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.
Highlights
The myriad information-theoretic applications of entanglement [1] have elevated it from being merely an interesting physical phenomenon to that of a resource
We show that while A-unital channels are the largest class of completely free channels for Fc(A|B), unital channels form the largest class of completely free channels for a previously defined, related set F ac(A|B), the set of all states whose conditional entropy remains non-negative under global unitary operations
We introduce the class of A-unital channels, and show that this is equal to the largest class of completely free channels for the set of states with non-negative conditional entropy (Fc(A|B))
Summary
The myriad information-theoretic applications of entanglement [1] have elevated it from being merely an interesting physical phenomenon to that of a resource. We prove that this class is exactly equal to Occmax(A|B), the largest class of completely free channels for F c(A|B), and is elegantly characterized by a property we call A-unitality.
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