Quantum key distribution is supposed to provide a high degree of certainty in the security of secret keys. That certainty is based on the laws of physics, and all attacks against quantum keys have exploited implementation weaknesses, rather than the underlying physics. Unlike mathematical methods of encryption, quantum key distribution does not provide a key that is difficult to figure out. Instead, the nature of the key generation process allows any interloper to be detected—you know if your key is secret or not.

At present, quantum key distribution is limited to about 70km to 100km between the two nodes, because fiber optical cables tend to absorb the photons used to carry the key. To provide end-to-end distribution between, say, Paris and Berlin, you either need to trust the third parties in between (so each node has its own pair of keys that it has generated with neighboring nodes) or have a quantum memory at each node. A quantum memory allows you to store each qubit and then teleport its state to the next node. At the end of the key-generation process, teleporting ensures that a single shared key is generated between the end-points, and the intermediate nodes have no knowledge of the key.

Therein lies a weakness: maybe the memories at the intermediate can be exploited, allowing a secret key to be intercepted without detection. To close that particular exploit, a group of researchers has proposed a clever way to scramble a quantum memory.

Scrambled memory for everyone

This has wider implications than just for quantum key distribution. Over the past 5 to 10 years, the concept of secure computing has gained a lot of currency. A computer you don't own performs calculations for you, but no one else can access the data or even the algorithm being run. The idea is that you—the user of the facility—should not have to trust the facility or any of the other users. Instead, the structure of the computer should not allow anyone to determine any information about the computation being performed.

To ensure that is the case, it needs to be impossible to read out the state of the memory in a useful way. In classical computers, one can think about memory encryption schemes. But quantum computers, unfortunately, are rather transparent in how they store information. Anyone with some knowledge and access to the hardware should be able to read the memory out. They could even do this without destroying the quantum state of the qubit (quantum bit), allowing them to perform their own computation on your information. Or, they could potentially grab part of an encryption key while it's being transmitted.

How to make a quantum elephant

The solution is to encrypt quantum memory. A recent theory paper provides a method to do that for qubits based on photons. To understand it, we need to take a step back to see how a photon can be stored in a quantum memory, one that might consist of a gas of atoms that have three energetic states. The first two states are a ground state and a storage state. These two states have very similar energies, but it is impossible for the atom to transfer directly from the ground state to the storage state. Moving between quantum states must conserve energy, momentum, and angular (or spin) momentum, which is not possible for all transitions. In particular, the atoms are chosen so that a transition from the ground state to the storage state does not conserve spin momentum.

The third state is an excited state. For the atom to enter this state, a significant amount of energy in the form of a photon is required. So, the atom can go from the ground state to the excited state by absorbing a photon. And the atom can go from the excited state to either the ground state or the storage state by emitting a photon. Hence, our ground state and storage state are linked to each other via the excited state.

Our quantum memory is constructed by putting all the atoms in the ground state. The qubit photon is tuned so that it has approximately the same energy as the transition between the ground state and the excited state. Finally, we have a control light pulse, which is tuned to match the energy difference between the storage state and the excited state.

Now, if the photonic qubit is flying through the memory at the same time as a control light pulse, it will excite atoms to the excited state, while the control light pulse will stimulate the atom to emit a photon and enter the storage level. Our qubit is now stored somewhere in the cloud of atoms. To get the qubit back, we simply shine the control light field into the cloud again. An atom in the storage state will absorb a photon and emit our qubit again.

There is obviously a bit more to this. Technically, the qubit information is stored in the phase relationship between the atoms in the storage state and the atoms in the ground state, which is why the timing of the control pulses is important. This relationship is also why information can only be stored for a limited time.

Hiding the information in plain sight

You can store multiple qubits by storing each in a different part of the cloud of atoms. If each qubit has a slightly different color, then the control light pulse must also have a slightly different brightness (I won't go into the reasons for this, suffice to say that the strength of the light field shifts the energy of the excited state). So, if we shine the control light field through the cloud from the side and make sure that the brightness of the light varies, then each qubit will be stored at a particular location in the cloud. Normally, this is done by smoothly varying the brightness of the control light pulse from dim to bright.

It turns out that this approach can also be used to encrypt our memory as well. First, we set up our control light field so that its intensity varies randomly in space. This can be done by shining it through frosted glass, for instance. Now, we set up our qubit as a pulse of light (it's still a single photon). As a pulse, the qubit has a well-defined arrival time, but its color is very uncertain. In fact, that single photon has multiple colors at the same time (yes, this is quantum mechanics). As a result, it is stored throughout the cloud with a probability that depends on the brightness of the control light field. But that brightness varies randomly in space, so the probability also has a spatial dependence.

Now, if we want to read the photon out again, we have to match the intensity profile of the control light field. But that was randomly determined by a bit of frosted glass. The researchers computed that, after storage, a second (but not matched) randomly generated control light field was unable to retrieve the qubit. Nor was a uniform light field successful in accessing the qubit.

To test how accurately one must guess the random pattern, the researchers tested how accurately the qubit was retrieved after the correct pattern was shifted sideways slightly. They showed that the qubit could not be retrieved if the pattern was shifted by about one part in one thousand.

Seeking: A solid engineer

And that brings up the weakness of the scheme: alignment. The light pattern has to be generated by a device, and the spatial relationship between the device and the atomic cloud has to remain fixed to a very high degree of accuracy. To put it in perspective: if the cloud of atoms is 3mm long, then the light pattern cannot be displaced by more than 3μm. The pattern is generated outside the vacuum chamber that holds the cloud, and the light has to propagate by some 50mm (it's likely to be more than that) to reach the cloud. The angular accuracy of the light propagation direction has to be better than 0.003 degrees, and the cloud cannot drift by more than 3μm during a storage period.

Fortunately, there are more sensible ways to achieve the same thing. This whole scheme will work much better using crystals, where, instead of atomic clouds, bits are stored in ions that are doped into material. To achieve alignment, one could even glue an lcd to the side of the crystal and use random pixel settings to generate the storage key. Distances would be much smaller, and positioning is more stable. Even so, I know from colleagues that the type of experiment that is proposed here is very alignment sensitive and will require quite a bit of work to get right.

Despite that, I think this is a pretty cool idea and jives well with recent work on storing multiple qubits in a single crystal. This might be combined to create a memory that can store a relatively high density of qubits, while also hiding them from public view.

Physical Review A, 2017, DOI: 10.1103/PhysRevA.95.061805