Conference

Suppose you are given m copies of an unknown n-qubit stabilizer state. How many copies do you need before you can figure out exactly what state it is? Just to specify the state requires about n^2/2 bits, so certainly m is at least n/2. Using only single-copy measurements, we show how to identify the state with high probability using m=O(n^2) copies. If one can make joint measurements, O(n) copies is sufficient.This is joint work with Scott Aaronson.

As became apparent during Koenraad\'s talk, there are some important subleties to concepts like \'flat prior\' and \'uniform distribution\'... especially over probability simplices and quantum state spaces. This is a key problem for Bayesian approaches. Perhaps we\'re more interested in Jeffreys priors, Bures priors, or even something induced by the Chernoff bound! I\'d like to start a discussion of the known useful distributions over quantum states & processes, and I nominate Karol Zyckowski to lead it off.

Estimation of quantum Hamiltonian systems is a pivotal challenge to modern quantum physics and especially plays a key role in quantum control. In the last decade, several methods have been developed for complete characterization of a \'superopertor\', which contains all information about a quantum dynamical process. However, it is not fully understood how the estimated elements of the superoperator could lead to a systematic reconstruction of many-body Hamiltonians parameters generating such dynamics. Moreover, it is often desirable to utilize the relevant information obtained from quantum process estimation experiments for optimal control of a quantum device. In this work, we introduce a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we develop a dynamical equation for the evolution of the superoperator acting on the system. This equation does not presume any Markovian or perturbative assumptions, hence it provides a broad framework for analysis of arbitrary quantum dynamics. As a result, we demonstrate that one can efficiently estimate certain classes of Hamiltonians via application of particular quantum process tomography schemes. We also show that, by appropriate modification in the data analysis techniques, the parameter estimation procedures can be implemented with calibrated faulty state generators and measurement devices. Furthermore, we propose an optimal control theoretic approach for manipulating quantum dynamics of Hamiltonian systems, specifically for the task of decoherence suppression.

We report an experiment on reconstructing the quantum state of bright (macroscopic) polarization-squeezed light generated in a birefringent (polarization-maintaining) fibre due to the Kerr nonlinearity. The nonlinearity acts on both H and V polarization components, producing quadrature squeezing; by controlling the phase shift between the H and V components one can make the state squeezed in any Stokes observable. The tomography is performed by measuring histograms for a series of Stokes observables, and the resulting histograms (tomograms) are processed in a way similar to the classical 3D Radon transformation. At the output, we obtain the polarization Q-function, which in the case of large photon numbers coincides with the polarization W-function. An interesting extension of the performed experiment will be going down to lower photon numbers (mesoscopic quantum states), and we expect a different behaviour of polarization W and Q functions in this case. An experiment on producing such states is discussed.

I will discuss a few case studies of coherent control experiments and how we use quantum esstimation to motivate improved experiments. Examples from NMR with physical and logical quits, electron/nuclear spin systems and persistent current flux qubits