"The CPT theorem says that CPT symmetry holds for all physical phenomena, or more precisely, that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry." says CPT symmetry Wikipedia article, suggesting that all processes have CPT-symmetric analogues.
However, there are popular doubts regarding some, especially measurement:
Example of wavefunction collapse is atom deexcitation, releasing energy - it is reversible, but it requires providing energy e.g. in form of photon to excite back an atom. Can measurement be seen this way - that there is always some accompanying process like energy release, which would need to be also reversed? For example in Stern-Gerlach: spin tilting to parallel or anti-parallel alignment to avoid precession in strong magnetic field - does it have some accompanied process like energy release? Can it be observed?
Another somehow problematic example is stimulated emission used in laser - causing photon emission, which finally e.g. excites a target, later by light path. Does it have time/CPT-symmetric analogue: some stimulated absorption - causing photon absorption, which e.g. deexcites a target, earlier by light path?
Quantum algorithms usually start with state preparation: all 0/1 qubits are initially fixed to let say <0|. Could there be time/CPT analogue of state preparation: fixing values but at the end (as |0>)?
One of cosmological examples is Big Bang: which hypothesis of the point of start of time seems in disagreement with CPT theorem - instead suggesting some symmetric twin of Big Bang before it, like in cyclic model of universe. Is hypothesis of the point of start of time in agreement with CPT theorem? Could these two possibilities be distinguished experimentally?
What other processes are seen as problematic from time/CPT symmetry perspective?
Which can be defended, and which essentially require some fundamental asymmetry?
Violating CPT theorem would require pointing its incorrect assumption - which one is the most likely?