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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) symmetry1. 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 antiparticle2$${\bar{{\Xi }}}^{+}$$ Ξ ¯ + , has enabled a direct determination of the weak-phase difference, (ξP − ξS) = (1.2 ± 3.4 ± 0.8) × 10−2 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 methods3. Finally, we provide an independent measurement of the recently debated Λ decay parameter αΛ (refs. 4,5). The $${\Lambda }\bar{{\Lambda }}$$ Λ Λ ¯ asymmetry is in agreement with and compatible in precision to the most precise previous measurement4.

A combination of measurements sensitive to the CP violation angle γ of the Cabibbo-Kobayashi-Maskawa unitarity triangle and to the charm mixing parameters that describe oscillations between D0 and $$ \overline{D} $$ D ¯ 0 mesons is performed. Results from the charm and beauty sectors, based on data collected with the LHCb detector at CERN’s Large Hadron Collider, are combined for the first time. This method provides an improvement on the precision of the charm mixing parameter y by a factor of two with respect to the current world average. The charm mixing parameters are determined to be $$ x=\left({0.400}_{-0.053}^{+0.052}\right)\% $$ x = 0.400 − 0.053 + 0.052 % and y = $$ \left({0.630}_{-0.030}^{+0.033}\right)\% $$ 0.630 − 0.030 + 0.033 % . The angle γ is found to be γ = $$ \left({65.4}_{-4.2}^{+3.8}\right){}^{\circ} $$ 65.4 − 4.2 + 3.8 ° and is the most precise determination from a single experiment.

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