Volume monogamy of quantum steering ellipsoids for multi-qubit systems

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Cheng, Shuming; Milne, Antony; W. Hall, Michael J and Wiseman, Howard M. 2016. Volume monogamy of quantum steering ellipsoids for multi-qubit systems. Physical Review A, 94(042105), ISSN 2469-9926 [Article]

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Official URL: https://journals.aps.org/pra/abstract/10.1103/Phys...

Abstract or Description

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.

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https://doi.org/10.1103/PhysRevA.94.042105