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arXiv:quant-ph/0003140 · Physical Review A

Absorption-free discrimination between semitransparent objects

Graeme Mitchison, Serge Massar

Published Feb 13, 2001• 32 citations
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Abstract

Absorption-free (also known as ``interaction-free'') measurement aims to detect the presence of an opaque object using a test particle without that particle being absorbed by the object. Here we consider semitransparent objects that have an amplitude $\ensuremath{\alpha}$ of transmitting a particle while leaving the state of the object unchanged and an amplitude $\ensuremath{\beta}$ of absorbing the particle. The task is to devise a protocol that can decide which of two known transmission amplitudes is present while ensuring that no particle is absorbed by the object. We show that the probabilities of being able to achieve this are limited by an inequality. This inequality implies that absorption-free distinction between complete transparency and any partial transparency is always possible with probabilities approaching 1, but that two partial transparencies can only be distinguished with probabilities less than 1.

DOI
10.1103/physreva.63.032105

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•Jul 14, 1996•0 citations
Absorption-free (also known as ``interaction-free'') measurement aims to detect the presence of an opaque object using a test particle without that particle being absorbed by the object. Here we consider semitransparent objects that have an amplitude \ensuremathα\ensuremath{\alpha}\ensuremathα of transmitting a particle while leaving the state of the object unchanged and an amplitude \ensuremathβ\ensuremath{\beta}\ensuremathβ of absorbing the particle. The task is to devise a protocol that can decide which of two known transmission amplitudes is present while ensuring that no particle is absorbed by the object. We show that the probabilities of being able to achieve this are limited by an inequality. This inequality implies that absorption-free distinction between complete transparency and any partial transparency is always possible with probabilities approaching 1, but that two partial transparencies can only be distinguished with probabilities less than 1.
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.
We discuss the effect of semitransparency in a quantum-Zeno-like interaction-free measurement setup, a quantum-physics based approach that might significantly reduce sample damage in imaging and microscopy. With an emphasis on applications in electron microscopy, we simulate the behavior of probe particles in an interaction-free measurement setup with semitransparent samples, and we show that the transparency of a sample can be measured in such a setup. However, such a measurement is not possible without losing (i.e., absorbing or scattering) probe particles in general, which causes sample damage. We show how the amount of lost particles can be minimized by adjusting the number of round trips through the setup, and we explicitly calculate the amount of lost particles in measurements which either aim at distinguishing two transparencies or at measuring an unknown transparency precisely. We also discuss the effect of the sample causing phase shifts in interaction-free measurements. Comparing the resulting loss of probe particles with a classical measurement of transparency, we find that interaction-free measurements only provide a benefit in two cases: first, if two semitransparent samples with a high contrast are to be distinguished, interaction-free measurements lose less particles than classical measurements by a factor that increases with the contrast. This implies that interaction-free measurements with zero loss are possible if one of the samples is perfectly transparent. A second case where interaction-free measurements outperform classical measurements is if three conditions are met: the particle source exhibits Poissonian number statistics, the number of lost particles cannot be measured, and the transparency is larger than approximately 12\frac{1}{2}21​. In all other cases, interaction-free measurements lose as many probe particles as classical measurements or more. Aside from imaging of gray levels, another possible application for interaction-free measurements is the detection of arbitrarily small phase shifts in transparent samples.
An interaction-free measurement system with a polarization-based Mach-Zehnder interferometer structure is analyzed for semitransparent objects. Here, it is shown that the interaction-free measurement of such objects with 100% detection efficiency is possible in principle if the system loss is negligible. The influence of two system imperfections, the system loss and the low quantum efficiency of the photon detectors, on the interaction-free measurement is also analyzed. Although the two system imperfections limit the maximal detection efficiency that can be achievable, the quantum efficiency of the photon detectors is less important when the system loss becomes small.
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.
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].