Relative entropies of quantum channels with applications in resource theory

Abstract

Entropic quantifiers of states lie at the cornerstone of the quantum information theory. While a quantum state can be abstracted as a device that only has outputs, the most general quantum device is a quantum channel that also has inputs. In this work, we extend the entropic quantifiers of states to the ones of channels. In the one-shot and asymptotic scenarios, we propose relative entropies of channels under the task of hypothesis testing. Then, we define the entropy of channels based on relative entropies from the target channel to the completely depolarising channel. We also study properties of relative entropies of channels and the interplay with entanglement. Finally, based on relative entropies of channels, we propose general resource theories of channels and discuss the coherence of general channels and measurements, and the entanglement of channels.

16 pages, 2 figures

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Cited by in corpus (19)

• Operational Resource Theory of Quantum Channels
• Amortized Channel Divergence for Asymptotic Quantum Channel Discrimination
• Resource theory of asymmetric distinguishability for quantum channels
• Quantifying the resource content of quantum channels: An operational approach
• Entropy of a quantum channel
• Universal and Operational Benchmarking of Quantum Memories
• Memory effects in quantum metrology
• One-Shot Manipulation of Dynamical Quantum Resources
• Quantifying dynamical coherence with dynamical entanglement
• Measurement Device Independent Verification of Quantum Channels
• Quantum gate verification and its application in property testing
• One-shot manipulation of entanglement for quantum channels
• Imaginarity of quantum channels: Refinement and Alternative
• Entanglement resource theory of quantum channel
• What is Entropy? A new perspective from games of chance
• One-shot manipulation of coherence in dynamic quantum resource theory
• Relating entropies of quantum channels
• Inevitable Negativity: Additivity Commands Negative Quantum Channel Entropy
• Process tensor distinguishability measures