论文标题
3D紧凑型光子电路，用于在任何有限维度中实现Qudits的量子状态层析成像
3D compact photonic circuits for realizing quantum state tomography of qudits in any finite dimension
论文作者
论文摘要
在这项工作中，我们提出了三维光子电路设计，以确保电路复杂性的大幅度降低，目的是进行N维路径Qudits的量子状态层析成像。在这项工作中选择的POVM（正算子值量度）确保，对于奇数维度，这种过程是最小的。我们的建议包括组织构成电路作为正方形阵列的波导，由n个垂直扇区组成，由n个波导组成，每个波导都在垂直方向上排列。基于所选POVM的对称性，作用在初始量子系统上的干涉仪可以分为三个不同的单一操作的序列。这些操作在电路的每个垂直扇区或层上独立起作用，从而简化了它们的确定。因此，我们获得了电路，使得梁裂的数量遵守量子系统尺寸的多项式功能，而在当前建议中，该数量以4度的多项式函数增长。除了光学深度从我们方案中的量子系统减小的Quadratics函数降低。这些结果证实了我们提案中光子电路的复杂性的显着降低。
In this work, we propose three-dimensional photonic circuit designs that guarantee a considerable reduction in the complexity of circuits for the purpose of performing quantum state tomography of N-dimensional path qudits. The POVM (Positive Operator-Valued Measure) chosen in this work ensures that, for odd dimensions, such process is minimal. Our proposal consists of organizing the waveguides that form the circuit as a square array formed by N vertical sectors composed of N waveguides each, arranged in the vertical direction. Based on the symmetry of the chosen POVM, the interferometer acting on the initial quantum system can be divided into a sequence of three different unitary operations. These operations act independently on each vertical sector, or layer, of the circuit, which simplifies their determination. We have thus obtained circuits such that the number of beam splitters obeys a polynomial function of degree 3 with the quantum system dimension, whereas in current proposals this quantity grows with a polynomial function of degree 4. Besides that, the optical depth is reduced from a quadratic to a linear function of the quantum system dimension in our scheme. These results confirm the remarkable reduction of the complexity of the photonic circuits in our proposal.
