paper / renatorenner / 26d ago
The paper investigates the operational justification of independent and identically distributed (IID) state assumptions in information theory. It demonstrates that resources described by "almost-IID" states, arising from operationally motivated symmetry assumptions via de Finetti theorems, are as effective as truly IID states for information processing. This is evidenced by the asymptotic convergence of conditional entropy for almost-IID states to that of IID states.
quantum-physicsinformation-theoryalmost-iid-statesconditional-entropysquashed-entanglementarxiv-paper
“Information-theoretic techniques often rely on the assumption of independent and identically distributed (IID) states.”
paper / renatorenner / Jan 26
Representing quantum system states using outcome probabilities of measurements presents an inherent conflict. To maintain operational meaningfulness, the mapping from a quantum state to its probability representation must exhibit topological robustness. However, this robustness prevents the simultaneous preservation of crucial structural information, such as the subsystem structure of the quantum system.
quantum-physicsquantum-foundationsprobability-distributionsquantum-measurementsquantum-state
“The state of a quantum system can be represented by a vector of outcome probabilities for a set of measurements.”
paper / renatorenner / Oct 16
Quantum nonlocality, distinct from classical correlations, is typically studied in Bell scenarios. However, the more complex triangle network, with its non-convex optimization problems, presents challenges. This research provides the first proof of non-classicality for the Elegant Joint Measurement (EJM) distribution within a triangle network, using a combination of causal inference (inflation), symmetry reductions, and Frank-Wolfe algorithms to derive computer-assisted proofs.
quantum-physicsquantum-systemsquantum-nonlocalitytriangle-networkelegant-joint-measurementcausal-inferenceoptimization
“Quantum systems in a network can exhibit non-classical correlations, a phenomenon known as quantum nonlocality.”
paper / renatorenner / Oct 9
This paper introduces a resource theory of gambling that extends the Kelly criterion to single-shot and finite-betting scenarios. It quantifies the value of a gambler's informational advantage over an odds-maker, revealing an optimal strategy that maximizes the probability of reaching a target return, characterized by Rényi divergences. This framework unifies economic and information-theoretic perspectives and is generalizable to quantum contexts, where quantum information and entanglement play a similar role.
quantum-physicsgame-theoryinformation-theorykelly-criteriondecision-makingrisk-managementresource-theory
“The Kelly criterion, traditionally interpreted for infinite repeated bets, can be extended to single-shot and finite-betting regimes.”
paper / renatorenner / Oct 6
This paper demonstrates a method for extracting uniform randomness from two causally independent processes, even when their inputs are correlated. This advances previous work that assumed conditional independence. The key innovation lies in leveraging spacelike separation to enforce channel independence, enabling randomness generation under more practical and physically justifiable assumptions for device-independent randomness amplification, including situations where an adversary possesses classical side information.
quantum-physicscryptographyrandomness-extractionquantum-informationcausal-independence
“Uniform randomness can be extracted from causally independent processes with potentially correlated inputs.”