论文标题
量子状态断层扫描作为数值优化问题
Quantum state tomography as a numerical optimization problem
论文作者
论文摘要
我们提出了一个框架，该框架将最有效的量子层析成像方案的追求作为优化问题，可以通过数值解决。该方法可以应用于广泛的相关设置，包括限于子系统的测量。为了说明这种方法的力量，我们提出了由Qubit-Qutrit系统构成的六维Hilbert空间的结果，可以实现，例如由Diamond的Nitro-Spin-1和两个电子自旋状态的N-14核自旋状态。量子组子系统的测量值由等级第三的投影仪，即半维子空间的投影仪表示。对于仅由Qubits组成的系统，可以在分析上表明，可以以信息为量子状态层析成像的信息最佳方式安排一组投影仪，从而形成所谓的相互无偏的子空间。我们的方法超出了仅量子位的系统，我们发现在第六个尺寸中，这样的一组相互宣传的子空间可以与与实际应用无关的偏差近似。
We present a framework that formulates the quest for the most efficient quantum state tomography scheme as an optimization problem which can be solved numerically. This approach can be applied to a broad spectrum of relevant setups including measurements restricted to a subsystem. To illustrate the power of this method we present results for the six-dimensional Hilbert space constituted by a qubit-qutrit system, which could be realized e.g. by the N-14 nuclear spin-1 and two electronic spin states of a nitrogen-vacancy center in diamond. Measurements of the qubit subsystem are expressed by projectors of rank three, i.e., projectors on half-dimensional subspaces. For systems consisting only of qubits, it was shown analytically that a set of projectors on half-dimensional subspaces can be arranged in an informationally optimal fashion for quantum state tomography, thus forming so-called mutually unbiased subspaces. Our method goes beyond qubits-only systems and we find that in dimension six such a set of mutually-unbiased subspaces can be approximated with a deviation irrelevant for practical applications.
