Quantum mechanics is, mathematically, quite simple. But it has implications that require people to think differently about the world. One particularly hard-to-grasp idea is that, on the surface, some knowledge precludes obtaining other knowledge. This is a consequence of how we obtain it.

In an innovative experiment, researchers from Austria have demonstrated how to recover that lost information. Before you get the wrong impression, though, this is completely in agreement with the rules of quantum mechanics—it is simply a very clever way of playing with quantum states.

Quantum magic

Before looking at the experiment, note what makes this interesting. The keywords that turn up in these sorts of articles are superposition states and measurement. Imagine that we have 100 electrons, sitting in a magnetic field. Their individual magnetic fields are all, thanks to the applied field, pointing in the same direction. Now, we turn on a microwave for a specific period of time. Chosen correctly, all 100 electrons flip their fields so that they point in exactly the opposite direction. If we make a measurement, all electrons report the same spin. If we cut the time of the microwave pulse in half, however, something very strange happens: all the electrons end up with their fields pointing in both directions at once. This is called a superposition state.



Quantum superposition Superposition is nothing more than addition for waves. Let's say we have two sets of waves that overlap in space and time. At any given point, a trough may line up with a peak, their peaks may line up, or anything in between. Superposition tells us how to add up these waves so that the result reconstructs the patterns that we observe in nature. Read more…

Once we make a measurement, though, we find half the electrons have their fields pointing in one direction and half have their fields pointing in the opposite direction—the superposition state vanishes. You might immediately think it was never there in the first place: we simply put in half the energy, so only half the electrons responded.

But this is incorrect. We know that we get superposition states because we've looked. We can create a situation where, if the electrons were not in superposition state, we observe one result, and if they're in a superposition state, we observe something different. Even though we know it is a superposition state, every measurement on a single electron reports that its field is either pointing with the applied field or against the applied field.

This behavior tells us that, when we make a measurement, we destroy the superposition state and place the electron in a single pure state. We can't tell anything about the superposition state other than that it included the state that we measured.

Why should we care?

This property of quantum mechanics has made quantum computing a little bit more difficult. If everything goes well, at the end of a calculation, a qubit (quantum bit) will be in a superposition of the right answer and the wrong answer. Although the probability of the right answer should be much higher than that of the wrong answer, there is always a chance of getting the wrong answer. In very fast quantum computers, we would just run the calculation a few times and take the most frequent answer as the correct answer. But what if your computer is slow?

The ideal situation is to be able to take a measurement, then reconstruct the original superposition state so that repeated measurements could be used (ensuring that the most probable state can be determined). However, for a single particle, that is impossible. To overcome this problem, researchers have done the obvious: they spread their qubit over three particles. Even with three particles, however, measuring all three then taking a majority vote on the answer may not be good enough.

So the researchers decided to be clever. In their scheme, the qubit is encoded between two states of an ionized calcium atom. To provide redundancy, the qubit is then entangled with two other qubits. (You can think of this as creating two mirror images of the quantum state of the qubit in two other particles. This isn't a technically correct description, but it should help you get the point). Now, we have our three qubits, each of which encodes a single quantum bit of information.

Quantum entanglement Quantum entanglement is one of the most misused concepts around. Entanglement is delicate, rare, and short-lived. At its heart, quantum entanglement is nothing more or less than a correlation between two apparently separate quantum objects. Having discovered that, you might ask "so what is all the fuss about?" The answer lies deep in quantum mechanics. Read more…

But, unlike our electron in the magnetic field where there are only two possible states, the calcium ion has many, many states available to it. The researchers make use of a total of four states. One state corresponds to a logical zero, while a second corresponds to a logical one. (I'll call the other two states the measurement state and the hidden state.)

One laser connects the measurement state to the logical one state, while a second laser connects the logical one state to the hidden state. To measure a state, we turn on the first laser. The qubit falls into either the logical one or logical zero, based on the probabilities of the superposition state. If it ends up in logical one, the laser light is scattered by the ion and is detected. Hence a pulse on the photodetector indicates a logic one, while the absence of light signals a logical zero. That is the measurement process.

The second laser simply changes the definition of the qubit. Initially, a qubit is a superposition of the logical one and logical zero states. After the laser pulse, the qubit is a superposition between the hidden state and the logical zero state. In this case, the qubit cannot be evaluated by the measurement process.

The researchers take advantage of this by placing two of the three qubits into the hidden state, then measuring the remaining qubit to get an answer (logical one or zero). Then, after the measurement process, the hidden qubits are returned to their original states (a superposition of logical one and zero) and re-entangled with the original qubit. In doing so, the qubit is placed back in its original superposition state.

By repeating this process, the researchers can measure the state as many times as required to ensure that they know which logical state was the most frequent. Indeed, through multiple measurements, the researcher can obtain the relative probabilities of logical one and logical zero of the original superposition state.

In terms of advances for practical quantum computers, this may not mean a huge amount. However, it demonstrates a technique that will be critical for a working quantum computer. So in this sense, it is a very important step. But the issue may be with the implementation; the work was done with trapped ions, and it's hard to believe that trapped ions, floating in a vacuum, are the future of quantum computing.

Physical Review Letters, 2013, DOI: 10.1103/PhysRevLett.110.070403

Listing image by David Singleton