Related papers: Compactly accessible categories and quantum key di…
We explore finite-field frameworks for quantum theory and quantum computation. The simplest theory, defined over unrestricted finite fields, is unnaturally strong. A second framework employs only finite fields with no solution to x^2+1=0,…
The familiar adjunction between ordered sets and completely distributive lattices can be extended to generalised metric spaces, that is, categories enriched over a quantale (a lattice of "truth values"), via an appropriate distributive law…
We prove the security of Gaussian continuous-variable quantum key distribution against arbitrary attacks in the finite-size regime. The novelty of our proof is to consider symmetries of quantum key distribution in phase space in order to…
In this work, we use tools from non-standard analysis to introduce infinite-dimensional quantum systems and quantum fields within the framework of Categorical Quantum Mechanics. We define a dagger compact category *Hilb suitable for the…
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…
We take quantum theory and replace $\mathbb{C}$ by $\mathbb{C}[\varepsilon]$ where $\varepsilon^2=0$, i.e. we extend quantum theory to the ring of dual complex numbers. The aim is to develop a common language in which to treat continuous…
Harnessing the potential computational advantage of quantum computers for machine learning tasks relies on the uploading of classical data onto quantum computers through what are commonly referred to as quantum encodings. The choice of such…
We formalize the simulation paradigm of cryptography in terms of category theory and show that protocols secure against abstract attacks form a symmetric monoidal category, thus giving an abstract model of composable security definitions in…
The field of quantum information is becoming more known to the general public. However, effectively demonstrating the concepts underneath quantum science and technology to the general public can be a challenging job. We investigate, extend,…
We investigate the main limitations which prevent the continuous-variable quantum key distribution protocols from achieving long distances in the finite-size setting. We propose a double-modulation protocol which allows using each state for…
Quantum key distribution (QKD) provides secure keys resistant to code-breaking quantum computers. As headed towards commercial application, it is crucial to guarantee the practical security of QKD systems. However, the difficulty of…
Quantum key distribution (QKD) is a family of protocols for growing a private encryption key between two parties. Despite much progress, all ground-based QKD approaches have a distance limit due to atmospheric losses or in-fibre…
There is a big gap between theory and practice in quantum key distribution (QKD) because real devices do not satisfy the assumptions required by the security proofs. Here, we close this gap by introducing a simple and practical…
Distributed quantum information processing seeks to overcome the scalability limitations of monolithic quantum devices by interconnecting multiple quantum processing nodes via classical and quantum communication. This approach extends the…
For any small quantaloid $\Q$, there is a new quantaloid $\D(\Q)$ of diagonals in $\Q$. If $\Q$ is divisible then so is $\D(\Q)$ (and vice versa), and then it is particularly interesting to compare categories enriched in $\Q$ with…
In this didactical note I review in depth the rationale for using generalised canonical distributions in quantum statistics. Particular attention is paid to the proper definitions of quantum entropy and quantum relative entropy, as well as…
Quantum key distribution (QKD) is the first quantum information task to reach the level of mature technology, already fit for commercialization. It aims at the creation of a secret key between authorized partners connected by a quantum…
We demonstrate that, in certain cases, quantization and the classical limit provide functors that are "almost inverse" to each other. These functors map between categories of algebraic structures for classical and quantum physics,…
Quantum key distribution (QKD) promises information-theoretic security based on quantum mechanics and idealized device models. Practical implementations, however, deviate from these models due to unavoidable device imperfections, and…
In continuous-variable quantum computation, identifying key elements that enable a quantum computational advantage is a long-standing issue. Starting from the standard results on the necessity of Wigner negativity, we develop a…