Volume monogamy of quantum steering ellipsoids for multi-qubit systems
| Autor: | Cheng, Shuming, Milne, Antony, Hall, Michael J. W., Wiseman, Howard M. |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Phys. Rev. A 94, 042105 (2016) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevA.94.042105 |
| Popis: | 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. Comment: 8 pages, 2 figures. Add some Refs and a conjecture |
| Databáze: | arXiv |
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