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arXiv · 2607.26225

Supermartingales in Quantum Resources Theories: Where do quantum resources go when you're watching?

Katarzyna Macieszczak·Robert L. Jack
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Abstract

We establish a connection between quantum resource theory and probability theory, under repeated application of free operations. We show that strong monotonicity of a resource measure implies that the resource is a supermartingale. We then use the optional stopping and martingale convergence theorems to derive bounds on the efficiency of post-selection, and other free adaptive strategies. We also describe the asymptotic dynamics of the conditional state, where resource fluctuations are necessarily absent, showing one of two distinct phenomena occurs: resource vanishing or resource freezing.

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Katarzyna Macieszczak, Robert L. Jack. 2026-07-28. Supermartingales in Quantum Resources Theories: Where do quantum resources go when you're watching?. https://arxiv.org/abs/2607.26225

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