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

• URL: http://arxiv.org/abs/2010.14795v2
• Date: Thu, 11 Mar 2021 01:56:36 GMT
• Title: Randomness for quantum channels:Genericity of catalysis and quantum advantage of uniformness
• Authors: Seok Hyung Lie and Hyunseok Jeong
• Abstract summary: We first show that every quantum channel that can be implemented with a randomness source without leaking information to it must be a randomness source. Second, we show that non-degenerate catalysts should be used classically when no extra dimension is allowed, which leads to the fact that quantum advantage of a catalytic process strictly comes from the uniformness of the randomness source.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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 first show that every quantum channel that can be implemented with a randomness source without leaking information to it must be a catalysis. For that purpose, we prove a new no-go theorem that generalizes the no-hiding theorem, the no-secret theorem that states no quantum information can be shared with other system as a secret without leaking some information. Second, we show that non-degenerate catalysts should be used classically when no extra dimension is allowed, 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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