  We describe the Quantum Test of the Equivalence principle and Space Time
(QTEST), a concept for an atom interferometry mission on the International
Space Station (ISS). The primary science objective of the mission is a test of
Einstein's equivalence principle with two rubidium isotope gases at a precision
of better than 10$^{-15}$. Distinct from the classical tests is the use of
quantum wave packets and their expected large spatial separation in the QTEST
experiment. This dual species atom interferometer experiment will also be
sensitive to time-dependent equivalence principle violations that would be
signatures for ultralight dark-matter particles. In addition, QTEST will be
able to perform photon recoil measurements to better than 10$^{-11}$ precision.
This improves upon terrestrial experiments by a factor of 100, enabling an
accurate test of the standard model of particle physics and contributing to
mass measurement, in the proposed new international system of units (SI), with
significantly improved precision. The predicted high measurement precision of
QTEST comes from the microgravity environment on ISS, offering extended free
fall times in a well-controlled environment. Suppression of systematic errors
by use of symmetric interferometer configurations and rejection of common-mode
errors drives the QTEST design. It uses Bragg interferometry with a single
laser beam at the "magic" wavelength, where the two isotopes have the same
polarizability, for mitigating sensitivities to vibrations and laser noise,
imaging detection for correcting cloud initial conditions and maintaining
contrast, modulation of the atomic hyperfine states for reduced sensitivity to
magnetic field gradients, two source regions for simultaneous time reversal
measurements and redundancy, and modulation of the gravity vector using a
rotating platform to reduce otherwise difficult systematics to below
10$^{-16}$.
