Though immensely successful, the standard model of particle physics does not offer any explanation as to why our Universe contains so much more matter than antimatter. A key to a dynamically generated matter-antimatter asymmetry is the existence of processes that violate the combined charge conjugation and parity (CP) symmetry . As such, precision tests of CP symmetry may be used to search for physics beyond the standard model. However, hadrons decay through an interplay of strong and weak processes, quantified in terms of relative phases between the amplitudes. Although previous experiments constructed CP observables that depend on both strong and weak phases, we present an approach where sequential two-body decays of entangled multi-strange baryon-antibaryon pairs provide a separation between these phases. Our method, exploiting spin entanglement between the double-strange Ξ baryon and its antiparticle Formula: see text, has enabled a direct determination of the weak-phase difference, (ξ  - ξ ) = (1.2 ± 3.4 ± 0.8) × 10  rad. Furthermore, three independent CP observables can be constructed from our measured parameters. The precision in the estimated parameters for a given data sample size is several orders of magnitude greater than achieved with previous methods . Finally, we provide an independent measurement of the recently debated Λ decay parameter α (refs.  ). The Formula: see text asymmetry is in agreement with and compatible in precision to the most precise previous measurement .