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arXiv:quant-ph/9909083 · Physical Review Letters

High-Efficiency Quantum Interrogation Measurements via the Quantum Zeno Effect

Paul G. Kwiat, Andrew G. White, J. R. Mitchell, Olaf Nairz, Gregor Weihs, Harald Weinfurter, Anton Zeilinger

Published Dec 6, 1999• 213 citations
arXivHTMLPDF

Abstract

The phenomenon of quantum interrogation allows one to optically detect the presence of an absorbing object, without the measuring light interacting with it. In an application of the quantum Zeno effect, the object inhibits the otherwise coherent evolution of the light, such that the probability that an interrogating photon is absorbed can in principle be arbitrarily small. We have implemented this technique, achieving efficiencies of up to $73%$, and consequently exceeding the $50%$ theoretical maximum of the original ``interaction-free'' measurement proposal. We have also predicted and experimentally verified a previously unsuspected dependence on loss.

DOI
10.1103/physrevlett.83.4725

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The phenomenon of quantum interrogation allows one to optically detect the presence of an absorbing object, without the measuring light interacting with it. In an application of the quantum Zeno effect, the object inhibits the otherwise coherent evolution of the light, such that the probability that an interrogating photon is absorbed can in principle be arbitrarily small. We have implemented this technique, achieving efficiencies of up to 7373%73, and consequently exceeding the 5050%50 theoretical maximum of the original ``interaction-free'' measurement proposal. We have also predicted and experimentally verified a previously unsuspected dependence on loss.
Summary form only given.Using the complementary wave-like and particle-like natures of photons, one can make interaction-free measurements (IFM)-the presence of an object can be determined with no photons being absorbed. By using an application of the quantum Zeno effect (weakly and repeatedly testing for the object's presence so that the otherwise coherent evolution of the interrogating photon is inhibited), we have demonstrated the feasibility of IFMs with an efficiency of >85%, higher than that possible in the original IFM scheme, where, at most, half of the measurements could be interaction free. We also investigate various interaction-free imaging systems, demonstrate imaging with a resolution <5 /spl mu/m, and define the limits to these systems. We also discuss in which sense interaction-free measurements really are not.
Using a hybrid of a simple interference technique and an application of the quantum Zeno effect, it is possible to optically determine the presence of an absorbing object with an arbitrarily low probability that a photon is actually absorbed. We have demonstrated the feasibility of systems in which up to 85% of the measurements could be “interaction-free”. Also, we have started investigating the possibility of using these techniques to allow “interaction-free” imaging of objects; our prototype schemes have shown resolutions of less than 10 µm. Finally, we present a curious phenomenon that occurs when the object in question is only partially transmitting, which should allow a seeming violation of Beer’s law.
It is now well-understood that the complementary wave- and particle-like natures of quanta enable one to make measurements that are “interaction-free” -- one can determine the presence or absence of an object, even a completely absorbing object, without any photons being absorbed. The first proposal of such a scheme was limited to an efficiency of 50% -- at most half of the measurements could be interaction free [1]. By using an application of the Quantum Zeno effect, one can in fact have the fraction of interaction-free measurements arbitrarily close to one [2].
We present here a quantum tripwire, which is a quantum optical interrogation technique capable of detecting an intrusion with very low probability of the tripwire being revealed to the intruder. Our scheme combines interaction-free measurement (IFM) with the quantum Zeno effect in order to interrogate the presence of the intruder without interaction. The tripwire exploits a curious nonlinear behaviour of the quantum Zeno effect we discovered, which occurs in a lossy system. We also employ a statistical hypothesis testing protocol, allowing us to calculate a confidence level of IFM after a given number of trials. As a result, our quantum intruder alert system is robust against photon loss and dephasing under realistic atmospheric conditions and its design minimizes the probabilities of false positives and false negatives as well as the probability of becoming visible to the intruder.
Interaction-free measurement infers the presence of an absorbing object from a photon that, in the counterfactual sense, never interacted with it, and is widely described as a route to minimally invasive sensing. We ask what it actually buys, in estimation-theoretic terms. Written as a channel-estimation problem, the Elitzur-Vaidman interferometer carries exactly half the Fisher information about the object's transmissivity that direct transmission probing does, and the two schemes deliver identical Fisher information per absorbed photon. For measuring how transparent something is, the interferometer buys nothing. The advantage lies in discrimination, and we show that what it requires is not that the object be opaque but that the competing hypothesis be the object's absence. Against empty space the Chernoff information per absorbed photon grows almost linearly, as the number of Zeno cycles times its logarithm, even for a weakly absorbing object; between two partial transparencies it does not grow at all. Parasitic loss in the cycle caps the advantage. The number of conclusive interrogations per absorbed photon reaches a maximum inversely proportional to the loss per cycle, at an optimal cycle number that is likewise inversely proportional to it, which identifies the loss per cycle as the figure of merit governing how far interaction-free sensing can be pushed. Finally, the negative result is not special to the interferometer. For a single photon meeting a memoryless, non-dispersive object any number of times through arbitrary fixed optics, the accessible quantum Fisher information never exceeds that of the same incident flux spent on independent single-pass probes, and is generically far below it. This recovers the bound of Massar, Mitchison and Pironio for this class, by a short argument that also identifies when it is tight.
The quantum Zeno effect describes the inhibition of quantum evolution by frequent measurements. Here, we propose a scheme for entangling two given photons based on this effect. We consider a linear-optics set-up with an absorber medium whose two-photon absorption rate ξ2γξ_{2γ}ξ2γ​ exceeds the one-photon loss rate ξ1γξ_{1γ}ξ1γ​. In order to reach an error probability PerrorP_{\rm error}Perror​, we need ξ1γ/ξ2γ<2Perror2/π2ξ_{1γ}/ξ_{2γ}<2P_{\rm error}^2/π^2ξ1γ​/ξ2γ​<2Perror2​/π2, which is a factor of 64 better than previous approaches (e.g., by Franson et al). Since typical media have $ξ_{2γ}