Only uniform randomness can yield quantum advantages

Seok Hyung Lie, Hyunseok Jeong

Published Oct 28, 2020• 3 citations

Abstract

Randomness can help one to implement quantum maps that cannot be realized in a deterministic fashion. Recently, it was discovered that explicitly treating a randomness source as a quantum system could double the efficiency as a catalyst for some tasks. In this work, we generalize this result to general randomness-utilizing processes and show that the gap between the efficiencies of classical and quantum catalytic randomness is generic. To explore the achievability of catalysis of quantum randomness, we first show that the second law of thermodynamics holds for general randomness-utilizing processes: the amount of randomness never decreases. Especially, for two important randomization processes, dephasing and erasure maps, randomness sources are forced to be used catalytically, i.e., in such a way that the randomness is preserved exactly. Second, we show that non-degenerate catalysts should be used classically, which leads to the fact that the quantum advantage of a catalytic process strictly comes from the uniformness of the randomness source. Finally, we discuss a method to circumvent the previous result that achieves quantum advantage with non-degenerate catalyst uniformized by employing extra work space.

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