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arXiv:quant-ph/0109080 · Physical Review A

Linear optics and projective measurements alone suffice to create large-photon-number path entanglement

Hwang Lee, Pieter Kok, Nicolas J. Cerf, Jonathan P. Dowling

Published Mar 1, 2002• 130 citations
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Abstract

We propose a method for preparing maximal path entanglement with a definite photon-number N, larger than two, using projective measurements. In contrast with the previously known schemes, our method uses only linear optics. Specifically, we exhibit a way of generating four-photon, path-entangled states of the form $|4,0〉+|0,4〉,$ using only four beam splitters and two detectors. These states are of major interest as a resource for quantum interferometric sensors as well as for optical quantum lithography and quantum holography.

DOI
10.1103/physreva.65.030101

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We propose a method for preparing maximal path entanglement with a definite photon-number N, larger than two, using projective measurements. In contrast with the previously known schemes, our method uses only linear optics. Specifically, we exhibit a way of generating four-photon, path-entangled states of the form ∣4,0〉+∣0,4〉,|4,0〉+|0,4〉,∣4,0〉+∣0,4〉, using only four beam splitters and two detectors. These states are of major interest as a resource for quantum interferometric sensors as well as for optical quantum lithography and quantum holography.
We present a scheme to produce an entangled four-photon W state by using linear optical elements. The symmetrical setup of linear optical elements consists of four beam splitters, four polarization beam splitters, and four mirrors. A photon Einstein-Podolsky-Rosen pair and two single photons are required as the input modes. The projection on the W state can be made by a four-photon coincidence measurement. Further, we show that by means of a horizontally oriented polarizer in front of one detector, the W state of three photons can be generated.
The technique of projective measurements in linear optics can provide apparent, efficient nonlinear interaction between photons, which is technically problematic otherwise. We present an application of such a technique to prepare large photon-number path entanglement. Large photon-number path entanglement is an important resource for Heisenberg-limited optical interferometry, where the sensitivity of phase measurements can be improved beyond the usual shot-noise limit. A similar technique can also be applied to signal the presence of a single photon without destroying it. We further show how to build a quantum repeater for long-distance quantum communication.
We show how an idealized measurement procedure can condense photons from two modes into one and how, by feeding forward the results of the measurement, it is possible to generate efficiently superposition states commonly called N00N states. For the basic procedure sources of number states leak onto a beam splitter, and the output ports are monitored by photodetectors. We find that detecting a fixed fraction of the input at one output port suffices to direct the remainder to the same port, with high probability, however large the initial state. When instead photons are detected at both ports, macroscopic quantum superposition states are produced. We describe a linear-optical circuit for making the components of such a state orthogonal, and another to convert the output to a N00N state. Our approach scales exponentially better than existing proposals. Important applications include quantum imaging and metrology.
We theoretically demonstrate a method for producing the maximally path-entangled state $(1/\sqrt{2})(|N,0〉+\mathrm{exp}[\mathrm{iN}\ensuremath{\varphi}]|0,N〉)$ using intensity-symmetric multiport beam splitters, single photon inputs, and either photon-counting postselection or conditional measurement. The use of postselection enables successful implementation with non-unit efficiency detectors. We also demonstrate how to make the same state more conveniently by replacing one of the single photon inputs by a coherent state.