Quantum Control and Measurement Tools for Cold Atom Qudits
Quantum control and measurement over complex systems plays an important role in quantum information science. The use of large state space systems (qudits) may prove advantageous for quantum information tasks if good laboratory tools for qudit control can be developed. Over the past years we have implemented a protocol for arbitrary unitary transformations in the 16 dimensional hyperfine ground manifold of Cesium 133 atoms, driving the system with phase modulated rf and microwave magnetic fields and using the tools of optimal control to find appropriate control waveforms. More recently, we have focus our attention in the development of good ways to characterize the behavior of our system. In principle quantum tomography (QT) is an ideal tool, capable of providing complete information about an unknown state (QST) or process (QPT). In practice, the protocols used for QT are resource intensive and scale poorly with system size. Theoretical work on QST has identified sets of POVM elements that are optimal under varying assumptions, in each case prescribing a minimal number of measurements of a given structure. Laboratory exploration of these POVM constructions has, however, been constrained by the ability to control SPAM errors and generate accurate test states and processes in all but the simplest quantum systems. Here we present the findings from a comprehensive experimental study comparing 6 different POVM constructions and 3 different state estimators, using our 16 dimensional system as our testbed. Our results show a clear trade-off between efficiency and robustness to experimental error, with mutually unbiased bases achieving the best compromise in our system and reaching a QST fidelity of ~98% in d = 16. We have further used a minimal set of intelligently chosen probe states to implement QPT, testing the scheme on randomly chosen unitary processes in Hilbert spaces of varying dimension, and reaching a QPT fidelity of ~90% in d = 16.