instrument has a third output:

I_{S}^{nd} (Y) = z \sum ∣ z ⟩ ⟨ z ∣_{R} \otimes P_{z} Y P_{z}, P_{z} = ∣ z ⟩ ⟨ z ∣_{S} \otimes 1_{B} .

It retains $S$ , but its output record $R$ is classical. These three maps have different declared outputs and are not identified.

The circuits studied here use (eq:coherentcopy). The nonselective comparator arises by tracing its additional carrier, not by renaming (eq:coherentcopy) as (eq:destructive).

Displayed formulas in this passage

En01-A@1#eq:coherentcopy · line 794
$V (∣ z ⟩_{S} \otimes ∣ b ⟩_{B}) = ∣ z ⟩_{S} \otimes ∣ z ⟩_{A} \otimes ∣ b ⟩_{B} .$
En01-A@1#eq:destructive · line 804
$M_{S} (Y) = z \sum ∣ z ⟩ ⟨ z ∣_{R} \otimes (⟨ z ∣_{S} \otimes 1_{B}) Y (∣ z ⟩_{S} \otimes 1_{B}),$
En01-A@1#eq:nondestructive · line 813
$I_{S}^{nd} (Y) = z \sum ∣ z ⟩ ⟨ z ∣_{R} \otimes P_{z} Y P_{z}, P_{z} = ∣ z ⟩ ⟨ z ∣_{S} \otimes 1_{B} .$