Tomographic Quantum Cryptography Protocols are Reference Frame Independent

TL;DR

This paper analyzes reference frame independent quantum key distribution protocols in higher dimensions, relating them to tomographically complete protocols and discussing finite key bounds, aiming to improve their security estimates.

Contribution

It connects existing protocols to tomographically complete schemes and compares approaches to finite key bounds, proposing potential improvements.

Findings

Existing finite key bounds can be improved.

Relation established between reference frame independent and tomographically complete protocols.

Discussion on two approaches to finite key bounds.

Abstract

We consider the class of reference frame independent protocols in d dimensions for quantum key distribution, in which Alice and Bob have one natural basis that is aligned and the rest of their frames are unaligned. We relate existing approaches to tomographically complete protocols. We comment on two different approaches to finite key bounds in this setting, one direct and one using the entropic uncertainty relation and suggest that the existing finite key bounds can still be improved.