Manuscript En04-A@1 · En04-A.tex · section · bab77211

Pauli compression for a Clifford encoder

A genuine Clifford criterion and a responding deformation › Pauli compression for a Clifford encoder · lines 1064–1079

Cliffordness makes this test algebraic; it does not predetermine its answer. The CNOT copying example fails the test because the residual $Z$ compresses to logical $Z$ .

A nonresponding Clifford baseline is

V_{0} ∣ ψ ⟩ = ∣ ψ ⟩_{R} ∣ 0 ⟩_{B} .

A less trivial baseline prepares a Bell syndrome on $R_{1} B$ while keeping $R_{0} = C$ . Then $B$ is fixed in $I_{2} /2$ , even though it is entangled with a radiation syndrome. Constancy does not require a product output or a pure residual.

Displayed formulas in this passage

unlabeled · line 1071
$V_{0} ∣ ψ ⟩ = ∣ ψ ⟩_{R} ∣ 0 ⟩_{B} .$

Nearby in this section

section: Pauli compression for a Clifford encoder
theorem: Theorem: Clifford constancy criterion