arXiv 1310.35302013-10quant-ph

双量子比特态的对称扩张

Symmetric Extension of Two-Qubit States

Jianxin Chen, Zhengfeng Ji, David Kribs, Norbert Lütkenhaus, Bei Zeng

备注：: 10 pages, no figure. comments are welcome. Version 2: introduction rewritten
发表信息：: Phys. Rev. A 90, 032318 (2014)
DOI：: 10.1103/PhysRevA.90.032318

摘要：

量子密钥分发使用公共讨论协议来建立共享密钥。在探索这类协议的极限时，底层二分态$ρ_{AB}$的对称可扩展性的性质起着重要的作用。如果存在三分状态$ρ_{ABB'}$，则二分状态$ρ_{AB}$是对称可扩展的，使得$AB$边缘状态与$AB'$边缘状态相同，即$ρ_{AB'}=ρ_{AB}$。对于对称可扩展状态$ρ_{AB}$，公共讨论协议的首要任务是打破这种对称可扩展性。因此刻画所有具有对称扩张的二分量子态是非常重要的。我们证明了一个简单的解析公式，即两量子比特态$ρ_{AB}$允许对称扩张当且仅当$\tr(ρ_B^2)\geq \tr(ρ_{AB}^2)-4\sqrt{\det{ρ_{AB}}}$。考虑到对称扩张问题与量子边际问题之间的密切关系，我们的结果也为具有重叠边际的量子边际问题提供了第一个解析的充分必要条件.

英文摘要：

Quantum key distribution uses public discussion protocols to establish shared secret keys. In the exploration of ultimate limits to such protocols, the property of symmetric extendibility of underlying bipartite states $ρ_{AB}$ plays an important role. A bipartite state $ρ_{AB}$ is symmetric extendible if there exits a tripartite state $ρ_{ABB'}$, such that the $AB$ marginal state is identical to the $AB'$ marginal state, i.e. $ρ_{AB'}=ρ_{AB}$. For a symmetric extendible state $ρ_{AB}$, the first task of the public discussion protocol is to break this symmetric extendibility. Therefore to characterize all bi-partite quantum states that possess symmetric extensions is of vital importance. We prove a simple analytical formula that a two-qubit state $ρ_{AB}$ admits a symmetric extension if and only if $\tr(ρ_B^2)\geq \tr(ρ_{AB}^2)-4\sqrt{\det{ρ_{AB}}}$. Given the intimate relationship between the symmetric extension problem and the quantum marginal problem, our result also provides the first analytical necessary and sufficient condition for the quantum marginal problem with overlapping marginals.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文