Entropic uncertainty and measurement reversibility

TL;DR

This paper enhances the entropic uncertainty relation with quantum side information by incorporating a state-dependent term that measures measurement reversibility, linking measurement disturbance to quantum uncertainty.

Contribution

It introduces a new state-dependent lower bound in the EUR-QSI that quantifies measurement disturbance and demonstrates its experimental validation on IBM Quantum hardware.

Findings

The new bound tightens the EUR-QSI by including measurement reversibility.

Experimental results on IBM Quantum Experience agree with theoretical predictions.

The approach unifies measurement disturbance with quantum uncertainty principles.

Abstract

The entropic uncertainty relation with quantum side information (EUR-QSI) from [Berta et al., Nat. Phys. 6, 659 (2010)] is a unifying principle relating two distinctive features of quantum mechanics: quantum uncertainty due to measurement incompatibility, and entanglement. In these relations, quantum uncertainty takes the form of preparation uncertainty where one of two incompatible measurements is applied. In particular, the "uncertainty witness" lower bound in the EUR-QSI is not a function of a post-measurement state. An insightful proof of the EUR-QSI from [Coles et al., Phys. Rev. Lett. 108, 210405 (2012)] makes use of a fundamental mathematical consequence of the postulates of quantum mechanics known as the non-increase of quantum relative entropy under quantum channels. Here, we exploit this perspective to establish a tightening of the EUR-QSI which adds a new state-dependent term in the lower bound, related to how well one can reverse the action of a quantum measurement. As such, this new term is a direct function of the post-measurement state and can be thought of as quantifying how much disturbance a given measurement causes. Our result thus quantitatively unifies this feature of quantum mechanics with the others mentioned above. We have experimentally tested our theoretical predictions on the IBM Quantum Experience and find reasonable agreement between our predictions and experimental outcomes.