Generalized self-testing and the security of the 6-state protocol

TL;DR

This paper extends self-testing of quantum apparatus to include complex amplitudes, enabling secure 6-state quantum key distribution within a self-tested framework, overcoming previous limitations to real Hilbert spaces.

Contribution

It introduces a family of complex conjugation-based simulations allowing meaningful self-testing of quantum devices with complex amplitudes, including a secure 6-state QKD protocol.

Findings

Self-testing can be extended to complex amplitudes.

A new family of simulations based on complex conjugation is defined.

Secure 6-state QKD is achievable within this self-tested framework.

Abstract

Self-tested quantum information processing provides a means for doing useful information processing with untrusted quantum apparatus. Previous work was limited to performing computations and protocols in real Hilbert spaces, which is not a serious obstacle if one is only interested in final measurement statistics being correct (for example, getting the correct factors of a large number after running Shor's factoring algorithm). This limitation was shown by McKague et al. to be fundamental, since there is no way to experimentally distinguish any quantum experiment from a special simulation using states and operators with only real coefficients. In this paper, we show that one can still do a meaningful self-test of quantum apparatus with complex amplitudes. In particular, we define a family of simulations of quantum experiments, based on complex conjugation, with two interesting properties. First, we are able to define a self-test which may be passed only by states and operators that are equivalent to simulations within the family. This extends work of Mayers and Yao and Magniez et al. in self-testing of quantum apparatus, and includes a complex measurement. Second, any of the simulations in the family may be used to implement a secure 6-state QKD protocol, which was previously not known to be implementable in a self-tested framework.