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The distillable entanglement of a bipartite quantum state does not exceed its entanglement cost. This well known inequality can be understood as a second law of entanglement dynamics in the asymptotic regime of entanglement manipulation, excluding the possibility of perpetual entanglement extraction machines that generate boundless entanglement from a finite reserve. In this paper, I establish a refined second law of entanglement dynamics that holds for the non-asymptotic regime of entanglement manipulation. 

Abstract We develop a resource theory of symmetric distinguishability, the fundamental objects of which are elementary quantum information sources, i.e. sources that emit one of two possible quantum states with given prior probabilities. Such a source can be represented by a classical-quantum state of a composite system XA , corresponding to an ensemble of two quantum states, with X being classical and A being quantum. We study the resource theory for two different classes of free operations: (i) CPTP A , which consists of quantum channels acting only on A , and (ii) conditional doubly stochastic maps acting on XA . We introduce the notion of symmetric distinguishability of an elementary source and prove that it is a monotone under both these classes of free operations. We study the tasks of distillation and dilution of symmetric distinguishability, both in the one-shot and asymptotic regimes. We prove that in the asymptotic regime, the optimal rate of converting one elementary source to another is equal to the ratio of their quantum Chernoff divergences, under both these classes of free operations. This imparts a new operational interpretation to the quantum Chernoff divergence. We also obtain interesting operational interpretations of the Thompson metric, in the context of the dilution of symmetric distinguishability.