Local quantum uncertainty for multipartite quantum systems

TL;DR

This paper extends the concept of local quantum uncertainty to multipartite systems, providing a closed-form formula and calculating it for various three- and four-qubit states, revealing how quantum correlations can be efficiently quantified.

Contribution

The paper introduces a generalized formula for local quantum uncertainty in multi-qubit systems and demonstrates its calculation for several important quantum states.

Findings

Closed-form formula for multi-qubit local quantum uncertainty.

Quantum correlations can be measured by local measurements on any single qubit in symmetric states.

Local quantum uncertainty varies across bipartitions in general states.

Abstract

Local quantum uncertainty captures purely quantum correlations excluding their classical counterpart. This measure is quantum discord type, however with the advantage that there is no need to carry out the complicated optimization procedure over measurements. This measure is initially defined for bipartite quantum systems and a closed formula exists only for $2 \otimes d$ systems. We extend the idea of local quantum uncertainty to multi-qubit systems and provide the similar closed formula to compute this measure. We explicitly calculate local quantum uncertainty for various quantum states of three and four qubits, like GHZ state, W state, Dicke state, Cluster state, Singlet state, and Chi state all mixed with white noise. We compute this measure for some other well known three qubit quantum states as well. We show that for all such symmetric states, it is sufficient to apply measurements on any single qubit to compute this measure, whereas in general one has to apply measurements on all parties as local quantum uncertainties for each bipartition can be different for an arbitrary quantum state.