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arXiv · 2312.17088

Single-shot entanglement manipulation of states and channels revisited

Thomas Theurer·Kun Fang·Gilad Gour
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Abstract

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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Thomas Theurer, Kun Fang, Gilad Gour. 2023-12-28. Single-shot entanglement manipulation of states and channels revisited. https://doi.org/10.1109/tit.2025.3570770

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