The operator entanglement of two-qubit gates is quantified by Schmidt strength and linear entropy. It is known that the measures are inequivalent in capturing the nonlocal features of two-qubit operators. While Schmidt strength is known to be violating chaining property, in this paper, we show that the linear entropy also fails to satisfy the property. Further, we argue that the chaining property of the measures does not provide a tight lower bound on the number of gates required to perform a particular quantum operation.
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