Giovannini D, Romero J, Leach J, Dudley A, Forbes A, Padgett M J
School of Physics and Astronomy, SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom.
School of Physics and Astronomy, SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom and Department of Physics, SUPA, University of Strathclyde, Glasgow G4 ONG, United Kingdom.
Phys Rev Lett. 2013 Apr 5;110(14):143601. doi: 10.1103/PhysRevLett.110.143601. Epub 2013 Apr 2.
Mutually unbiased bases (MUBs) play a key role in many protocols in quantum science, such as quantum key distribution. However, defining MUBs for arbitrary high-dimensional systems is theoretically difficult, and measurements in such bases can be hard to implement. We show experimentally that efficient quantum state reconstruction of a high-dimensional multipartite quantum system can be performed by considering only the MUBs of the individual parts. The state spaces of the individual subsystems are always smaller than the state space of the composite system. Thus, the benefit of this method is that MUBs need to be defined for the small Hilbert spaces of the subsystems rather than for the large space of the overall system. This becomes especially relevant where the definition or measurement of MUBs for the overall system is challenging. We illustrate this approach by implementing measurements for a high-dimensional system consisting of two photons entangled in the orbital angular momentum degree of freedom, and we reconstruct the state of this system for dimensions of the individual photons from d = 2 to 5.
相互无偏基（MUBs）在量子科学的许多协议中起着关键作用，例如量子密钥分发。然而，为任意高维系统定义MUBs在理论上是困难的，并且在这样的基下进行测量可能难以实现。我们通过实验表明，仅考虑单个部分的MUBs就可以对高维多体量子系统进行高效的量子态重构。各个子系统的态空间总是小于复合系统的态空间。因此，这种方法的好处是需要为子系统的小希尔伯特空间而不是整个系统的大空间定义MUBs。在为整个系统定义或测量MUBs具有挑战性的情况下，这一点尤为重要。我们通过对由两个在轨道角动量自由度上纠缠的光子组成的高维系统进行测量来说明这种方法，并针对单个光子从d = 2到5的维度重构该系统的状态。
