I find the title extremely misleading. Projecting always loses information about the full state, so in that sense there no time symmetry, as the arrow of time is irreversible.
Yes, if you consider one branch of the wavefunction, you have less than full information than the full state you branched from. But, the analogous situation would apply to a merger of different branches—you would have less than full information in one of the initial branches regarding the full resulting merged state.
I find the title extremely misleading. Projecting always loses information about the full state, so in that sense there no time symmetry, as the arrow of time is irreversible.
Yes, if you consider one branch of the wavefunction, you have less than full information than the full state you branched from. But, the analogous situation would apply to a merger of different branches—you would have less than full information in one of the initial branches regarding the full resulting merged state.