Optimal local expansion of W states using linear optics and Fock states
Rikizo Ikuta, Toshiyuki Tashima, Takashi Yamamoto, Masato Koashi, and, Nobuyuki Imoto

TL;DR
This paper determines the highest success probability for expanding N-photon W states to (N + n)-photon states using linear optics, revealing optimal configurations with specific beam splitters.
Contribution
It provides the first analytical derivation of the maximum success probability for local W state expansion with passive linear optics and Fock states.
Findings
Maximum success probability derived for W state expansion.
Optimal optical circuit configuration identified.
Success probability depends on specific beam splitter arrangements.
Abstract
We derive the maximum success probability of the circuits with passive linear optics for expanding an N-photon W state to an (N + n)-photon W state, by accessing only one photon of the initial W state and adding n photons in a Fock state. We show that the maximum success probability is achieved by a polarization-dependent beamsplitter and n-1 polarization-independent beamsplitters.
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