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Abstract:
Balanced homodyning, heterodyning and unbalanced homodyning are the three
well-known sampling techniques used in quantum optics to characterize all
possible photonic sources in continuous-variable quantum information theory. We
show that for all quantum states and all observable-parameter tomography
schemes, which includes the reconstructions of arbitrary operator moments and
phase-space quasi-distributions, localized sampling with unbalanced homodyning
is always tomographically more powerful (gives more accurate estimators) than
delocalized sampling with heterodyning. The latter is recently known to often
give more accurate parameter reconstructions than conventional marginalized
sampling with balanced homodyning. This result also holds for realistic
photodetectors with subunit efficiency. With examples from first- through
fourth-moment tomography, we demonstrate that unbalanced homodyning can
outperform balanced homodyning when heterodyning fails to do so. This new
benchmark takes us one step towards optimal continuous-variable tomography with
conventional photodetectors and minimal experimental components.