Rumor has it that a certain group in the US *may* have made some progress but not sure how much.
Their device is based on using positrons in a Rydberg or other highly excited quantum state based on tuned lasers to generate what they are describing as a "Dirac Hole generator".
If it is able to lift a 5mm diameter silicon disk weighing about 180mg against gravity using off the shelf 22Na as they describe then to scale it up is feasible albeit somewhat expensive.
What is not clear is whether CERN's antimatter storage unit can be retrofitted with a conduit to direct the positrons into the drive which is also under vacuum, electromagnetic shielding keeping air out until at >60K feet where power can be ramped down without losing efficiency and other important aspects like radiation shielding of the crew capsule and cryogenic coolants.
It may be less of a problem however as any 511keV gamma rays would be produced upon annihilation with electrons which due to the quantum effects might be several seconds ie >1200 feet away from the craft.