For single-shot discrimination of unitary channels, product and maximally entangled probes are equivalent for two channels, but in every dimension at least 3 there are unitary families where non-maximally entangled probes outperform maximally entangled ones.
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Limitation of maximally entangled probes for single-shot distinguishability of unitaries
For single-shot discrimination of unitary channels, product and maximally entangled probes are equivalent for two channels, but in every dimension at least 3 there are unitary families where non-maximally entangled probes outperform maximally entangled ones.