Overcoming entropic limitations on asymptotic state transformations through probabilistic protocols
Overcoming entropic limitations on asymptotic state transformations through probabilistic protocols
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DOI：
10.1103/physreva.107.042401
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发表时间：
2022-09
影响因子：
2.9
通讯作者：
Bartosz Regula;Ludovico Lami;M. Wilde
中科院分区：
文献类型：
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作者：
Bartosz Regula;Ludovico Lami;M. Wilde
已知量子相对熵在一般资源理论环境中确定量子态的渐近可转换性中起关键作用，通常构成渐近制度中相关的唯一单调性。我们表明，这不再是这样的情况下，当一个允许随机协议，可能只成功与一些概率，在这种情况下，量子相对熵是不足以表征渐近状态变换的速率，和一个新的熵量的基础上正则化的希尔伯特投影度量开始发挥作用。这样的场景是由这样一种设置激发的，其中与量子态的变换相关联的成本（通常被认为是给定状态的副本数量）被标识为实现协议所需的量子存储器的大小。我们的方法允许构建转换协议，实现严格高于相对熵所施加的速率。针对资源蒸馏这一任务，给出了概率蒸馏协议渐近速率的强匡威界，并证明了它们在相关环境下是紧的，如非纠缠操作的纠缠蒸馏.这概括和扩展了以前已知的仅适用于确定性协议的限制。我们的方法是基于最近的结果，概率一杆变换以及一个新的渐近均分属性的投影相对熵。
The quantum relative entropy is known to play a key role in determining the asymptotic convertibility of quantum states in general resource-theoretic settings, often constituting the unique monotone that is relevant in the asymptotic regime. We show that this is no longer the case when one allows stochastic protocols that may only succeed with some probability, in which case the quantum relative entropy is insufficient to characterize the rates of asymptotic state transformations, and a new entropic quantity based on a regularization of the Hilbert projective metric comes into play. Such a scenario is motivated by a setting where the cost associated with transformations of quantum states, typically taken to be the number of copies of a given state, is instead identified with the size of the quantum memory needed to realize the protocol. Our approach allows for constructing transformation protocols that achieve strictly higher rates than those imposed by the relative entropy. Focusing on the task of resource distillation, we give broadly applicable strong converse bounds on the asymptotic rates of probabilistic distillation protocols, and show them to be tight in relevant settings such as entanglement distillation with non-entangling operations. This generalizes and extends previously known limitations that only applied to deterministic protocols. Our methods are based on recent results for probabilistic one-shot transformations as well as a new asymptotic equipartition property for the projective relative entropy.