TY - JOUR
T1 - Symmetric Extension of Two-Qubit States
JF - Physical Review A
Y1 - 2014
A1 - Jianxin Chen
A1 - Zhengfeng Ji
A1 - David Kribs
A1 - Norbert Lütkenhaus
A1 - Bei Zeng
AB - 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 $\rho_{AB}$ plays an important role. A bipartite state $\rho_{AB}$ is symmetric extendible if there exits a tripartite state $\rho_{ABB'}$, such that the $AB$ marginal state is identical to the $AB'$ marginal state, i.e. $\rho_{AB'}=\rho_{AB}$. For a symmetric extendible state $\rho_{AB}$, 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 $\rho_{AB}$ admits a symmetric extension if and only if $\tr(\rho_B^2)\geq \tr(\rho_{AB}^2)-4\sqrt{\det{\rho_{AB}}}$. 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.
VL - 90
UR - http://arxiv.org/abs/1310.3530v2
CP - 3
J1 - Phys. Rev. A
U5 - 10.1103/PhysRevA.90.032318
ER -