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• W3208587035 abstract "The significance of negative quantum conditional entropy is underscored by its ubiquity in information processing tasks like dense coding, state merging and one-way entanglement distillation. Mere presence of entanglement is not sufficient for these tasks, a fact underpinned by the existence of entangled quantum states with non-negative conditional entropy. This stimulates one to go beyond the paradigm of entanglement theory and probe the hitherto unexplored area of operations influencing quantum conditional entropy. To this end, we introduce the class of A-unital channels. We characterize them and demonstrate that A-unital channels are to states having non-negative conditional entropy what separable channels are to separable states. We also show that A-unital channels form the largest class of channels that do not decrease the conditional entropy of any state, a relation analogous to unital channels and entropy. A comparative study between A-unital and other channels crucial to the resource theory of entanglement is done to further exemplify the distinction with entanglement theory. Contrary to the apparent view that non-local unitary operations can decrease conditional entropy to sub-zero levels, there exist states whose conditional entropy remains non-negative even under this action. Termed as states having absolute conditional entropy, they prove to be robust against non-local unitary action. In the present submission, the completely free operations for such states are also characterized. Finally, since von Neumann entropy is the mainspring of these discussions, the bounds on the conditional entropy of states having a given entropy are derived. The definition of A-unital channels naturally lends itself to a procedure for determining membership of channels in this class. Thus, this work is valuable for the detection of resourceful channels in the context of conditional entropy." @default.
• W3208587035 created "2021-11-08" @default.
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• W3208587035 date "2021-10-24" @default.
• W3208587035 modified "2023-09-27" @default.
• W3208587035 title "A-unital Operations and Quantum Conditional Entropy" @default.
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• W3208587035 hasPublicationYear "2021" @default.
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