> Abstract: Among the most fundamental questions in the manipulation of quantum resources such as entanglement is the possibility of reversibly transforming all resource states. The key consequence of this would be the identification of a unique entropic resource measure that exactly quantifies the limits of achievable transformation rates. Remarkably, previous results claimed that such asymptotic reversibility holds true in very general settings; however, recently those findings have been found to be incomplete, casting doubt on the conjecture. Here we show that it is indeed possible to reversibly interconvert all states in general quantum resource theories, as long as one allows protocols that may only succeed probabilistically. Although such transformations have some chance of failure, we show that their success probability can be ensured to be bounded away from zero, even in the asymptotic limit of infinitely many manipulated copies. As in previously conjectured approaches, the achievability here is realised through operations that are asymptotically resource non-generating, and we show that this choice is optimal: smaller sets of transformations cannot lead to reversibility. Our methods are based on connecting the transformation rates under probabilistic protocols with strong converse rates for deterministic transformations, which we strengthen into an exact equivalence in the case of entanglement distillation.
> The key consequence of this would be the identification of a unique entropic resource measure that exactly quantifies the limits of achievable transformation rates
IIRC I read on Wikipedia one day that Bell's actually says there's like a 60% error rate?(!)
Also I don't understand QKD 'repeaters'; to 'store a forward' wave function implies that the transmitted wave state is collapsed, but that's not a MITM if it's keyed and time synchronized? Is there no good way to amplify quantum photonic signal without distorting / transforming it?
> smaller sets of transformations cannot lead to reversibility
> FWIU, there are various types of quantum entropy; entanglement and non-entanglement entropy. Quantum discord [2]:
>> In quantum information theory, quantum discord is a measure of nonclassical correlations between two subsystems of a quantum system. It includes correlations that are due to quantum physical effects but do not necessarily involve quantum entanglement.
> "Designing three-way entangled and nonlocal two-way entangled single particle states via alternate quantum walks" (2024) https://arxiv.org/abs/2402.05080 :
>> Herein, we generate three-way entanglement from an initially separable state involving three degrees of freedom of a quantum particle, which evolves via a 2D alternate quantum walk employing a resource-saving single-qubit coin. We achieve maximum possible values for the three-way entanglement quantified by the π-tangle between the three degrees of freedom. We also generate optimal two-way nonlocal entanglement, quantified by the negativity between the nonlocal position degrees of freedom of the particle. This prepared architecture using quantum walks can be experimentally realized with a photon.
Isn't there more total entropy if there is n-way entanglement?
> Abstract: Among the most fundamental questions in the manipulation of quantum resources such as entanglement is the possibility of reversibly transforming all resource states. The key consequence of this would be the identification of a unique entropic resource measure that exactly quantifies the limits of achievable transformation rates. Remarkably, previous results claimed that such asymptotic reversibility holds true in very general settings; however, recently those findings have been found to be incomplete, casting doubt on the conjecture. Here we show that it is indeed possible to reversibly interconvert all states in general quantum resource theories, as long as one allows protocols that may only succeed probabilistically. Although such transformations have some chance of failure, we show that their success probability can be ensured to be bounded away from zero, even in the asymptotic limit of infinitely many manipulated copies. As in previously conjectured approaches, the achievability here is realised through operations that are asymptotically resource non-generating, and we show that this choice is optimal: smaller sets of transformations cannot lead to reversibility. Our methods are based on connecting the transformation rates under probabilistic protocols with strong converse rates for deterministic transformations, which we strengthen into an exact equivalence in the case of entanglement distillation.