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Randomness can help one to implement quantum maps that cannot be realized ina deterministic fashion. Recently, it was discovered that explicitly treating arandomness source as a quantum system could double the efficiency as a catalystfor some tasks. In this work, we first show that every quantum channel that canbe implemented with a randomness source without leaking information to it mustbe a catalysis. For that purpose, we prove a new no-go theorem that generalizesthe no-hiding theorem, the no-secret theorem that states no quantum informationcan be shared with other system as a secret without leaking some information.Second, we show that non-degenerate catalysts should be used classically whenno extra dimension is allowed, which leads to the fact that the quantumadvantage of a catalytic process strictly comes from the uniformness of therandomness source. Finally, we discuss a method to circumvent the previousresult that achieves quantum advantage with non-degenerate catalyst uniformizedby employing extra work space.

Randomness for quantum channels:Genericity of catalysis and quantum advantage of uniformness