Dual-path state reconstruction scheme for propagating quantum microwaves and detector noise tomography

Quantum state reconstruction involves measurement devices that are usually described by idealized models, but not known in full detail in experiments. For weak propagating microwaves, the detection process requires linear amplifiers which obscure the signal with random noise. Here, we introduce a theory which nevertheless allows one to use these devices for measuring all quadrature moments of propagating quantum microwaves based on cross-correlations from a dual-path amplification setup. Simultaneously, the detector noise properties are determined, allowing for tomography. We demonstrate the feasibility of our novel concept by proof-of-principle experiments with classical mixtures of weak coherent microwaves.Comment: 11 pages, 3 figure

Critical behavior in 3D gravitational collapse of massless scalar fields

We present results from a study of critical behavior in 3D gravitational collapse with no symmetry assumptions. The source of the gravitational field is a massless scalar field. This is a well-studied case for spherically symmetric gravitational collapse, allowing us to understand the reliability and accuracy of the simulations. We study both supercritical and subcritical evolutions to see if one provides more accurate results than the other. We find that even for nonspherical initial data with 35% of the power in the ℓ=2 spherical harmonic, the critical solution is the same as in spherical symmetry