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

TL;DR

This paper explores how randomness sources can enable quantum channel implementation, revealing that catalytic processes require uniform randomness and can be enhanced with additional workspace to achieve quantum advantage.

Contribution

It proves a new no-go theorem for quantum channels implemented with randomness sources and clarifies the role of uniform randomness in catalytic quantum processes.

Findings

Quantum channels without information leakage must be catalytic.

Non-degenerate catalysts are classical when no extra dimension is used.

Quantum advantage stems from the uniformness of the randomness source.

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.