Wigner tomography of two qubit states and quantum cryptography

TL;DR

This paper demonstrates how SIC POVM-based tomography, exemplified by the Singapore protocol, optimizes two-qubit state reconstruction for quantum cryptography, highlighting its connection to Wigner representations and proposing a new QKD protocol involving a third party.

Contribution

It introduces the use of SIC POVM tomography in QKD, linking it to Wigner functions, and proposes a novel protocol with third-party control over key generation.

Findings

SIC POVM tomography provides optimal reconstruction accuracy.

Deep connections between SIC POVM and Wigner representations are established.

A new QKD protocol with third-party control is proposed.

Abstract

Tomography of the two qubit density matrix shared by Alice and Bob is an essential ingredient for guaranteeing an acceptable margin of confidentiality during the establishment of a secure fresh key through the Quantum Key Distribution (QKD) scheme. We show how the Singapore protocol for key distribution is optimal from this point of view, due to the fact that it is based on so called SIC POVM qubit tomography which allows the most accurate full tomographic reconstruction of an unknown density matrix on the basis of a restricted set of experimental data. We illustrate with the help of experimental data the deep connections that exist between SIC POVM tomography and discrete Wigner representations. We also emphasise the special role played by Bell states in this approach and propose a new protocol for Quantum Key Distribution during which a third party is able to concede or to deny A POSTERIORI to the authorized users the ability to build a fresh cryptographic key.