Volume monogamy of quantum steering ellipsoids for multi-qubit systems

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, 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 multi-qubit states remains valid under the addition of local noise. We investigate this quantitatively for the experimentally relevant example of isotropic noise.

arXiv comment8 pages, 2 figures. Add some Refs and a conjecture

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Cited by in corpus (32)

• Quantum Steering
• Demonstration of monogamy relations for Einstein-Podolsky-Rosen steering in Gaussian cluster states
• Experimental validation of quantum steering ellipsoids and tests of volume monogamy relations
• Einstein-Podolsky-Rosen steering: Its geometric quantification and witness
• Anisotropic invariance and the distribution of quantum correlations
• Versatile Multipartite Einstein-Podolsky-Rosen Steering via a Quantum Frequency Comb
• Einstein-Podolsky-Rosen Steering and Quantum Steering Ellipsoids: Optimal Two-Qubit States and Projective Measurements
• Shareability of Quantum Steering and its Relation with Entanglement
• Full multipartite steering inseparability, genuine multipartite steering and monogamy for continuous variable systems
• Visualizing quantum phase transitions in the XXZ model via the quantum steering ellipsoid
• Quantification of Wigner Negativity Remotely Generated via Einstein-Podolsky-Rosen Steering
• Quantification of quantum steering in a Gaussian Greenberger-Horne-Zeilinger state
• Shareability of steering in 2-producible states
• Experimental verification of the steering ellipsoid zoo via two-qubit states
• Monogamy relations of all quantum correlation measures for multipartite quantum systems
• Canonical steering ellipsoids of pure symmetric multiqubit states with two distinct spinors and volume monogamy of steering
• On the power of one pure steered state for EPR-steering with a pair of qubits
• Monogamy relations for nonclassical correlations of multi-qubit states
• Trade-off relations of l_1-norm coherence for multipartite systems
• Geometric picture for SLOCC classification of pure permutation symmetric three-qubit states
• Note on Product-Form Monogamy Relations for Nonlocality and Other Correlation Measures
• Maximum Violation of Monogamy of Entanglement for Indistinguishable Particles by Measures that are Monogamous for Distinguishable Particles
• Distribution of spin correlation strengths in multipartite systems
• On the notion of quantum copulas
• Operational simultaneous correlations in complementary bases of bipartite states via one-sided semi-device-independent steering
• Conditional states and entropy in qudit-qubit systems
• Trade-off relations on CHSH tests for multi-qubit pure states
• Quantum Assemblage Tomography
• Protection of quantum steering ellipsoids in non-Markovian environments
• Cyclic Einstein-Podolsky-Rosen Steering
• Monogamy inequalities for entanglement using continuous variable measurements
• Entanglement and volume monogamy features of permutation symmetric N-qubit pure states with N-distinct spinors: GHZ and WWbar states