Tight constraints on probabilistic convertibility of quantum states
Tight constraints on probabilistic convertibility of quantum states
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DOI：
10.22331/q-2022-09-22-817
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发表时间：
2021-12
期刊：
影响因子：
6.4
通讯作者：
Bartosz Regula
中科院分区：
文献类型：
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作者：
Bartosz Regula
受某些量子资源理论的限制，我们发展了两种利用概率协议来描述量子态操纵的一般方法。首先，我们给出了利用最近引入的基于Hilbert射影度规的资源单调得到的量子态之间存在物理变换的一般必要条件。在所有的仿射量子资源理论中(如相干性、不对称性、形象性)以及在纠缠蒸馏中，我们证明了单调为非资源生成操作下的一次资源转换提供了一个充要条件，因此对所有概率协议都不可能有更好的限制。我们使用单调建立了改进的单次概率资源提取协议和多拷贝概率资源提取协议的性能界限。作为对这一方法的补充，我们通过一族凸优化问题介绍了在资源非生成映射下确定资源转换可实现概率的一般方法。我们展示了它在广泛类型的资源理论中紧密地描述了单次概率蒸馏的特征，允许准确地分析在蒸馏最大资源状态时的概率和误差之间的权衡。我们证明了这两种方法在量子纠缠蒸馏研究中的有效性。
We develop two general approaches to characterising the manipulation of quantum states by means of probabilistic protocols constrained by the limitations of some quantum resource theory. First, we give a general necessary condition for the existence of a physical transformation between quantum states, obtained using a recently introduced resource monotone based on the Hilbert projective metric. In all affine quantum resource theories (e.g. coherence, asymmetry, imaginarity) as well as in entanglement distillation, we show that the monotone provides a necessary and sufficient condition for one-shot resource convertibility under resource-non-generating operations, and hence no better restrictions on all probabilistic protocols are possible. We use the monotone to establish improved bounds on the performance of both one-shot and many-copy probabilistic resource distillation protocols. Complementing this approach, we introduce a general method for bounding achievable probabilities in resource transformations under resource-non-generating maps through a family of convex optimisation problems. We show it to tightly characterise single-shot probabilistic distillation in broad types of resource theories, allowing an exact analysis of the trade-offs between the probabilities and errors in distilling maximally resourceful states. We demonstrate the usefulness of both of our approaches in the study of quantum entanglement distillation.