制备-测量场景中绝对纠缠集的认证
Certification of Absolutely Entangled Sets in the Prepare-and-Measure Scenario
- HUN-REN Institute for Nuclear Research（匈牙利研究与创新网络核研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出半设备无关框架，通过SDP层级和见证值上界，在制备-测量场景中系统认证绝对纠缠集，并给出两量子比特随机访问码的具体认证示例。
AI中文摘要：
绝对纠缠集（AES）是一组态的集合，其中至少有一个成员在任何全局酉变换下保持纠缠。我们开发了一个半设备无关框架，用于从维度受限的制备-测量关联中认证这一性质。当见证值超过给定维度下可分离制备所能达到的最大值时，即可排除所有非AES实现。为了对该极限进行上界估计，我们构建了一个针对可分离制备定制的半定规划（SDP）层级。对于两量子比特随机访问码见证，SDP上界与启发式下界在报告精度内一致，从而给出了具体的AES认证。我们还提出了针对包含目标纯态AES的扩展制备集的见证的一般构造方法。基于等角紧框架、最小AES和互不偏基的示例进一步展示了该方法的适用范围。总之，我们的结果为在半设备无关量子信息协议中系统且实验可行地认证AES建立了途径。
英文摘要：
An absolutely entangled set (AES) is a collection of states for which at least one member remains entangled under any choice of global unitary transformation. We develop a semi-device-independent framework for certifying this property from dimensionally bounded prepare-and-measure correlations. A witness value above the maximum attainable with separable preparations of a given dimension rules out every non-AES realization. To upperbound this limit, we construct a semidefinite-programming (SDP) hierarchy tailored to separable preparations. For a two-qubit random-access-code witness, the SDP upper bound and the heuristic lower bound coincide to the reported precision, yielding a concrete AES certification. We also formulate a general construction of witnesses for extended preparation sets containing target pure-state AESs. Examples based on equiangular tight frames, a minimal AES, and mutually unbiased bases further illustrate the scope of the method. In summary, our results establish a systematic and experimentally feasible approach to the certification of AESs in semi-device-independent quantum information protocols.
