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A Pauli gate applies a Pauli matrix as a unitary operator to a qubit. The Pauli X gate, Pauli Y gate and Pauli Z gate are common correction operations in quantum teleportation.

The rotation gate about the Pauli X gate axis commutes with $X$. The J gate convention gives $J(\alpha )J(0)=H\mathrm{diag}(1,e^{i\alpha })H=e^{i\alpha /2}{R}_x(\alpha )$, differing from the standard axis rotation only by global phase.

The binary Lüders rule measurement of singlet versus triplet preserves the entire triplet subspace, but its nonselective channel permits signalling. Starting with $|00⟩$, Bob retains $|0⟩$. If Alice instead applies a local Pauli X gate, the input is $|10⟩$ and the channel outputs the equal mixture of $|{\Psi }^{+}⟩$ and $|{\Psi }^{-}⟩$; Bob has reduced density matrix $I/2$. Thus no spacelike local implementation can realize this channel. A Bell-state nondemolition measurement has a finer triplet readout and a different nonselective channel, so this obstruction does not exclude it.