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arXiv:1004.0608 · Physical Review A

Optimal local expansion of W states using linear optics and Fock states

Rikizo Ikuta, Toshiyuki Tashima, Takashi Yamamoto, Masato Koashi, Nobuyuki Imoto

Published Jan 24, 2011• 33 citations
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Abstract

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 achieved by a polarization-dependent beamsplitter and $n\ensuremath{-}1$ polarization-independent beamsplitters.

DOI
10.1103/physreva.83.012314

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We derive the maximum success probability of circuits with passive linear optics for postselectively expanding an NNN-photon WWW state to an (N+n)(N+n)(N+n)-photon WWW state, by accessing only one photon of the initial WWW state and adding nnn photons in a Fock state. We show that the maximum success probability is achieved by a polarization-dependent beamsplitter and n\ensuremath−1n\ensuremath{-}1n\ensuremath−1 polarization-independent beamsplitters.
We introduce an elementary optical gate for expanding polarization entangled WWW states in which every pair of photons is entangled alike. The gate is composed of a pair of 50:50 beamsplitters and ancillary photons in the two-photon Fock state. By seeding one of the photons in an nnn-photon WWW state into this gate, we obtain an (n+2)(n+2)(n+2)-photon WWW state after postselection. This gate gives a better efficiency and a simpler implementation than previous proposals for WWW-state preparation.
The fundamental gates of linear optics quantum computation are realized by using single photons sources, linear optics, and photon counters. Success of these gates is conditioned on the pattern of photons detected without using feedback. Here it is shown that the maximum probability of success of these gates is typically strictly less than 1. For the one-mode nonlinear sign shift, the probability of success is bounded by 1/2. For the conditional sign shift of two modes, this probability is bounded by 3/4. These bounds are still substantially larger than the highest probabilities shown to be achievable so far, which are 1/4 and 2/27, respectively.
Recently it was realized that linear optics and photodetectors with feedback can be used for theoretically efficient quantum information processing. The first of three steps toward efficient linear optics quantum computation is to design a simple postselected gate that implements a nonlinear phase shift on one mode. Here a computational strategy is given for finding postselected gates for bosonic qubits with helper photons. A more efficient conditional sign flip gate is obtained. What is the maximum efficiency for such gates? This question is posed and it is shown that the probability of success cannot be 1.