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arXiv · 1411.7977

Quantifying entanglement of a two-qubit system via measurable and invariant moments of its partially transposed density matrix

Karol Bartkiewicz·Jiří Beran·Karel Lemr·Michał Norek·Adam Miranowicz
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Abstract

We describe a direct method to determine the negativity of an arbitrary two-qubit state in experiments. The method is derived by analyzing the relation between the purity, negativity, and a universal entanglement witness for two-qubit entanglement. We show how the negativity of a two-qubit state can be calculated from just three experimentally accessible moments of the partially transposed density matrix of a two-photon state. Moreover, we show that the negativity can be given as a function of only six invariants, which are linear combinations of nine invariants from the complete set of 21 fundamental and independent two-qubit invariants. We analyze the relation between these moments and the concurrence for some classes of two-qubit states (including the X states, as well as pure states affected by the amplitude-damping and phase-damping channels). We also discuss the possibility of using the universal entanglement witness as an entanglement measure for various classes of two-qubit states. Moreover, we analyze how noise affects the estimation of entanglement via this witness.

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Karol Bartkiewicz, Jiří Beran, Karel Lemr, Michał Norek, Adam Miranowicz. 2015-04-10. Quantifying entanglement of a two-qubit system via measurable and invariant moments of its partially transposed density matrix. https://doi.org/10.1103/physreva.91.022323

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