Monogamy

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Shuming Cheng - One of the best experts on this subject based on the ideXlab platform.

  • experimental validation of quantum steering ellipsoids and tests of volume Monogamy relations
    Physical Review Letters, 2019
    Co-Authors: Chao Zhang, Shuming Cheng, Michael J W Hall, Howard Mark Wiseman, Li Li, Qiuyue Liang, Yunfeng Huang, Chuanfeng Li, Geoff J Pryde
    Abstract:

    : The set of all qubit states that can be steered to by measurements on a correlated qubit is predicted to form an ellipsoid-called the quantum steering ellipsoid-in the Bloch ball. This ellipsoid provides a simple visual characterization of the initial two-qubit state, and various aspects of entanglement are reflected in its geometric properties. We experimentally verify these properties via measurements on many different polarization-entangled photonic qubit states. Moreover, for pure three-qubit states, the volumes of the two quantum steering ellipsoids generated by measurements on the first qubit are predicted to satisfy a tight Monogamy relation, which is strictly stronger than the well-known Monogamy of entanglement for concurrence. We experimentally verify these predictions, using polarization and path entanglement. We also show experimentally that this Monogamy relation can be violated by a mixed entangled state, which nevertheless satisfies a weaker Monogamy relation.

  • volume Monogamy of quantum steering ellipsoids for multiqubit systems
    Physical Review A, 2016
    Co-Authors: Shuming Cheng, Antony Milne, Michael J W Hall, Howard Mark Wiseman
    Abstract:

    The quantum steering ellipsoid can be used to visualise two-qubit states, and thus provides a generalisation of the Bloch picture for the single qubit. Recently, a Monogamy relation for the volumes of steering ellipsoids has been derived for pure 3-qubit states and shown to be stronger than the celebrated Coffman-Kundu-Wootters (CKW) inequality. We first demonstrate the close connection between this volume Monogamy relation and the classification of pure 3-qubit states under stochastic local operations and classical communication (SLOCC). We then show that this Monogamy relation does not hold for general mixed 3-qubit states and derive a weaker Monogamy relation that does hold for such states. We also prove a volume Monogamy relation for pure 4-qubit states (further conjectured to hold for the mixed case), and generalize our 3-qubit inequality to n qubits. Finally, we study the effect of noise on the quantum steering ellipsoid and find that the volume of any two-qubit state is non-increasing when the state is exposed to arbitrary local noise. This implies that any volume Monogamy relation for a given class of multiqubit states remains valid under the addition of local noise. We investigate this quantitatively for the experimentally relevant example of isotropic noise.

Howard Mark Wiseman - One of the best experts on this subject based on the ideXlab platform.

  • experimental validation of quantum steering ellipsoids and tests of volume Monogamy relations
    Physical Review Letters, 2019
    Co-Authors: Chao Zhang, Shuming Cheng, Michael J W Hall, Howard Mark Wiseman, Li Li, Qiuyue Liang, Yunfeng Huang, Chuanfeng Li, Geoff J Pryde
    Abstract:

    : The set of all qubit states that can be steered to by measurements on a correlated qubit is predicted to form an ellipsoid-called the quantum steering ellipsoid-in the Bloch ball. This ellipsoid provides a simple visual characterization of the initial two-qubit state, and various aspects of entanglement are reflected in its geometric properties. We experimentally verify these properties via measurements on many different polarization-entangled photonic qubit states. Moreover, for pure three-qubit states, the volumes of the two quantum steering ellipsoids generated by measurements on the first qubit are predicted to satisfy a tight Monogamy relation, which is strictly stronger than the well-known Monogamy of entanglement for concurrence. We experimentally verify these predictions, using polarization and path entanglement. We also show experimentally that this Monogamy relation can be violated by a mixed entangled state, which nevertheless satisfies a weaker Monogamy relation.

  • volume Monogamy of quantum steering ellipsoids for multiqubit systems
    Physical Review A, 2016
    Co-Authors: Shuming Cheng, Antony Milne, Michael J W Hall, Howard Mark Wiseman
    Abstract:

    The quantum steering ellipsoid can be used to visualise two-qubit states, and thus provides a generalisation of the Bloch picture for the single qubit. Recently, a Monogamy relation for the volumes of steering ellipsoids has been derived for pure 3-qubit states and shown to be stronger than the celebrated Coffman-Kundu-Wootters (CKW) inequality. We first demonstrate the close connection between this volume Monogamy relation and the classification of pure 3-qubit states under stochastic local operations and classical communication (SLOCC). We then show that this Monogamy relation does not hold for general mixed 3-qubit states and derive a weaker Monogamy relation that does hold for such states. We also prove a volume Monogamy relation for pure 4-qubit states (further conjectured to hold for the mixed case), and generalize our 3-qubit inequality to n qubits. Finally, we study the effect of noise on the quantum steering ellipsoid and find that the volume of any two-qubit state is non-increasing when the state is exposed to arbitrary local noise. This implies that any volume Monogamy relation for a given class of multiqubit states remains valid under the addition of local noise. We investigate this quantitatively for the experimentally relevant example of isotropic noise.

Michael J W Hall - One of the best experts on this subject based on the ideXlab platform.

  • experimental validation of quantum steering ellipsoids and tests of volume Monogamy relations
    Physical Review Letters, 2019
    Co-Authors: Chao Zhang, Shuming Cheng, Michael J W Hall, Howard Mark Wiseman, Li Li, Qiuyue Liang, Yunfeng Huang, Chuanfeng Li, Geoff J Pryde
    Abstract:

    : The set of all qubit states that can be steered to by measurements on a correlated qubit is predicted to form an ellipsoid-called the quantum steering ellipsoid-in the Bloch ball. This ellipsoid provides a simple visual characterization of the initial two-qubit state, and various aspects of entanglement are reflected in its geometric properties. We experimentally verify these properties via measurements on many different polarization-entangled photonic qubit states. Moreover, for pure three-qubit states, the volumes of the two quantum steering ellipsoids generated by measurements on the first qubit are predicted to satisfy a tight Monogamy relation, which is strictly stronger than the well-known Monogamy of entanglement for concurrence. We experimentally verify these predictions, using polarization and path entanglement. We also show experimentally that this Monogamy relation can be violated by a mixed entangled state, which nevertheless satisfies a weaker Monogamy relation.

  • volume Monogamy of quantum steering ellipsoids for multiqubit systems
    Physical Review A, 2016
    Co-Authors: Shuming Cheng, Antony Milne, Michael J W Hall, Howard Mark Wiseman
    Abstract:

    The quantum steering ellipsoid can be used to visualise two-qubit states, and thus provides a generalisation of the Bloch picture for the single qubit. Recently, a Monogamy relation for the volumes of steering ellipsoids has been derived for pure 3-qubit states and shown to be stronger than the celebrated Coffman-Kundu-Wootters (CKW) inequality. We first demonstrate the close connection between this volume Monogamy relation and the classification of pure 3-qubit states under stochastic local operations and classical communication (SLOCC). We then show that this Monogamy relation does not hold for general mixed 3-qubit states and derive a weaker Monogamy relation that does hold for such states. We also prove a volume Monogamy relation for pure 4-qubit states (further conjectured to hold for the mixed case), and generalize our 3-qubit inequality to n qubits. Finally, we study the effect of noise on the quantum steering ellipsoid and find that the volume of any two-qubit state is non-increasing when the state is exposed to arbitrary local noise. This implies that any volume Monogamy relation for a given class of multiqubit states remains valid under the addition of local noise. We investigate this quantitatively for the experimentally relevant example of isotropic noise.

Geoff J Pryde - One of the best experts on this subject based on the ideXlab platform.

  • experimental validation of quantum steering ellipsoids and tests of volume Monogamy relations
    Physical Review Letters, 2019
    Co-Authors: Chao Zhang, Shuming Cheng, Michael J W Hall, Howard Mark Wiseman, Li Li, Qiuyue Liang, Yunfeng Huang, Chuanfeng Li, Geoff J Pryde
    Abstract:

    : The set of all qubit states that can be steered to by measurements on a correlated qubit is predicted to form an ellipsoid-called the quantum steering ellipsoid-in the Bloch ball. This ellipsoid provides a simple visual characterization of the initial two-qubit state, and various aspects of entanglement are reflected in its geometric properties. We experimentally verify these properties via measurements on many different polarization-entangled photonic qubit states. Moreover, for pure three-qubit states, the volumes of the two quantum steering ellipsoids generated by measurements on the first qubit are predicted to satisfy a tight Monogamy relation, which is strictly stronger than the well-known Monogamy of entanglement for concurrence. We experimentally verify these predictions, using polarization and path entanglement. We also show experimentally that this Monogamy relation can be violated by a mixed entangled state, which nevertheless satisfies a weaker Monogamy relation.

Jieci Wang - One of the best experts on this subject based on the ideXlab platform.

  • Monogamy of einstein podolsky rosen steering in the background of an asymptotically flat black hole
    Annalen der Physik, 2018
    Co-Authors: Jieci Wang, Jiliang Jing
    Abstract:

    We study the behavior of Monogamy deficit and Monogamy asymmetry for Einstein-Podolsky-Rosen steering of Gaussian states under the influence of the Hawking effect. We demonstrate that the Monogamy of quantum steering shows an extreme scenario in the curved spacetime: the first part of a tripartite system cannot individually steer two other parties, but it can steer the collectivity of the remaining two parties. We also find that the Monogamy deficit of Gaussian steering, a quantifier of genuine tripartite steering, are generated due to the influence of the Hawking thermal bath. Our results elucidate the structure of quantum steering in tripartite quantum systems in curved spacetime.