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

• URL: http://arxiv.org/abs/2607.26225v1
• Date: Tue, 28 Jul 2026 20:00:00 GMT
• Title: Supermartingales in Quantum Resources Theories: Where do quantum resources go when you're watching?
• Abstract summary: We show that strong monotonicity of a resource measure implies that the resource is a supermartingale.<n>We derive bounds on the efficiency of post-selection, and other free adaptive strategies.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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