Entropic Energy-Time Uncertainty Relation

Understand

Energy-time uncertainty plays an important role in quantum foundations and technologies, and it was even discussed by the founders of quantum mechanics.

• However, standard approaches (e.g., Robertson's uncertainty relation) do not apply to energy-time uncertainty because, in general, there is no Hermitian operator associated with time.
• Following previous approaches, we quantify time uncertainty by how well one can read off the time from a quantum clock.
• We then use entropy to quantify the information-theoretic distinguishability of the various time states of the clock.