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Resource theory of unextendibility and nonasymptotic quantum capacity
Physical Review A ( IF 2.9 ) Pub Date : 2021-08-02 , DOI: 10.1103/physreva.104.022401
Eneet Kaur , Siddhartha Das , Mark M. Wilde , Andreas Winter

In this paper, we introduce the resource theory of unextendibility as a relaxation of the resource theory of entanglement. The free states in this resource theory are the k-extendible states, associated with the inability to extend quantum entanglement in a given quantum state to multiple parties. The free channels are k-extendible channels, which preserve the class of k-extendible states. We define several quantifiers of unextendibility by means of generalized divergences and establish their properties. By utilizing this resource theory, we obtain nonasymptotic upper bounds on the rate at which quantum communication or entanglement preservation is possible over a finite number of uses of an arbitrary quantum channel assisted by k-extendible channels at no cost. These bounds are significantly tighter than previously known bounds for both the depolarizing and erasure channels. Finally, we revisit the pretty strong converse for the quantum capacity of antidegradable channels and establish an upper bound on the nonasymptotic quantum capacity of these channels.

中文翻译:

不可扩展性和非渐近量子容量的资源理论

在本文中,我们引入了不可扩展的资源理论,作为对纠缠资源理论的放松。该资源理论中的自由状态是- 可扩展状态,与无法将给定量子状态中的量子纠缠扩展到多方有关。免费频道是- 可扩展的通道,保留了 - 可扩展的状态。我们通过广义发散定义了几个不可扩展性的量词并建立了它们的属性。通过利用这种资源理论,我们获得了在有限次数的任意量子信道的辅助下使用量子通信或纠缠保持可能的速率的非渐近上限- 免费的可扩展渠道。这些界限比之前已知的去极化和擦除通道的界限要严格得多。最后,我们重新审视了抗降解通道的量子容量的强逆,并建立了这些通道的非渐近量子容量的上限。
更新日期:2021-08-02
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