Fine-grained lower limit of entropic uncertainty in the presence of quantum memory

TL;DR

This paper derives a new entropic uncertainty relation incorporating fine-graining, establishing an ultimate precision limit for measurements with quantum memory, and demonstrates its implications for quantum key security.

Contribution

It introduces a fine-grained entropic uncertainty relation that tightens bounds for two-qubit states and relates to quantum key distribution security.

Findings

Tightens the lower bound for two-qubit states with maximally mixed marginals.

Aligns with recent experimental results on entangled and Bell-diagonal states.

Implications for enhancing security in quantum key generation protocols.

Abstract

The limitation on obtaining precise outcomes of measurements performed on two non-commuting observables of a particle as set by the uncertainty principle in its entropic form, can be reduced in the presence of quantum memory. We derive a new entropic uncertainty relation based on fine- graining, which leads to an ultimate limit on the precision achievable in measurements performed on two incompatible observables in the presence of quantum memory. We show that our derived uncertainty relation tightens the lower bound set by entropic uncertainty for members of the class of two-qubit states with maximally mixed marginals, while accounting for the recent experimental results using maximally entangled pure states and mixed Bell-diagonal states. An implication of our uncertainty relation on the security of quantum key generation protocols is pointed out.