用不完全测量数据定量验证纠缠度和量子数
Quantitative verification of entanglement and fidelities from incomplete measurement data
摘要：
量子信息领域的许多实验都是以产生多体纠缠态为目标的。量化实际产生的纠缠量原则上可以使用全状态断层扫描来完成。这种方法需要确定一个参数集，该参数集随着量子比特的数量呈指数增长，即使对于中等数量的粒子也变得不可行。然而，从密度矩阵上的部分信息可以得到实验制备的纠缠的非平凡界限。在这种情况下，需要解决的基本问题，然后制定为：什么是最小纠缠的量子态的纠缠内容是兼容的可用测量数据？我们制定的问题数学采用半定规划理论的方法，然后解决这个问题的情况下，实验的目标是创建图形状态。我们考虑的观测量是稳定子组的生成元，因此测量设置的数量仅随量子比特的数量线性增长。我们提供的解析解以及数值方法，可以直接应用到实验中，并比较得到的边界与模拟数据的全状态层析成像的结果。
英文摘要：
Many experiments in quantum information aim at creating multi-partite entangled states. Quantifying the amount of entanglement that was actually generated can, in principle, be accomplished using full-state tomography. This method requires the determination of a parameter set that is growing exponentially with the number of qubits and becomes infeasible even for moderate numbers of particles. Non-trivial bounds on experimentally prepared entanglement can however be obtained from partial information on the density matrix. The fundamental question that needs to be addressed in this context is then formulated as: What is the entanglement content of the least entangled quantum state that is compatible with the available measurement data? We formulate the problem mathematically employing methods from the theory of semi-definite programming and then address this problem for the case, where the goal of the experiment is the creation of graph states. The observables that we consider are the generators of the stabilizer group, thus the number of measurement settings grows only linearly in the number of qubits. We provide analytical solutions as well as numerical methods that may be applied directly to experiments, and compare the obtained bounds with results from full-state tomography for simulated data.
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