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The Elitzur-Vaidman [EV] bomb tester, first described in 1993, is a wonderful "pre-Shor's algorithm" application of quantum information. The original paper is written in the language of Mach-Zhender interferometers, beam splitters, detectors, and an amount of transparency of a silvered mirror, and doesn't use the terms qubit or quantum gates but instead for example refers to a photon going to the "right" as $|1\rangle$, and going "up" as $|2\rangle$. The paper contends that optimally they can test about one half of all live bombs without causing an explosion.

However, Kwiat, Weinfurter, and Zeilinger [KWZ] describe an improved bomb tester in a Scientific American article from 1996, titled "Quantum Seeing in the Dark". This can test for the presence of a live bomb with arbitrary accuracy, by reusing the photon and relying on the quantum Zeno effect to freeze the photon in a particular basis. Although Elitzur and Vaidman also considered reusing a photon, the improvement of [KWZ] posits to rotate the photon by an amount $\epsilon$ if the bomb is a dud (and to have it reset if the bomb is live).

Quantum Seeing in the Dark

I really love this improvement, as it naively seems counter to many hypotheses about where and why quantum computers can algorithmically outperform classical computers. In the tester as described in [KWZ], there is only a single qubit, which shouldn't be entangled to anything$^\dagger$, and yet there seems to be something nontrivially achieved over and above what can be done classically.

From whence does the power of [KWZ], which only uses a single qubit and relies on the quantum Zeno effect, come?

Are there a lot of air-quotes in my assessment above? For example is there really an "improvement" over what's achievable classically, or is it nonsense to consider a classical bomb tester? Is this improvement merely a parlor trick and not an "algorithm", or is it as I suspect more profound than that? If we were to pray at the Church of the Higher Hilbert Space would we find that the qubit that gets rotated is in actuality "entangled" with whether or not the bomb is live or a dud?

Although a careful reading of [KWZ] notes that they do use downcoversion to create entangled photons, this only appears to aid in their experimental setup and is not critical for the algorithm.

Mark Spinelli
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    have you read about "counterfactual computation" at all? This is probably heading in the algorithmic direction you're heading for. – DaftWullie Apr 05 '22 at 06:42
  • @DaftWullie thanks for your suggestion! I'm starting to read Jozsa's Quantum Effects in Algorithms, which appears to anticipate this tension between entanglement and the quantum Zeno effect on one qubit. Jozsa also appears to go to the church of the larger Hilbert space, maybe in equation (9). That's where the entanglement may lie (?) – Mark Spinelli Apr 05 '22 at 14:07
  • After passing a beam splitter the photon becomes entangled with a route in the interferometer, isn't it? – Danylo Y Apr 05 '22 at 17:37
  • Perhaps in the original setup of [EV] that might be true? But in "Quantum Seeing in the Dark" we don't need a beam-splitter; we can just as easily measure the polarization of the photons. One photon either gets rotated (if the bomb is a dud) or doesn't (if the bomb is live). – Mark Spinelli Apr 05 '22 at 17:48

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