Entropic uncertainty and measurement reversibility

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.

v2: 14 pages, 3 figures; includes experimental results from IBM Quantum Experience

References in corpus (20)

• Black Holes: Complementarity or Firewalls?
• The Uncertainty Principle in the Presence of Quantum Memory
• Entropic Uncertainty Relations and their Applications
• Tight Finite-Key Analysis for Quantum Cryptography
• The Uncertainty Relation for Smooth Entropies
• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Conjectured Strong Complementary Information Tradeoff
• Is Entanglement Monogamous?
• Uncertainty relations from simple entropic properties
• Performing Quantum Computing Experiments in the Cloud
• Experimental test of Mermin inequalities on a 5-qubit quantum computer
• Recoverability in quantum information theory
• A Monogamy-of-Entanglement Game With Applications to Device-Independent Quantum Cryptography
• Entanglement sampling and applications
• Uncertainty, Monogamy, and Locking of Quantum Correlations
• Strengthened Monotonicity of Relative Entropy via Pinched Petz Recovery Map
• Position-Momentum Uncertainty Relations in the Presence of Quantum Memory
• An Entropic Uncertainty Principle for Quantum Measurements
• Extended quantum conditional entropy and quantum uncertainty inequalities
• Relative entropy derivation of the uncertainty principle with quantum side information

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