An effective maximum likelihood method is suggested to characterize the absorption/amplification properties of active optical media through homodyne detection.
We propose a refined iterative likelihood-maximization algorithm for reconstructing a quantum state from a set of tomographic measurements. The algorithm is characterized by a very high convergence rate and features a simple adaptive procedure that ensures likelihood increase in every iteration and convergence to the maximum-likelihood state. We apply the algorithm to homodyne tomography of optical states and quantum tomography of entangled spin states of trapped ions and investigate its convergence properties.
It is shown that holomorphic (infinitely differentiable) video signals of sufficient duration are, in principle, capable of propagating in an environment with population inversion (and gain dominance over absorption at least at low frequencies) without significant distortion and significant amplification at a superluminal group velocity. The practical implementation of this effect is limited not so much by the distortion or amplification of the video signal itself, as by the maximum size (and amplification of extraneous signals at the maximum gain frequency) of actually existing active media. At best, with reasonable amplification coefficients of real-world active media, one can hope for the amount of time ahead of the vacuum speed of light by the video signal on the order of its own duration.
We present a fully Gaussian and experimentally feasible scheme for the simultaneous estimation of the four real parameters that characterize a two-channel optical network. The scheme utilizes a two-mode squeezed probe and balanced homodyne detection at both output ports, for which we derive the complete classical Fisher information matrix analytically. Our scheme achieves the Heisenberg-scaling sensitivity for all four parameters simultaneously, enabling full multiparameter characterization of the two-channel interferometric network. We further show, by maximum-likelihood estimation, that the corresponding multiparameter Cramér-Rao bounds are saturated with a modest number of experimental repetitions and for low photon number. The scheme establishes a practical route to Heisenberg-scaling multiparameter Gaussian metrology for a two-channel network, with direct relevance to calibration and sensing in integrated photonics and distributed quantum-enhanced measurement architectures.