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arXiv:quant-ph/0507216 · Optics Letters

Interconvertibility of single-rail optical qubits

Dominic William Berry, Alexander I. Lvovsky, Barry C. Sanders

Published Jan 1, 2006• 18 citations
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Abstract

We show how to convert between partially coherent superpositions of a single photon with the vacuum by using linear optics and postselection based on homodyne measurements. We introduce a generalized quantum efficiency for such states and show that any conversion that decreases this quantity is possible. We also prove that our scheme is optimal by showing that no linear optical scheme with generalized conditional measurements, and with one single-rail qubit input, can improve the generalized efficiency.

DOI
10.1364/ol.31.000107

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We show how to convert between partially coherent superpositions of a single photon with the vacuum by using linear optics and postselection based on homodyne measurements. We introduce a generalized quantum efficiency for such states and show that any conversion that decreases this quantity is possible. We also prove that our scheme is optimal by showing that no linear optical scheme with generalized conditional measurements, and with one single-rail qubit input, can improve the generalized efficiency.
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We analyze the problem of increasing the efficiency of single-photon sources or single-rail photonic qubits via linear optical processing and destructive conditional measurements. We allow for the use of coherent states and do not limit to photon-counting measurements. We conjecture that, with the limitation that multiphoton components in the output are not permitted, it is not possible to increase the efficiency. We prove this conjecture for several important special cases, and provide extensive numerical results for the general case.
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Entanglement is the basic building block of linear optical quantum computation, and as such understanding how to generate it in detail is of great importance for optical architectures. We prove that Bell states cannot be generated using only three photons in the dual-rail encoding, and give strong numerical evidence for the optimality of the existing four photon schemes. In a setup with a single photon in each input mode, we find a fundamental limit on the possible entanglement between a single mode Alice and arbitrary Bob. We investigate and compare other setups aimed at characterizing entanglement in settings more general than dual-rail encoding. The results draw attention to the trade-off between the entanglement a state has and the probability of postselecting that state, which can give surprising constant bounds on entanglement even with increasing numbers of photons.