  Measurements can be viewed as interactions between systems and specifically
prepared pointers. Ideally, these interactions create accurate copies of the
information corresponding to the diagonal of the system's density operator with
respect to the measurement basis. However, establishing measurement outcomes as
objective facts requires redundancy. We therefore consider the problem of
unitarily distributing this information to several quantum memories. We show
that the accuracy of this broadcasting process is limited by thermodynamic
restrictions on preparing the memories in pure states: ideal broadcasting is
impossible using finite resources. For finite-temperature memories we put
forward a lower bound on the entropy production of the broadcasting process.
This Holevo-Landauer bound demonstrates that the mixedness of the initial
memory limits the ability to accurately broadcast information to more than one
memory component, thus fundamentally restricting the creation of redundancies
while maintaining the integrity of the original information. Finally, we show
how the full information can be recovered in the classical limit -- via
coarse-graining or asymptotically as the number of subsystems of each memory
component increases -- thus elucidating how objective properties can emerge
despite inherent imperfections.
