  We study the sensitivity to physics beyond the standard model of precise
top-quark pair production measurements at future lepton colliders. A global
effective-field-theory approach is employed, including all dimension-six
operators of the Warsaw basis which involve a top-quark and give rise to
tree-level amplitudes that interfere with standard-model $e^+e^-\to t\,\bar
t\to bW^+\bar bW^-$ ones in the limit of vanishing $b$-quark mass. Four-fermion
and CP-violating contributions are taken into account. Circular-collider-, ILC-
and CLIC-like benchmark run scenarios are examined. We compare the constraining
power of various observables to a set of statistically optimal ones which
maximally exploit the information contained in the fully differential $bW^+\bar
bW^-$ distribution. The enhanced sensitivity gained on the linear contributions
of dimension-six operators leads to bounds that are insensitive to quadratic
ones. Even with statistically optimal observables, two centre-of-mass energies
are required for constraining simultaneously two- and four-fermion operators.
The impact of the centre-of-mass energy lever arm is discussed, that of beam
polarization as well. A realistic estimate of the precision that can be
achieved in ILC- and CLIC-like operating scenarios yields individual limits on
the electroweak couplings of the top quark that are one to three orders of
magnitude better than constraints set with Tevatron and LHC run I data, and
three to two hundred times better than the most optimistic projections made for
the high-luminosity phase of the LHC. Clean global constraints can moreover be
obtained at lepton colliders, robustly covering the multidimensional
effective-field-theory space with minimal model dependence.
