  We present a lattice QCD calculation of the pseudoscalar decay constants fK,
fD and fDs performed using the gauge configurations produced by the European
Twisted Mass Collaboration with Nf = 2 + 1 + 1 dynamical quarks, which include
in the sea, besides two light mass degenerate quarks, also the strange and
charm quarks with masses close to their values in the real world. The
simulations are based on a unitary setup for the two light mass-degenerate
quarks and on a mixed action approach for the strange and charm quarks. We use
data simulated at three different values of the lattice spacing in the range
0.06 - 0.09 fm and at pion masses in the range 210 - 450 MeV. Our main results
are: fK+ / fpi+ = 1.184 (16), fK+ = 154.4 (2.0) MeV, which incorporate the
leading strong isospin breaking correction due to the up- and down-quark mass
difference, and fK = 155.0 (1.9) MeV, fD = 207.4 (3.8) MeV, fDs = 247.2 (4.1)
MeV, fDs / fD = 1.192 (22) and (fDs / fD) / (fK / fpi) = 1.003 (14) obtained in
the isospin symmetric limit of QCD. Combined with the experimental measurements
of the leptonic decay rates of kaon, pion, D- and Ds-mesons our results lead to
the following determination of the CKM matrix elements: |Vus| = 0.2269 (29),
|Vcd| = 0.2221 (67) and |Vcs| = 1.014 (24). Using the latest value of |Vud|
from superallowed nuclear beta decays the unitarity of the first row of the CKM
matrix is fulfilled at the permille level.
