de Gois Carlos, Plávala Martin, Schwonnek René, Gühne Otfried
Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany.
Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167, Hannover, Germany.
Phys Rev Lett. 2023 Jul 7;131(1):010201. doi: 10.1103/PhysRevLett.131.010201.
High-dimensional quantum steering can be seen as a test for the dimensionality of entanglement, where the devices at one side are not characterized. As such, it is an important component in quantum informational protocols that make use of high-dimensional entanglement. Although it has been recently observed experimentally, the phenomenon of high-dimensional steering is lacking a general certification procedure. We provide necessary and sufficient conditions to certify the entanglement dimension in a steering scenario. These conditions are stated in terms of a hierarchy of semidefinite programs, which can also be used to quantify the phenomenon using the steering dimension robustness. To demonstrate the practical viability of our method, we characterize the dimensionality of entanglement in steering scenarios prepared with maximally entangled states measured in mutually unbiased bases. Our methods give significantly stronger bounds on the noise robustness necessary to experimentally certify high-dimensional entanglement.
高维量子导引可被视为对纠缠维度的一种检验，其中一侧的设备无需进行特征描述。因此，它是利用高维纠缠的量子信息协议中的一个重要组成部分。尽管最近已通过实验观测到高维导引现象，但高维导引现象仍缺乏通用的认证程序。我们提供了在导引场景中认证纠缠维度的充要条件。这些条件以半定规划层次结构的形式表述，也可用于使用导引维度鲁棒性来量化该现象。为了证明我们方法的实际可行性，我们对在相互无偏基中测量的最大纠缠态所制备的导引场景中的纠缠维度进行了特征描述。我们的方法在实验认证高维纠缠所需的噪声鲁棒性方面给出了显著更强的界限。
