Single-shot entanglement manipulation of states and channels revisited
arxiv(2023)
摘要
We study entanglement distillation and dilution of states and channels in the
single-shot regime. With the help of a recently introduced conversion distance,
we provide compact closed-form expressions for the dilution and distillation of
pure states and show how this can be used to efficiently calculate these
quantities on multiple copies of pure states. These closed-form expressions
also allow us to obtain second-order asymptotics. We then prove that the
epsilon-single-shot entanglement cost of mixed states is given exactly in terms
of an expression containing a suitably smoothed version of the conditional
max-entropy. For pure states, this expression reduces to the smoothed
max-entropy of the reduced state. Based on these results, we bound the
single-shot entanglement cost of channels. We then turn to the one-way
entanglement distillation of states and channels and provide bounds in terms of
a quantity we denote coherent information of entanglement.
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