ИСТИНА

Quantum state tomography is an essential tool required for the development and debugging of quantum devices. One of its goals is to provide estimation with higher fidelity for a given number of measured copies of the input state. Usually, this goal is achieved using adaptive measurements, where the measurement sequence is constantly tuned to an estimator of the input state. The authors of recent work [1] proposed a novel adaptive tomographic protocol that does not resolve to a decomposition of unity. Therefore it can be more advantageous in terms of achievable fidelity than conventional protocols, which form a decomposition of unity. During protocol development, the authors rely on an analogy from special relativity theory. We reformulate the protocol in terms of rank-preserving (RP) transformations of density matrices (so this protocol will be denoted as RP). The original work [1] contains only numerical study. We present an experimental realization of RP protocol. The experiments are performed with polarization degrees of freedom of single photons. Photons are produced using a heralded single-photon source, where a type-II spontaneous parametric down-conversion with a degenerate collinear phase matching in a PPKTP crystal occurs. We compare the performance of the adaptive RP protocol with measurements in random bases and with another adaptive strategy (Eigen), which includes measurements in the eigenbasis of the current estimate [2]. As expected, infidelity scaling for both adaptive schemes is 1-F = c/N with the number N of input states. However, prefactor c for RP is approximately two times smaller as the one for Eigen protocol. Also, we numerically investigated several protocol modifications. They include complementation to the decomposition of unity and different choices of the underlying protocol, which is subject to RP transformation. We find that, when the protocol is complemented, its accuracy drops and becomes similar to Eigen protocol. The change of the underlying protocol hardly affects RP protocol accuracy. [1] Yu. I. Bogdanov, N. A. Bogdanova, B. I. Bantysh, Yu. A. Kuznetsov, "The concept of weak measurements and the super-efficiency of quantum tomography," Proc. SPIE 11022, International Conference on Micro- and Nano-Electronics 2018, 110222O (15 March 2019). [2] D. H. Mahler, Lee A. Rozema, Ardavan Darabi, Christopher Ferrie, Robin Blume-Kohout, and A. M. Steinberg "Adaptive Quantum State Tomography Improves Accuracy Quadratically," Phys. Rev. Lett. 111, 183601 (2013)