Abstract
The entropic uncertainty relation with quantum side information (EUR-QSI) from (Berta et al 2010 Nat. Phys. 6 659) 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 2012 Phys. Rev. Lett. 108 210405) 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.
Highlights
The uncertainty principle is one of the cornerstones of modern physics, providing a striking separation between classical and quantum mechanics [1]
This latter refinement, known as the entropic uncertainty relation with quantum side information (EUR-QSI), is the culmination of a sequence of works spanning many decades [3,4,5,6,7,8,9,10,11,12] and is the one on which we focus here
Tripartite uncertainty relations capture an additional feature of quantum mechanics, namely the monogamy of entanglement [14]
Summary
6 659) is a unifying principle relating two distinctive features of quantum this work must maintain attribution to the mechanics: quantum uncertainty due to measurement incompatibility, and entanglement. 108 210405) 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 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 postmeasurement state and can be thought of as quantifying how much disturbance a given measurement causes.
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