The search for CP violation in interactions of the Higgs boson with either fermions or bosons provides attractive reference measurements in the Particle Physics Community Planning Exercise (a.k.a. "Snowmass"). Benchmark measurements of CP violation provide a limited and well-defined set of parameters that could be tested at the proton, electron-positron, photon, and muon colliders, and compared to those achieved through study of virtual effects in electric dipole moment measurements. We review the current status of these CP -sensitive studies and provide projections to future measurements. ContentsI. Introduction II. Framework of the Higgs CP study for Snowmass III. Prospects of Higgs CP measurements at a photon collider IV. Prospects of Higgs CP measurements at a muon collider A. Muon collider at the H boson pole B. High-energy muon collider V. Prospects of Higgs CP measurements at a hadron collider A. Gluon fusion process at a hadron collider B. The Hγγ and HZγ couplings at a hadron collider C. The HZZ and HW W couplings at a hadron collider D. The Ht t coupling at a hadron collider E. The H → τ + τ − process at a hadron collider VI. Prospects of Higgs CP measurements at an electron-positron collider A. The V H process at an electron-positron collider B. The VBF process at an electron-positron collider C. The t tH process at an electron-positron collider D. The H → τ + τ − and other decay processes at an electron-positron collider VII. Comparison to EDM measurements VIII. Summary A. Recent updates of the studies at a hadron collider B. Recent updates of the studies at an electron-positron collider C. EDM constraints References

The LHC effective field theory working group gathers members of the LHC experiments and the theory community to provide a framework for the interpretation of LHC data in the context of EFT. In this note we discuss experimental observables and corresponding measurements in analysis of the Higgs, top, and electroweak data at the LHC. We review the relationship between operators and measurements relevant for the interpretation of experimental data in the context of a global SMEFT analysis. One of the goals of ongoing effort is bridging the gap between theory and experimental communities working on EFT, and in particular concerning optimised analyses. This note serves as a guide to experimental measurements and observables leading to EFT fits and establishes good practice, but does not present authoritative guidelines how those measurements should be performed.