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arXiv · 1606.02390

Volume monogamy of quantum steering ellipsoids for multi-qubit systems

Shuming Cheng·Antony Milne·Michael J. W. Hall·Howard M. Wiseman
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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.

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Shuming Cheng, Antony Milne, Michael J. W. Hall, Howard M. Wiseman. 2016-06-08. Volume monogamy of quantum steering ellipsoids for multi-qubit systems. https://doi.org/10.1103/physreva.94.042105

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