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arXiv:quant-ph/0112002 · Physical Review A

Creation of large-photon-number path entanglement conditioned on photodetection

Pieter Kok, Hwang Lee, Jonathan P. Dowling

Published Apr 15, 2002• 302 citations
arXivHTMLPDF

Abstract

Large-photon-number path entanglement is an important resource for enhanced precision measurements and quantum imaging. We present a general constructive protocol to create any large-photon-number path-entangled state based on the conditional detection of single photons. The influence of imperfect detectors is considered and an asymptotic scaling law is derived.

DOI
10.1103/physreva.65.052104

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Large-photon-number path entanglement is an important resource for enhanced precision measurements and quantum imaging. We present a general constructive protocol to create any large-photon-number path-entangled state based on the conditional detection of single photons. The influence of imperfect detectors is considered and an asymptotic scaling law is derived.
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.
In this paper, we propose two protocols for generating super-resolving single-photon (SRSP) number-path-entangled states from general maximally number-path-entangled NOON states. It is our purpose to show that, contrary to popular belief, a field in a single-photon state can carry multifold phase information. We also show that both protocols generate the desired state with different probabilities depending on the type of detectors being used. Such SRSP number-path-entangled states preserve high resolving power but lack the requirement of a multiphoton absorbing resist, which may serve as a proof-of-principle prototype for quantum lithography in the future.
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 propose a protocol for generating photon-number entanglement through sequential parametric down-conversion processes. This protocol is fully compatible with linear optics experiments and can be easily implemented as an extension of the path-identity scheme. We present a detailed scheme for the creation of heralded two-mode photon-number high-dimensional entanglement with the form of $|00\ensuremath{\rangle}+|11\ensuremath{\rangle}+|22\ensuremath{\rangle}$. In addition, the protocol enables us to easily generate various photon-number-entangled states, which have potential applications in quantum communication, quantum precision measurements, and continuous-variable quantum information.
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.