Heisenberg exchange echo ($PUPU=e^{-iJtZ\otimes Z}$)

For $H=J(XX+YY+ZZ)/2$, $U=e^{-itH}$, and an individually applied Pauli Z gate $P=Z\otimes I$, conjugation gives $PHP=J(-XX-YY+ZZ)/2$. The paired Pauli operators $XX,YY,ZZ$ commute with one another, soTwo equal free-evolution intervals, each of duration $t$, therefore cancel exchange while retaining the Ising coupling. This spin echo is exact for instantaneous ideal gates; a finite pulse requires accounting for the interaction during the pulse. A simultaneous Pauli Z gate on each spin commutes with $H$ and cannot perform the same cancellation. The physical availability of the individual gate is a separate quantum control requirement.