Ultimate limits of quantum hacking

Quantum key distribution (QKD) protocols have theoretical security proofs showing them to be secure against any possible attack but these proofs make some assumptions which may not hold in real implementations of the protocols. This means that there are a number of weaknesses that can allow QKD protocols to be hacked, such as their fragility against "side channel" attacks. These are attacks where the eavesdropper targets both the quantum channel between Alice and Bob and their setups.
This is an emerging field with important implications for the practical security of next generation secure quantum networks, like the one currently being developed in the UK. Similar approaches may be investigated with the aim of jamming a potential quantum radar, which is a device able to detect faint objects in the regime of extremely low photon numbers. By exploring the ultimate limits of quantum hacking, I will provide important benchmarks for testing fundamental applications of next-generation quantum technologies.
My immediate research will primarily focus on six topics.
1. Practical quantum hacking.
2. Private capacities of quantum channels and quantum channels with side channels.
3. Quantum machine learning of program states.
4. Channel simulation using teleportation stretching.
5. Simulation of channels using port based teleportation (PBT).
6. Development of useful formulae for Gaussian states.
The study of practical quantum hacking will involve studying various QKD protocols (including both DV and CV protocols) in the presence of side-channels of various types. Most immediately, this will focus on an extension to previous work about Trojan horse side-channels in the CV no-switching protocol, considering the effect of attenuation of the Trojan horse mode by the trusted parties.
I will attempt to establish strong bounds on the maximum private capacities of different types of quantum channels and channels with side channels. In order to maximise the private capacity of a channel with a side-channel over all protocols, a clear mathematical model of the side-channel must be developed in such a way that the side-channel definition does not depend on the protocol.
PBT can be used to simulate any possible channel, with the channel simulated depending on the resource state for the protocol (referred to as the program state). By designing a feedback mechanism, it is possible to make a system that "learns" the best program state to simulate a channel. I will attempt to design a system capable of converging to the best possible program state for simulating a given channel, with appropriately designed constraints on the program state.
Study of the last three topics will provide mathematical tools for researching the first three. I will carry out further reading into the literature regarding channel simulation by teleportation stretching. This will contribute to the research into the private capacities of quantum channels. Study of PBT will contribute to both the calculations of the private capacities of various channels and to the research into quantum machine learning of program states.
I will also attempt to develop useful mathematical tools for manipulating Gaussian states. In particular, I will focus on a method for finding the decomposition of the symplectic matrix in terms of simple optical components.
This work will be carried out using both analytical and numerical methods, and will involve the use of maths programs such as Matlab and Mathematica.
Some desired outcomes are to produce mathematical tools to allow calculation of the key rates of QKD protocols in the presence of side-channels of various types, to find theoretical and practical ways to mitigate the effects of side-channels and to find ultimate bounds on the private capacities of channels with side-channels. It is also desirable to produce more general mathematical tools for quantum information science, which could be applied to other open problems in the field.