Entropic uncertainty assisted by temporal memory

TL;DR

This paper investigates how temporal memory, via sequential observations, can reduce the entropic uncertainty bounds in quantum measurements, extending the understanding of uncertainty relations with quantum side information.

Contribution

It introduces a novel approach showing that quantum temporal information can lower entropic uncertainty bounds, expanding the framework of uncertainty relations with memory.

Findings

Temporal correlations reduce entropy bounds

Sequential measurements improve measurement precision

Quantum memory effects influence uncertainty limits

Abstract

The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding entropies. Massen-Uffink entropic uncertainty relation (Phys. Rev. Lett. 60, 1103 (1988)) constrains the sum of entropies associated with incompatible measurements. The entropic uncertainty principle in the presence of quantum memory (Nature Phys. 6, 659 (2010)) brought about a fascinating twist by showing that quantum side information, enabled due to entanglement, helps in beating the uncertainty of non-commuting observables. Here we explore the interplay between temporal correlations and uncertainty. We show that with the assistance of a prior quantum temporal information achieved by sequential observations on the same quantum system at different times, the uncertainty bound on entropies gets reduced.