  We present lattice QCD results for masses and magnetic polarizabilities of
light and strange pseudoscalar mesons, chiral condensates, decay constants of
neutral pion, and neutral kaon in the presence of background magnetic fields
with $eB$ ranging up to around 3.35 GeV$^2$ ($\sim70~M_\pi^2$) in the vacuum.
The computations were carried out in (2+1)-flavor QCD mostly on $32^3 \times
96$ lattices using the highly improved staggered quark action with $M_{\pi}
\approx $ 220 MeV at zero temperature. We find that the masses of neutral
pseudoscalar mesons monotonously decrease as the magnetic field strength grows
and then saturate at a nonzero value, while there exists a nonmonotonous
behavior of charged pion and kaon masses in the magnetic field. We observe a
$qB$ scaling of the up and down quark flavor components of neutral pion mass,
neutral pion decay constant as well as the quark chiral condensates at 0.05
$\lesssim eB\lesssim$ 3.35 GeV$^2$. We show that the correction to the
Gell-Mann-Oakes-Renner relation involving the neutral pion is less than 6% and
the correction for the relation involving neutral kaon is less than 30% at
$eB\lesssim$ 3.35 GeV$^2$. We also derive the Ward-Takahashi identities for QCD
in the magnetic field in the continuum formulation including the relation
between integrated neutral pseudoscalar meson correlators and chiral
condensates.
