A-unital Operations and Quantum Conditional Entropy

• URL: http://arxiv.org/abs/2110.12527v3
• Date: Tue, 1 Feb 2022 14:08:07 GMT
• Title: A-unital Operations and Quantum Conditional Entropy
• Authors: Mahathi Vempati, Saumya Shah, Nirman Ganguly, Indranil Chakrabarty
• Abstract summary: We show that A-unital channels are the largest class of conditional entropy non-decreasing channels. We also prove that A-unital channels are precisely the completely free operations for the class of states with non-negative conditional entropy.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Negative quantum conditional entropy states are key ingredients for information theoretic tasks such as superdense coding, state merging and one-way entanglement distillation. In this work, we ask: how does one detect if a channel is useful in preparing negative conditional entropy states? We answer this question by introducing the class of A-unital channels, which we show are the largest class of conditional entropy non-decreasing channels. We also prove that A-unital channels are precisely the completely free operations for the class of states with non-negative conditional entropy. Furthermore, we study the relationship between A-unital channels and other classes of channels pertinent to the resource theory of entanglement. We then prove similar results for ACVENN: a previously defined, relevant class of states and also relate the maximum and minimum conditional entropy of a state with its von Neumann entropy. The definition of A-unital channels naturally lends itself to a procedure for determining membership of channels in this class. Thus, our work is valuable for the detection of resourceful channels in the context of conditional entropy.

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