Construction of a quantum repeater with linear optics

Abstract

We show how to create practical, efficient, quantum repeaters, employing double-photon guns, for long-distance optical quantum communication. The guns create polarization-entangled photon pairs on demand. One such source might be a semiconducter quantum dot, which has the distinct advantage over parametric down-conversion that the probability of creating a photon pair is close to one, while the probability of creating multiple pairs vanishes. The swapping and purifying components are implemented by polarizing beam splitters and probabilistic optical CNOT gates.PACS numbers: 42.79. Ta, 03.67.Hk, 42.79.Gn One year ago Knill, Laflamme, and Milburn demonstrated that efficient quantum computing is possible, in principle, with only linear optics and projective measurements [1]. In particular, when arbitrarily many auxiliary modes are available, one does not need the very weak nonlinearities assumed to be essential for these purposes. Subsequently, it was shown that the same resources (linear optics and projective measurements) can be used to create highly nonclassical number states [2,3]. These states are important for applications such as quantum lithography and quantum interferometry [4,5]. In addition, we showed that projective measurements enable interferometric quantum non-demolition measurements, again with only linear optics [6]. In this Letter, we continue this research program and show how one can make a practical quantum repeater with this technique.Quantum repeaters are essential for single-photon optical quantum comunication over distances longer than the attenuation length of the channels used [7,8]. Repeaters employ a combination of entanglement swapping [9] and entanglement purification or distillation [10]; i.e., multiple pairs of degraded entangled states are condensed into (fewer) maximally entangled states, after which swapping is used to extend the (now maximal) entanglement over greater distances. Both entanglement distillation and swapping have been demonstrated experimentally [11,12]. In this Letter, we present a practical protocol for optical quantum repeaters based on linear optics and a double-photon gun.Until now, the source for polarization-entangled photon pairs has mostly consisted of parametric downconverters, where a strong pump laser is sent through a nonlinear crystal. The interaction between the laser and the crystal results in entangled photon pairs. However, the output of these devices are not clean, maximally entangled, two-photon states, but rather a coherent superposition of multiple pairs.Suppose the effective interaction Hamiltonian of a parametric down-converter is given byHere, a † andb † are the usual creation operators of the two optical modes and H and V are orthogonal polarization directions. The operator,L + (L − ) is the creation (annihilation) operator for entangled photon pairs (in this case polarization singlets). The outgoing state of a spontaneous parametric down-converter is then given by |Ψ out = exp(iHt/ )|0 = ∞ n=0 N n (ǫL + ) n |0 . This expression is obta...

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