Forging quantum money (part 2 of 3)
This post is the second of a three-part series on the paper An adaptive attack on Wiesner’s quantum money. The other parts are:
- Wiesner’s scheme for quantum money, and why it was considered secure,
- An attack on Wiesner’s money scheme that shows it is not secure (with an aside into quantum bomb testing!) (this post),
- and, A modification of Wiesner’s scheme that resists this attack.
Now that we’re familiar with the Wiesner’s original scheme for quantum money, we can take a look at the “bomb testing” attack presented in the paper. The paper actually introduces two attacks, one more general than the other, but I’ll focus on the less general one; the bomb testing attack, because it’s more fun.
But before we see how it’s applied, let’s take a look at the bomb testing idea, because it’s very cool.
Bomb testing
Suppose I give you 10 bombs, some of which might be duds, and some which are live. Below is an interactive example of such a scheme:
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| Clicking on a bomb will attempt to detonate it. In this way you can see if a bomb is a dud or not. | |||||||||
The task is: Can you determine a test that separates the live bombs from the dud ones?
Classically, one approach would be to simply attempt to detonate each bomb. If the bomb goes off, then it was a live bomb, and if it doesn’t, it wasn’t! Simple enough, but it leaves us with no good bombs to actually use, and is reasonably fraught with danger.
Quantumly, it turns out there is something we can do that actually lets us know if the bomb is live or not, and keeps the bomb un-detonated!
Elitzur-Vaidman bomb tester
In this model, we suppose that our bombs are configured like so:
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| Live bomb: Has a single-photon detector. If a photon hits, it, it explodes. | Dud bomb: Does not have a photon detector. The photon will pass unchanged through this bomb, and the bomb itself does not explode. |
We then recall the operation of a Mach-Zender Interferometer.