Experimental investigation of entropic uncertainty relations and coherence uncertainty relations

TL;DR

This paper experimentally verifies entropic and coherence-based uncertainty relations in quantum mechanics using an all-optics platform, demonstrating their theoretical bounds and connection to quantum coherence relevant for quantum key distribution.

Contribution

It provides the first experimental demonstration of entropic and coherence uncertainty relations with high-fidelity bipartite states and explores their bounds and relation to quantum coherence.

Findings

Experimental results match theoretical predictions.

Lower bounds can be tightened using Holevo quantity and mutual information.

Entropic uncertainty is inversely related to quantum coherence.

Abstract

Uncertainty relation usually is one of the most important features in quantum mechanics, and is the backbone of quantum theory, which distinguishes from the rule in classical counterpart. Specifically, entropy-based uncertainty relations are of fundamental importance in the region of quantum information theory, offering one nontrivial bound of key rate towards quantum key distribution. In this work, we experimentally demonstrate the entropic uncertainty relations and coherence-based uncertainty relations in an all-optics platform. By means of preparing two kinds of bipartite initial states with high fidelity, i.e., Bell-like states and Bell-like diagonal states, we carry on local projective measurements over a complete set of mutually unbiased bases on the measured subsystem. In terms of quantum tomography, the density matrices of the initial states and the post-measurement states are reconstructed. It shows that our experimental results coincide with the theoretical predictions very well. Additionally, we also verify that the lower bounds of both the entropy-based and coherence-based uncertainty can be tightened by imposing the Holevo quantity and mutual information, and the entropic uncertainty is inversely correlated with the coherence. Our demonstrations might offer an insight into their uncertainty relations and their connection to quantum coherence in quantum information science, which might be applicable to the security analysis of quantum key distributions.