Low-dimensional quite noisy bound entanglement with cryptographic key

TL;DR

This paper introduces a broad class of bound entangled states capable of secure key distillation, including states near the boundary of PPT entangled states, with implications for quantum cryptography and experimental realization.

Contribution

It generalizes previous bound entangled states with key distillation to a wider class, including states with higher entropy and states inside the PPT entangled set.

Findings

Wider class includes states with higher entropy (up to 3.524).

Key distillation requires two-way protocols for the broader class.

States can tolerate noise while maintaining key distillability.

Abstract

We provide a class of bound entangled states that have positive distillable secure key rate. The smallest state of this kind is 4 \bigotimes 4. Our class is a generalization of the class presented in [1] (IEEE Trans. Inf. Theory 54, 2621 (2008); arXiv:quant-ph/0506203). It is much wider, containing, in particular, states from the boundary of PPT entangled states (all of the states in the class in [1] were of this kind) but also states inside the set of PPT entangled states, even, approaching the separable states. This generalization comes with a price: for the wider class a positive key rate requires, in general, apart from the one-way Devetak-Winter protocol (used in [1]) also the recurrence preprocessing and thus effectively is a two-way protocol. We also analyze the amount of noise that can be admixtured to the states of our class without losing key distillability property which may be crucial for experimental realization. The wider class contains key-distillable states with higher entropy (up to 3.524, as opposed to 2.564 for the class in [1]).