Particles directly produced at electron–positron colliders, such as the J/ψ meson, decay with relatively high probability into a baryon–antibaryon pair1. For spin-1/2 baryons, the pair can have the same or opposite helicites. A non-vanishing phase ΔΦ between the transition amplitudes to these helicity states results in a transverse polarization of the baryons2–4. From the joint angular distribution of the decay products of the baryons, this phase as well as the parameters characterizing the baryon and the antibaryon decays can be determined. Here, we report the measurement of ΔΦ = 42.4 ± 0.6 ± 0.5° using Λ → pπ− and Λ¯ → p¯ π+, n¯ π decays at BESIII. We find a value for the Λ → pπ− decay parameter of α− = 0.750 ± 0.009 ± 0.004, 17 ± 3% higher than the current world average, which has been used as input for all Λ polarization measurements since 19785,6. For Λ¯ → p¯ π+ we find α+ = −0.758 ± 0.010 ± 0.007, giving ACP = (α− + α+)/(α− − α+) = −0.006 ± 0.012 ± 0.007, a precise direct test of charge–parity symmetry (CP) violation in Λ decays.