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Optimal local expansion of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>W</mml:mi></mml:mrow></mml:math>states using linear optics and Fock states
We derive the maximum success probability of circuits with passive linear optics for postselectively 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 …