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One promising approach is to encode information not in individual quantum particles, such as single photons, but in properties of light that can vary smoothly, such as its amplitude and phase. These so-called continuous-variable quantum systems can be prepared and measured using technology closely related to the optical communication systems already used to transmit information.

This connection to existing technology makes continuous-variable systems attractive for practical applications. At the same time, it raises an important question: how much of the potential of quantum cryptography can actually be realised when real-world limitations such as signal loss, noise and measurement precision are taken into account?

PhD researcher Arpan Ray investigated this question by exploring how continuous-variable quantum systems can be used for both established and new cryptographic applications. He defended his PhD thesis at the Department of Mathematics and Computer Science on Tuesday, September 15.

Going beyond secure key exchange

One of the best-known applications of quantum cryptography is . It allows two parties to create a shared secret key that can later be used to encrypt messages. The laws of quantum physics make it possible to detect whether someone has tried to intercept the information while the key is being created.

A major challenge appears when the two parties are far apart. As the quantum signals travel through an optical fibre, they become weaker and are affected by noise. As a result, the two parties' measurements become less alike. Before they can use their measurements as a shared key, they need to correct their data and agree on the same information.

Arpan Ray developed a method based on randomly generated codebooks that allows this correction process to be carried out efficiently and in parallel. This is particularly useful when the signals are very weak, as they are over long distances. His approach also takes into account an important security issue: if some measurement data are discarded because they are too noisy, that decision can itself reveal information to an attacker.

Ray therefore includes this effect in the security analysis rather than treating it as a separate implementation detail.

Verifying where someone really is

Quantum cryptography can also be used for a very different purpose: checking someone's location.

Imagine that a person claims to be at a particular place. aims to test that claim using the laws of quantum physics and the fact that information cannot travel faster than light. Information can be sent from different locations and the responses can then be checked to determine whether they could really have come from the claimed position.

In practice, however, signals lose energy and pick up noise as they travel. Attackers may also work together and already share quantum resources. Ray studied how these imperfections affect the security of continuous-variable position-verification protocols.

His results show under which conditions the protocols can remain secure and how the security depends on factors such as signal loss, noise and the quantum resources available to attackers. This provides a way to connect the theoretical security of these protocols to the conditions that would occur in a real optical system.

Making quantum encryption harder to copy

A third part of the research looks at a different advantage of quantum information: unknown quantum states cannot in general be copied perfectly.

Ray investigated how this property can be used to create unclonable encryption. In such a system, an authorised recipient can decrypt a message, but an attacker cannot split the quantum-encrypted information into two parts that would both allow someone to decrypt the message later.

He developed two different approaches. The first uses specially prepared quantum states and relies on fundamental limits on how quantum information can be shared between different parties. The analysis also takes realistic effects such as limited signal strength, loss and noise into account.

The second approach provides an even stronger form of security. Even after the encryption key is revealed, two attackers who have divided the quantum ciphertext between them should not both be able to determine which of two possible messages was encrypted.

To achieve this, he developed a way of generating controlled quantum randomness that mimics the behaviour of truly random quantum operations while still taking the limitations of real optical systems into account.