SECURITY OF QUANTUM CRYPTOGRAPHY VIA SEMIDEFINITE PROGRAMMING

Abstract

Quantum cryptography has gained popularity in the recent years due to its promise of information-theoretic security. However, the security analyses of quantum cryptography based on analytical methods are often tailored to specific protocols as these methods typically rely on some underlying symmetry of the protocol. On the other hand, existing numerical methods are slow because they are based on nonlinear optimisation techniques and require the devices to be fully characterised. In this thesis, we present versatile numerical analyses of quantum cryptography with different levels of device characterisations. Our frameworks are based on semidefinite programming which makes them more computationally efficient than existing numerical frameworks.

In the first part of the thesis, we present a method to analyse the security of protocols with uncharacterised measurements. We give general recipes for one-sided device-independent and measurement-device-independent protocols. Then, we modified the framework to scenarios where only the average energy and the optical modes of the source are characterised. We apply this technique to analyse the security of quantum cryptography under Trojan horse attacks.

In the last part of the thesis, we switch our focus to protocols with fully characterised devices. We present a quantum key distribution protocol that is based on discrete-variable transmitter and homodyne measurement. We then analyse its security using a modification of an existing numerical framework where we recast the optimisation as semidefinite programming.