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Practical and Fast Gaussian State Estimation

Scott Glancy, National Institute of Standards and Technology

(Session 11 : Saturday from 11:45am - 12:15pm)

Many experiments on quantum systems involve the preparation and measurement of Gaussian states of a multi-system continuous variable Hilbert space. Examples include optical and microwave systems involving squeezing and linear interactions and nanomechanical resonators described with second order Hamiltonians. The state space that these systems access is much smaller than the full Hilbert space and can be fully characterized with a 2Nx2N covariance matrix and 2N means vector, where N is the number of individual modes or resonators. We describe here a very simple and fast method for estimating the covariance matrix and means vector from homodyne (or quadrature) measurement data collected at arbitrary phases. The method computes observed means of simple functions of the homodyne (phase, quadrature) pairs, which are easily related to the covariance matrix and means vector. We characterize uncertainty through a parametric bootstrap strategy. Our method is particularly useful for the analysis of large data sets.