Entropic time–energy uncertainty relations: an algebraic approach

Abstract

We address entropic uncertainty relations between time and energy or, more precisely, between measurements of an observable G and the displacement r of the G-generated evolution e−irG . We derive lower bounds on the entropic uncertainty in two frequently considered scenarios, which can be illustrated as two different guessing games in which the role of the guessers are fixed or not. In particular, our bound for the first game improves the previous result by Coles et al [Phys. Rev. Lett. 122 100401 (2019)]. To derive our bounds, we extend a recently proposed novel algebraic method by Gao et al [arXiv:1710.10038 [quant-ph]] which was used to derive both strong subadditivity and entropic uncertainty relations for measurements.

Time-energy uncertainty relation for noisy quantum metrology

“…Entropic uncertainty relations play a central role in quantum cryptography [11,15,16,90], and cryptographic schemes have been studied for quantum metrology [91]. It is possible that our parameter estimation trade-off can similarly form the basis of cryptographic schemes in which a parameter encoded in a quantum state is to be shielded from a malevolent eavesdropper.…”

“…Here, too, it is helpful to envision two parties, one attempting to measure time, the other attempting to measure energy. Indeed, such entropic time-energy uncertainty relations have recently been established [15,16].…”