Experimental demonstration of complementarity relations between quantum steering criteria

TL;DR

This paper experimentally verifies complementarity relations between different quantum steering criteria using two-photon states, showing how coherence measures influence steerability detection and deepening understanding of quantum correlations.

Contribution

It provides the first experimental demonstration of complementarity relations between quantum steering criteria based on various coherence measures.

Findings

Complementarity relations hold for coherence steering criteria in experiments.

Steering criterion based on skew information is more effective in detecting steerability.

Experimental results confirm the dependence of coherence measures on steering detection.

Abstract

The ability that one system immediately affects another one by using local measurements is regarded as quantum steering, which can be detected by various steering criteria. Recently, Mondal et al. [Phys. Rev. A 98, 052330 (2018)] derived the complementarity relations of coherence steering criteria, and revealed that the quantum steering of system can be observed through the average coherence of subsystem. Here, we experimentally verify the complementarity relations between quantum steering criteria by employing two-photon Bell-like states and three Pauli operators. The results demonstrate that if prepared quantum states can violate two setting coherence steering criteria and turn out to be steerable states, then it cannot violate the complementary settings criteria. Three measurement settings inequality, which establish a complementarity relation between these two coherence steering criteria, always holds in experiment. Besides, we experimentally certify that the strengths of coherence steering criteria dependent on the choice of coherence measure. In comparison with two setting coherence steering criteria based on l1 norm of coherence and relative entropy of coherence, our experimental results show that the steering criterion based on skew information of coherence is more stronger in detecting the steerability of quantum states. Thus, our experimental demonstrations can deepen the understanding of the relation between the quantum steering and quantum coherence.