New paper: Non-deterministic approximation of photon number discriminating detectors using non-discriminating detectors

Quantum computing is one of those mysterious fields that most people don’t have any familiarity with at all. This problem is excaccerbated by the fact that the literature in this field is typically very technical and out of reach to non-specialists. In fact, even I, as a student in the field, find it extremely difficult to follow the literature. Consequently, I’ve decided that whenever I publish a new paper, I’ll complement it with a layman’s description of the paper in this blog, hopefully in a form pallateable to those who have never even heard of the word physics before.

Several months ago my first physics paper was accepted for publication in the Journal of Optics B., entitled “Non-deterministic approximation of photon number discriminating detectors using non-discriminating detectors” (e-print quant-ph/0411114). This is quite a mouthful I confess, however the idea behind the paper is very simple and I’ll now attempt to explain it in as non-technical a manner as possible.

In optical quantum computing (see my previous post for an introduction), my area of research, we use photons, or particles of light, to represent qubits. One of the most fundamental requirements to experimentally realize optical quantum gates is photo-detectors. A photo-detector is simply a device which tells you when a photon hits it. However, there are two types of photo-detectors: discriminating (or number-resolving) and non-discriminating. A discriminating photo-detector is one which is able to tell you how many photons have hit it, whereas a non-discriminating detector can only tell you if one or more photons hit it, but not how many. In the long term, if we’re going to able to construct optical quantum computers, it turns out that we’ll need the former discriminating variety. However, building discriminating photo-detectors is very technologically challenging and presently we only have reliable non-discriminating ones. In this paper I describe how non-discriminating detectors can be used to approximate discriminating detectors. The proposal is non-deterministic, which simply means that the device doesn’t always work, but when it does, you can be very confident that it has worked correctly. Because the proposal in non-deterministic, it’s application is quite limited. However, there are still many experiments for which the proposal may be applicable.

My proposal describes a class of detectors which do the following. We have some unknown number of photons n, hitting our detector, and we want to know if the number of incident photons is m. If n=m our detector gives a response, otherwise it does not.

I’ll begin by explaining the simplest case, an m=1 detector. That is, a detector which tells us if there is exactly one incident photon. There are only two basic components we need to do this: a beamsplitter and two non-discriminating detectors. A beamsplitter is simply a device which, when a photon hits it, has some probability P, of going one way, and some other probability 1-P, of going the other. To construct our m=1 detector we will simply direct the incoming beam onto a very low reflectivity beamsplitter (i.e. very small P). At each of the beamsplitter outputs we place a non-discriminating detector. Now imagine that n=1, i.e. a single photon is incident on the beamsplitter. The photon has probability P of hitting the first detector, and probability 1-P of hitting the second detector. If we have two incident photons (i.e n=2) then the probability that both photons reach the first detector is P squared, and the rest of the time at least one of the photons will reach the second detector. In general, for an arbitary n-photon input state, the probability that all photons reach the first detector drops of exponentially as P to the power of n. Recall that P is chosen to be very small. Therefore, P squared is much smaller than P. This realization forms the basis of the proposal. We apply a so-called post-selection procedure. Namely, if the first photo-detector triggers, but the second does not, we can say with high probability that exactly one photon was incident on the beamsplitter, since the probability that multiple photons are all directed to the first detector is extremely low. If the second detector does trigger, we ignore the result as a failure. This is where the non-determinism comes in. So we see that using a low-reflectivity beamsplitter and two non-discriminating detectors we can construct a device which fails most of the time, but when it succeeds, tells us that we almost certainly had exactly one photon at the input.

The idea I just described for an m=1 detector can be generalized to construct arbitrary m-photon discriminating detectors, by using a chain of m beamsplitters instead of just one. In principle the idea works very well, however there is one experimental challenge in particular which limits its effectiveness. Specifically, experimental photo-detectors are inefficient, which means they don’t always click when a photon hits them. Let’s consider what this means in the context of the m=1 detector I described earlier. We said that when the first detector clicks, but the second does not, we can be fairly sure that we had exactly one photon in our input. Suppose, however, that the detectors are ineffecicient. This means that a photon might hit the second detector, but not trigger it. This means that we may have in fact had two incident photons, but we simply missed one of them. Clearly this makes the results erroneous. This problem of having inefficient detectors is actually quite signficant since present-day detectors are really quite inefficient. Nonetheless, with the future in mind, when highly efficienty detectors may be available, the proposal may find a use.

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