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

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.

arXiv comment9 pages, 3 figures; close to the version accepted in Physical Review Research

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Cited by in corpus (8)

• Catalysis of entanglement and other quantum resources
• The Min-entropy as a Resource for One-Shot Private State Transfer, Quantum Masking and State Transition
• Catalysis in Action via Elementary Thermal Operations
• Catalysis always degrades external quantum correlations
• Complete Characterization of Entanglement Embezzlement
• Faithfulness and sensitivity for ancilla-assisted process tomography
• Delocalized and Dynamical Catalytic Randomness and Information Flow
• Thermal operations from informational equilibrium