Entropic Energy-Time Uncertainty Relation
Author(s)Coles, Patrick J.; Katariya, Vishal; Lloyd, Seth; Marvian, Iman; Wilde, Mark M.
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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. Our main result is an entropic energy-time uncertainty relation for general time-independent Hamiltonians, stated for both the discrete-time and continuous-time cases. Our uncertainty relation is strong, in the sense that it allows for a quantum memory to help reduce the uncertainty, and this formulation leads us to reinterpret it as a bound on the relative entropy of asymmetry. Because of the operational relevance of entropy, we anticipate that our uncertainty relation will have information-processing applications.
DepartmentMassachusetts Institute of Technology. Department of Mechanical Engineering; Massachusetts Institute of Technology. Research Laboratory of Electronics
Physical Review Letters
American Physical Society
Coles, Patrick J. et al. "Entropic Energy-Time Uncertainty Relation." Physical Review Letters 122, 10 (March 2019): 100401 © 2019 American Physical Society
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