We propose a hybrid (continuous-discrete variable) quantum repeater protocol for long-distance entanglement distribution. Starting from states created by single-photon detection, we show how entangled coherent state superpositions can be generated by means of homodyne detection. We show that near-deterministic entanglement swapping with such states is possible using only linear optics and homodyne detectors, and we evaluate the performance of our protocol combining these elements.

We present a scheme for the amplification of Schrödinger cats that collapses two smaller states onto their constructive interference via a homodyne projection. We analyze the performance of the amplification in terms of fidelity and success rate when the input consists of either exact coherent state superpositions or of photon-subtracted squeezed vacua. The impact of imprecise homodyne detection and of impure squeezing is quantified. We also assess the scalability of iterated amplifications.Coherent state superpositions, or optical Schrödinger cat states, are widely recognized as promising resources in quantum information [1][2][3][4][5], quantum metrology [6][7][8], and fundamental tests [9][10][11][12]. In the near-orthogonal basis of coherent states γ|−γ = e −2γ 2 , two particular instances for these states arewhere the sign (±) of the superposition refers to the even and odd cat state, respectively. These states exhibit quasi-probability distributions in phase space which are distinctly non-classical. This makes them all the more challenging to generate deterministically as that would require strong Kerr-type non-linearities [13][14][15].One has then to resort to heralding techniques which, though probabilistic, need only linear optics and projective measurements [16]. These state-engineering schemes are nonetheless approximative and present a limitation in the fidelity they produce with ideal cat states. Photon-subtraction of squeezed vacuum, for example, is a well-established method to generate approximations of small amplitude cat states, colloquially referred to as Schrödinger kittens [17][18][19][20][21]. Even in the best experimental conditions, the fidelity between the photon-subtracted squeezed vacuum (PSSV) and an actual odd cat state |κ − (γ) degrades markedly for γ ≥ 1.2 [22]. Yet, for these states to be reliable resources in quantum computation, their fidelity with cat states at least as large as γ = 1.2 need to be maintained at near-unit fidelity [3,23]. Single-photon subtraction is only one example of several measurement-induced schemes which have been proposed to generate kitten states [20,[24][25][26][27][28][29]. However, none of these schemes can produce arbitrarily large cats in a single run. Ways to get around this issue have been devised using the recursive amplification of small, approximate cats [30,31]. For example, it was suggested in [32] to interfere a supply of delocalized single photons followed by homodyne heralding to generate large entangled cat states. These proposals have in common that they rely on the coherent mixing of two small cats, whereupon a projective measurement collapses one of the two outputs onto a constructive interference of the inputshence the amplification. Here, we shall pursue the same idea but make use solely of homodyne heralding for its relative simplicity and high quantum efficiency. We also demonstrate that the acceptance window of homodyne heralding can be widened to increase the success rate of the amplification while at the same time maintaining a s...

A comprehensive theory of the Weyl-Wigner formalism for the canonical pair angle-angular momentum is presented. Special attention is paid to the problems linked to rotational periodicity and angular-momentum discreteness.Comment: 15 pages, 2 color figures. To appear in Annals of Physic

In the course of recent work, we have discovered an error in the numerical simulations of the repeater. The error leads to a value of the rate which is too high.A plot of the corrected rate is shown in Fig. 1 along with the rate from the published Letter for comparison. At a distance of 1000 km, the corrected rate is lower by a factor of 95, leading to a value of 0.001 rather than 0.1 pairs/minute as stated in the Letter. The protocol thus does not compare as favorably against discrete-variable repeater schemes as originally claimed. At 600 km we can compare against the schemes of the review [1]. We find that the corrected rate is not better than, but rather on par with, the rate of the best previous schemes that do not use multiplexing, when a realistic single-photon detector efficiency of 50% is assumed.[1] N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, Rev. Mod. Phys. 83, 33 (2011) . FIG. 1 (color online). Comparison of the corrected (solid black line) and the erroneous (dashed black line) rate. The optimal values of the number of generation steps m (red dotted line), and connection steps n (blue dash-dotted line) for the corrected rate are also indicated, with values given on the right-hand axis.

We propose a complete tomographic reconstruction of any vortex state carrying orbital angular momentum. The scheme determines the angular probability distribution of the state at different times under free evolution. To represent the quantum state we introduce a bona fide Wigner function defined on the discrete cylinder, which is the natural phase space for the pair angle-angular momentum. The feasibility of the proposal is addressed.Comment: Final published versio