Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory

TL;DR

This paper introduces a new uncertainty relation that incorporates quantum discord and classical correlations, providing a tighter lower bound on measurement uncertainties in the presence of quantum memory, with implications for quantum cryptography.

Contribution

It presents a novel uncertainty relation that improves upon previous bounds by including quantum discord and classical correlations, enhancing understanding of quantum measurement uncertainties.

Findings

New lower bound on measurement uncertainty is tighter than previous bounds.

Quantum discord and classical correlations influence the predictability of measurement outcomes.

Application to quantum key distribution security and bounds on quantum state properties.

Abstract

Uncertainty relations capture the essence of the inevitable randomness associated with the outcomes of two incompatible quantum measurements. Recently, Berta et al. have shown that the lower bound on the uncertainties of the measurement outcomes depends on the correlations between the observed system and an observer who possesses a quantum memory. If the system is maximally entangled with its memory, the outcomes of two incompatible measurements made on the system can be predicted precisely. Here, we obtain a new uncertainty relation that tightens the lower bound of Berta et al., by incorporating an additional term that depends on the quantum discord and the classical correlations of the joint state of the observed system and the quantum memory. We discuss several examples of states for which our new lower bound is tighter than the bound of Berta et al. On the application side, we discuss the relevance of our new inequality for the security of quantum key distribution and show that it can be used to provide bounds on the distillable common randomness and the entanglement of formation of bipartite quantum states.