Single-shot entanglement manipulation of states and channels revisited

TL;DR

This paper advances the understanding of single-shot entanglement manipulation by deriving explicit formulas for distillation and dilution of pure states and channels, and establishing bounds for mixed states and channels using smooth entropies.

Contribution

It provides compact closed-form expressions for single-shot entanglement distillation and dilution, and links entanglement cost to smooth max-entropy, enhancing computational efficiency and theoretical insight.

Findings

Closed-form expressions for pure state entanglement distillation and dilution.

Exact formula for single-shot entanglement cost of mixed states using smoothed max-entropy.

Bounds on entanglement cost and distillation for channels and states.

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.