Broadcasting Quantum Information using Finite Resources

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.