Exploration of entropic uncertainty bound in a symmetric multi-qubit system under noisy channels

Considering one of the particles as a quantum memory in a bipartite system can remarkably improve the measurement accuracy for two incompatible observables. Herein, we study quantum-memory-assisted entropic uncertainty bound for an arbitrary two-qubit X-state, and then we get a clear formula as the entropic uncertainty bound. In the following, we examine analytically and numerically the dynamics of entropic uncertainty bound in a symmetric multi-qubit system under four types of noisy channels, i.e. phase-flip, amplitude damping, phase-damping, and depolarizing channels. Our results show that the entropic uncertainty bound dynamics is related to the number of particles and especially the noise channel used. Noteworthy, our remarks reveal that under the amplitude damping channel, the entropic uncertainty bound can be suppressed during the time. It turns out that under an amplitude damping channel, these results can be important in practical goals where the minimum uncertainty is required such as quantum computation.

Automated summary

By considering a particle as a quantum memory in a bipartite system, the measurement accuracy for two incompatible observables can be improved significantly. The study on the quantum-memory-assisted entropic uncertainty bound in an arbitrary two-qubit X-state reveals dynamics that are influenced by noisy channels and the number of particles. Notably, under the amplitude damping channel, the entropic uncertainty bound can be suppressed over time, which can have important implications for practical applications such as quantum computation.