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arXiv:quant-ph/0511189 · Physical Review A

Projection measurement of the maximally entangled N -photon state for a demonstration of the N -photon de Broglie wavelength

Fang‐Wen Sun, Z. Y. Ou, Guang‐Can Guo

Published Feb 10, 2006• 46 citations
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Abstract

We construct a projection measurement process for the maximally entangled $N$-photon state [the NOON state $(\ensuremath{\mid}N,0⟩+\ensuremath{\mid}0,N⟩)∕\sqrt{2}$] with only linear optical elements and photodetectors. This measurement process will give null result for any $N$-photon state that is orthogonal to the NOON state. We examine the projection process in more detail for $N=4$ by applying it to a four-photon state from type-II parametric down-conversion. This demonstrates an orthogonal projection measurement with a null result. This null result corresponds to a dip in a generalized Hong-Ou-Mandel interferometer for four photons. We find that the depth of the dip in this arrangement can be used to distinguish a genuine entangled four-photon state from two separate pairs of photons. We next apply the NOON state projection measurement to a four-photon superposition state from two perpendicularly oriented type-I parametric down-conversion processes. A successful NOON state projection is demonstrated with the appearance of the four-photon de Broglie wavelength in the interference fringe pattern.

DOI
10.1103/physreva.73.023808

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We construct a projection measurement process for the maximally entangled NNN-photon state [the NOON state (\ensuremath∣N,0⟩+\ensuremath∣0,N⟩)∕2(\ensuremath{\mid}N,0⟩+\ensuremath{\mid}0,N⟩)∕\sqrt{2}(\ensuremath∣N,0⟩+\ensuremath∣0,N⟩)∕2​] with only linear optical elements and photodetectors. This measurement process will give null result for any NNN-photon state that is orthogonal to the NOON state. We examine the projection process in more detail for N=4N=4N=4 by applying it to a four-photon state from type-II parametric down-conversion. This demonstrates an orthogonal projection measurement with a null result. This null result corresponds to a dip in a generalized Hong-Ou-Mandel interferometer for four photons. We find that the depth of the dip in this arrangement can be used to distinguish a genuine entangled four-photon state from two separate pairs of photons. We next apply the NOON state projection measurement to a four-photon superposition state from two perpendicularly oriented type-I parametric down-conversion processes. A successful NOON state projection is demonstrated with the appearance of the four-photon de Broglie wavelength in the interference fringe pattern.
A measurement process is constructed to project an arbitrary two-mode NNN-photon state to a maximally entangled NNN-photon state. The result of this projection measurement shows a typical interference fringe with an NNN-photon de Broglie wavelength. For an experimental demonstration, this measurement process is applied to a four-photon superposition state from two perpendicularly oriented type-I parametric down-conversion processes. Generalization to the projection measurement of an arbitrary NNN-photon state can be easily made and may have wide applications in quantum information. As an example, we formulate it for precision phase measurement.
Two schemes of projection measurement are realized experimentally to demonstrate the de Broglie wavelength of three photons without the need for a maximally entangled three-photon state (the NOON state). The first scheme is based on the proposal by Wang and Kobayashi (Phys. Rev. A {\bf 71}, 021802) that utilizes a couple of asymmetric beam splitters while the second one applies the general method of NOON state projection measurement to three-photon case. Quantum interference of three photons is responsible for projecting out the unwanted states, leaving only the NOON state contribution in these schemes of projection measurement.
Two schemes of projection measurement are realized experimentally to demonstrate the de Broglie wavelength of three photons without the need for a maximally entangled three-photon state (the NOON state). The first scheme is based on a proposal by [Wang and Kobayashi, Phys. Rev. A 71, 021802(R) (2005)] that utilizes a couple of asymmetric beam splitters while the second one applies the general method of NOON-state projection measurement to a three-photon case. Quantum interference of three photons is responsible for projecting out the unwanted states, leaving only the NOON-state contribution in these schemes of projection measurement. A detailed multimode analysis is made to account for imperfect situations in the experiments.
An experiment is performed to demonstrate the temporal distinguishability of a four-photon state and a six-photon state, both from parametric down-conversion. The experiment is based on a multiphoton interference scheme in a recently discovered projection measurement of a maximally entangled N-photon state. By measuring the visibility of the interference dip, we can distinguish the various scenarios in the temporal distribution of the pairs and, thus, quantitatively determine the degree of temporal distinguishability of a multiphoton state.
We report on an experimental demonstration of four-photon quantum interference using telecom-wavelength photons. The realization of multiphoton quantum interference is essential to linear optics quantum information processing and measurement-based quantum computing. We have developed a source that efficiently emits photon pairs in a pure spectrotemporal mode at a telecom-wavelength region, and have demonstrated quantum interference exhibiting reduced fringe intervals that correspond to a reduced de Broglie wavelength of up to the four-photon NOON state. Our result should open a path to practical quantum information processing using telecom-wavelength photons.