Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Verification of complementarity relations between quantum steering criteria using an optical system

Huan Yang, Zhiyong Ding, Xue‐Ke Song, Hao Yuan, Dong Wang, Jie Yang, Changjin Zhang, Liu Ye

Published Feb 10, 2021• 10 citations
Publisher

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 a system can be observed through the average coherence of a 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 they cannot violate the complementary settings criteria. Three measurement settings inequalities, which establish a set of complementarity relations between these two coherence steering criteria, are always obeyed by all prepared quantum states in experiment. In addition, we experimentally certify that the strengths of coherence steering criteria depend on the choice of coherence measure. In comparison with two setting coherence steering criteria based on ${l}_{1}$ norm of coherence and relative entropy of coherence, our experimental results show that the steering criterion based on skew information of coherence is the strongest in detecting the steerability of two-photon Bell-like states. Thus, our experimental demonstration can deepen the understanding of the relation between the quantum steering and quantum coherence.

DOI
10.1103/physreva.103.022207

Related papers

Experimental demonstration of complementarity relations between quantum steering criteria

Huan Yang, Zhiyong Ding, Xue‐Ke Song +5 more

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.

arXiv:2007.11320•Jul 22, 2020•0 citations

Experimental detection of quantum steerability based on the critical radius in an all-optical system

Xiao‐Gang Fan, Fa Zhao, Huan Yang +3 more

Quantum steering is the ability that one system affects another one without delay by performing local measurements. During the past few years, the research on quantum steering has been verified in a number of experiments by the choices of measurements. But this research cannot detect all steerable states. Recently, the definition of critical radius was proposed by Nguyen et al. [Phys. Rev. Lett. 122, 240401 (2019)]. The critical radius can detect all steerable states for two-qubit states. Therefore the critical radius can be regarded as the best method for detecting the steerability of two-qubit states. However, relevant experimental research is still lacking. In this work, for comparison, we experimentally investigate three steering criteria based on the critical radius, the geometric Bell-like inequality, and the three-setting measurements steering inequality and find that the critical radius can detect the most steerable states. Furthermore, we demonstrate that the critical radius satisfies the scaling property. The results show that we only need to calculate the critical radii of some quantum states to obtain the critical radii of more scaling quantum states. Thus this property can provide the convenience for detecting the steerability of many quantum states.

Physical Review A•Jan 20, 2023•3 citations

Unveiling quantum steering by quantum-classical uncertainty complementarity

Kuan-Yi Lee, Jhen-Dong Lin, Karel Lemr +5 more

One of the remarkable aspects of quantum steering is its ability to violate local uncertainty complementarity relations. In this vein of study, various steering witnesses have been developed. Here, we introduce a novel complementarity relation between the system’s quantum and classical uncertainties corresponding to the distillable coherence and the von Neumann entropy, respectively. We show that the proposed complementarity relation is tighter than the entropic uncertainty relation (EUR). Leveraging this result, we propose a steering witness that is more efficient than the EUR. From the operational perspective, the steering witness quantifies the amount of extra distillable coherence facilitated by quantum steerability. Notably, the proposed steering witness serves as a full entanglement measure for pure bipartite states–an ability that the EUR lacks. We also experimentally validate such a property through a photonic system. Furthermore, a deeper connection to the uncertainty principle is revealed by showcasing the steering-induced distillable coherence can quantify measurement incompatibility and quantum steerability under genuine incoherent operations. Our work establishes a clear quantitative and operational link between coherence and steering, which are vital resources of quantum technologies, and underscores our efforts in bridging the uncertainty principle with quantum coherence.

arXiv:2312.01055•npj Quantum Information•May 8, 2025•10 citations

Detecting the steerability through an optimized steering criterion in two-photon systems

Xiao‐Gang Fan, Fa Zhao, Huan Yang +3 more

The steerability of a quantum state can be detected by steering inequalities. The linear steering inequalities show that more steerable states can be discovered with the increase of measurements. In order to detect more steerable states in two-photon systems, we first theoretically derive an optimized steering criterion based on infinity measurements for an arbitrary two-qubit state. The steering criterion is only determined by the spin correlation matrix of the state, and do not require infinity measurements. Then, we prepared the Werner-like states in two-photon systems, and measure their spin correlation matrices. Finally, we apply three steering criteria, which include our steering criterion, the three-measurement steering criterion and the geometric Bell-like inequality, to distinguish the steerability of these states. The results show that our steering criterion can detect the most steerable states under the same experimental conditions. Thus, our work provides a valuable reference for detecting the steerability of quantum states.

Optics Express•Apr 27, 2023•4 citations

Steerability Of Local Quantum Coherence

Debasis Mondal, Tanumoy Pramanik, Arun Kumar Pati

The bipartite state is said to be steerable iff it does not have single system description, i.e., the bipartite state can not be explained by local hidden state model [Phys. Rev. Lett. {\bf 98}, 140402 (2007)]. Several steering inequalities have been derived using different local uncertainty relations to verify the control on the state of one subsystem by other. Here, we derive complementarity kind of relations between coherences measured on mutually unbiased bases using various coherence measures like the $l_1$-norm, relative entropy and skew information. Using these relations, we formulate steering inequalities to check whether one subsystem has control to the coherence of the other entangled subsystem. According to our results, all pure entangled states are maximally steerable but for mixed entangled states, coherence steerability needs stronger non-local correlation than the existing state steering inequalities. We also show that our steering criteria is monogamous.

•Aug 15, 2015•0 citations

Estimating quantum steering and Bell nonlocality through quantum entanglement in two-photon systems

Huan Yang, Fa Zhao, Xiao‐Gang Fan +6 more

Quantum entanglement, quantum steering and Bell nonlocality, as significant quantum resources in the field of quantum information science, can achieve variously valuable quantum information tasks. Among of them, quantum entanglement and Bell nonlocality are the weakest and strongest nonlocal correlations, respectively. One can capture the quantum steering and Bell nonlocality via violating steering inequality and Bell inequality, respectively. In general, the detections of quantum steering and Bell nonlocality are strictly harder than entanglement detection. Here, based on steering inequality test and quantum state tomography, we attain various nonlocal correlations and experimentally demonstrate that the estimations of quantum steering and Bell nonlocality can be realized according to the quantum entanglement of the prepared two-photon test states. The estimated efficiency of quantum steering is stronger than the one of Bell nonlocality in this scenario, i.e., more steerable two-photon test states can be verified through quantum entanglement. In addition, quantum steering and Bell nonlocality are bounded by the corresponding upper and lower bounds, and these bounds cannot be punctured by all prepared two-photon states in experiment. These results are conducive to understand the relations among these nonlocal correlations.

Optics Express•Jul 27, 2021•14 citations
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 a system can be observed through the average coherence of a 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 they cannot violate the complementary settings criteria. Three measurement settings inequalities, which establish a set of complementarity relations between these two coherence steering criteria, are always obeyed by all prepared quantum states in experiment. In addition, we experimentally certify that the strengths of coherence steering criteria depend on the choice of coherence measure. In comparison with two setting coherence steering criteria based on l1{l}_{1}l1​ norm of coherence and relative entropy of coherence, our experimental results show that the steering criterion based on skew information of coherence is the strongest in detecting the steerability of two-photon Bell-like states. Thus, our experimental demonstration can deepen the understanding of the relation between the quantum steering and quantum coherence.
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.
Quantum steering is the ability that one system affects another one without delay by performing local measurements. During the past few years, the research on quantum steering has been verified in a number of experiments by the choices of measurements. But this research cannot detect all steerable states. Recently, the definition of critical radius was proposed by Nguyen et al. [Phys. Rev. Lett. 122, 240401 (2019)]. The critical radius can detect all steerable states for two-qubit states. Therefore the critical radius can be regarded as the best method for detecting the steerability of two-qubit states. However, relevant experimental research is still lacking. In this work, for comparison, we experimentally investigate three steering criteria based on the critical radius, the geometric Bell-like inequality, and the three-setting measurements steering inequality and find that the critical radius can detect the most steerable states. Furthermore, we demonstrate that the critical radius satisfies the scaling property. The results show that we only need to calculate the critical radii of some quantum states to obtain the critical radii of more scaling quantum states. Thus this property can provide the convenience for detecting the steerability of many quantum states.
One of the remarkable aspects of quantum steering is its ability to violate local uncertainty complementarity relations. In this vein of study, various steering witnesses have been developed. Here, we introduce a novel complementarity relation between the system’s quantum and classical uncertainties corresponding to the distillable coherence and the von Neumann entropy, respectively. We show that the proposed complementarity relation is tighter than the entropic uncertainty relation (EUR). Leveraging this result, we propose a steering witness that is more efficient than the EUR. From the operational perspective, the steering witness quantifies the amount of extra distillable coherence facilitated by quantum steerability. Notably, the proposed steering witness serves as a full entanglement measure for pure bipartite states–an ability that the EUR lacks. We also experimentally validate such a property through a photonic system. Furthermore, a deeper connection to the uncertainty principle is revealed by showcasing the steering-induced distillable coherence can quantify measurement incompatibility and quantum steerability under genuine incoherent operations. Our work establishes a clear quantitative and operational link between coherence and steering, which are vital resources of quantum technologies, and underscores our efforts in bridging the uncertainty principle with quantum coherence.
The steerability of a quantum state can be detected by steering inequalities. The linear steering inequalities show that more steerable states can be discovered with the increase of measurements. In order to detect more steerable states in two-photon systems, we first theoretically derive an optimized steering criterion based on infinity measurements for an arbitrary two-qubit state. The steering criterion is only determined by the spin correlation matrix of the state, and do not require infinity measurements. Then, we prepared the Werner-like states in two-photon systems, and measure their spin correlation matrices. Finally, we apply three steering criteria, which include our steering criterion, the three-measurement steering criterion and the geometric Bell-like inequality, to distinguish the steerability of these states. The results show that our steering criterion can detect the most steerable states under the same experimental conditions. Thus, our work provides a valuable reference for detecting the steerability of quantum states.
The bipartite state is said to be steerable iff it does not have single system description, i.e., the bipartite state can not be explained by local hidden state model [Phys. Rev. Lett. {\bf 98}, 140402 (2007)]. Several steering inequalities have been derived using different local uncertainty relations to verify the control on the state of one subsystem by other. Here, we derive complementarity kind of relations between coherences measured on mutually unbiased bases using various coherence measures like the l1l_1l1​-norm, relative entropy and skew information. Using these relations, we formulate steering inequalities to check whether one subsystem has control to the coherence of the other entangled subsystem. According to our results, all pure entangled states are maximally steerable but for mixed entangled states, coherence steerability needs stronger non-local correlation than the existing state steering inequalities. We also show that our steering criteria is monogamous.
Quantum entanglement, quantum steering and Bell nonlocality, as significant quantum resources in the field of quantum information science, can achieve variously valuable quantum information tasks. Among of them, quantum entanglement and Bell nonlocality are the weakest and strongest nonlocal correlations, respectively. One can capture the quantum steering and Bell nonlocality via violating steering inequality and Bell inequality, respectively. In general, the detections of quantum steering and Bell nonlocality are strictly harder than entanglement detection. Here, based on steering inequality test and quantum state tomography, we attain various nonlocal correlations and experimentally demonstrate that the estimations of quantum steering and Bell nonlocality can be realized according to the quantum entanglement of the prepared two-photon test states. The estimated efficiency of quantum steering is stronger than the one of Bell nonlocality in this scenario, i.e., more steerable two-photon test states can be verified through quantum entanglement. In addition, quantum steering and Bell nonlocality are bounded by the corresponding upper and lower bounds, and these bounds cannot be punctured by all prepared two-photon states in experiment. These results are conducive to understand the relations among these nonlocal correlations.