2023/08/11 by Palash Pandya, Pandya, Palash, Wieśniak, Marcin
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2308.06245
openalex publication_date 2023/08/11 · openalex created_date 2023/08/15 · openalex updated_date 2026/07/28
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.