The possibility of having coherent superpositions is one of the hallmarks of quantum theory, powering applications like quantum metrology and determining the peculiar properties of quantum thermodynamics. In the presence of conservation laws, however, coherence cannot be created for free. But can perhaps a single “seed” of coherence be distributed from one quantum system to many others without loss?
In this work, Müller and Lostaglio prove that the answer is negative: even in the most general possible setup, such “broadcasting” of coherence is impossible. Thus, every use of coherence comes with a price — in particular, the timing information of quantum clocks cannot be read or distributed without disturbing the clock. This fundamental result explains several phenomena of quantum thermodynamics and determines intrinsic limitations for the repeatable use of a variety of quantum resources.
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