Arcos, Maite; (2025) Information-theoretic approaches to adversarial scenarios, quantum simulation, and quantum gravity. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

This thesis explores connections between information theory, economics, quantum physics, and gravity. Part I introduces adversarial resource theories, extending traditional re-source theories to settings involving strategic interactions. While standard approaches quantify resources for information-processing tasks, they often neglect adversarial or game-theoretic contexts—common in physics, cryptog-raphy, and economics. By incorporating tools from expected utility theory and zero-sum games, the thesis reinterprets Kelly betting through the lens of resource theories. We extend Kelly’s framework to finite-size regimes, formu-lating it as an optimisation problem with defined resources. This yields an equivalence with expected utility maximisation and allows for generalisation to scenarios with asymmetric information. We further show that generalised Kelly strategies arise as Nash equilibria in distributed adversarial games, and extend the formalism to quantum systems, linking it to entanglement concentration. Part II develops a mathematical framework for analogue quantum sim-ulation of fermionic systems using Jordan algebras. Whereas traditional simulations aim to preserve all observables, many practical tasks only re-quire encoding a subset. Our framework rigorously characterises such encodings for finite-dimensional C*-algebras, including the CAR algebra and its even-parity sector. These results addresses challenges in scalable quantum algorithms for fermionic systems. Part III applies holographic techniques to membrane nucleation, a higher-dimensional analogue of the Schwinger effect. We compute nucleation rates in both Minkowski and de Sitter spacetimes at strong coupling. By evaluating the Euclidean on-shell action for membranes coupled to antisymmetric tensor fields completely analytically, we derive exact critical field strengths and rates, offering insights into vacuum decay and non-perturbative quantum gravity.

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