Quantum channel probing [1,2] is a fundamental task studied in quantum statistical theory. The task is to estimate one or more parameters of a quantum channel based on data collected by quantum measurement of the channel's output using inputs (probes) in prepared quantum states. Different protocols and experiment arrangements are known to improve estimation; for example, by entangling probe states. Quantum Fisher information (through the quantum Cramer-Rao inequality) is the standard tool for assessing the statistical efficiency of a channel probing protocol or design. Channel probing offers many interesting problems --- different channels/parameters (random and fixed), robustness, resource trade-offs, known and new protocols --- for study.
Indefinite causal ordering (ICO) is one experiment design known to aid quantum channel probing . A goal of this research opportunity is to explore different types of ICO for channel probing, to derive the associated quantum Fisher informations, and to interpret them both statistically and physically. Also, ICO-assisted channel probing involves a network of channel copies, with implications for the analogous question of communication across a quantum network.
This post-doctoral research opportunity requires advanced training in estimation theory, experimental design, and linear algebra, as represented, for example, by doctoral study in mathematical statistics. Experience with quantum information science is welcome, but not required. This research opportunity in the Statistical Engineering Division of the National Institute of Standards and Technology (NIST) also offers the researcher opportunities for statistics collaboration in projects across NIST.
 Fujiwara, A., (2001). Quantum Channel Identification Problem. Physical Review A, 63, 042304.
 Frey, M., Collins, D., & Gerlach, K. (2011). Probing the qudit depolarizing channel. Journal of Physics A: Mathematical and Theoretical, 44(20), 205306.
 Frey, M. (2019). Indefinite causal order aids quantum depolarizing channel identification. Quantum Information Processing, 18(4), 96.
Statistical estimation; quantum estimation, Fisher information; channel probing; experiment design