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arXiv · 2308.06245

Minimum Hilbert-Schmidt distance for Schmidt rank 2 states

Palash Pandya
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Abstract

The Hilbert-Schmidt distance between two states is proven to be non-contractive under CPTP maps, and therefore is not considered as an entanglement measure. However, that alone does not imply that the minimum Hilbert-Schmidt distance from the set of separable states is not contractive as well. To the contrary, not only do we provide a closed-form expression, we also provide analytical and numerical proof that minimum Hilbert-Schmidt distance for a given bipartite quantum state of Schmidt rank 2 is non-increasing under LOCC. The minimisation is taken to be over the set of separable states. We apply the algorithm by Verstraete et al [Journal of Modern Optics, 49(8), 2002] for the derivation of the analytical expression and Nielsen's theorem for the proof of monotonicity of the distance under LOCC.

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Palash Pandya. 2023-08-11. Minimum Hilbert-Schmidt distance for Schmidt rank 2 states. https://arxiv.org/abs/2308.06245

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