Quantum Estimation: Theory and Practice
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.
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.
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
Quantum information technologies have recorded enormous progress within the recent fifteen years. They have developed from the early stage of thought experiments into nowadays almost ready-to-use technology. In view of many possible applications the question of efficient analysis and diagnostics of quantum systems appears to be crucial. The quantum state is not an observable and as such it cannot be measured in the traditional sense of thisword.
I will briefly describe our recent progress in solving some optimization problems involving metrology with multipath entangled photon states and optimization of quantum operations on such states. We found that in the problem of super-resolution phase measurement in the presence of a loss one can single out two distinct regimes: i) low-loss regime favoring purely quantum states akin the N00N states and ii) high-loss regime where generalized coherent states become the optimal ones.