Quantum mechanical uncertainty limitations on deep space navigation by Doppler tracking and very long baseline interferometry

摘要

The ultimate precision with which very long baseline interferometry (VLBI) can determine the angular position of a spacecraft is determined by the quantum mechanical limitations on the performance of the interferometer receivers and the quantum mechanical uncertainty relation ΔNΦ ≥ 1. It is shown that for the navigation of a typical deep space mission using present-day techniques, fundamental physics imposes the following limits on the precision of spacecraft navigation: (1) Minimum noise on determination of phase of spacecraft navigation tone, ΔΦmin ≈ 1.9 × 10- radians per AU, (2) minimum noise on determination of phase of VLBI navigation fringes, ΔΘmin ≈ 2.6 × 10- radians per AU, (3) minimum noise on determination of VLBI navigation fringe frequency, Δfmin ≈ 2.9 × 10- Hz per AU, (4) minimum noise on determination of VLBI group delay, Δτgmin ≈ 0.5 ps per AU, and (5) minimum noise on determination of spacecraft angular position, ΔΨmin ≈ 2.9 × 10- radians per AU. The above limitations which are a consequence of quantum mechanical uncertainty on the determinations of the phase of a spacecraft tracking signal may be circumvented in principle by the application of squeezed quantum states.