Scientific Method / Science & Exploration

Mere possibility of measurement makes QKD protocol secure

What if Eve listened, but heard nothing but noise?

Part of a working quantum key distribution system.



Let me self-plagiarize


Light has a property called polarization, which is measured with respect to a reference frame. So, for instance, horizontally polarized light has its electric field aligned with the ground, while vertically polarized light has its electric field aligned perpendicular to the ground. In between, we can have diagonal and anti-diagonal polarized light.

But the location of the ground is arbitrary. So the description of polarization consists of not just the measurement of the polarization, but also agreeing on a common frame of reference (called a basis set). It is these two factors that give QKD (QKD can also use other properties of light, but polarization is simplest to describe) its security.

To generate a key, Bob makes two choices: he chooses between two reference frames, and he chooses between two polarization states within a reference frame. After making that choice, he sends a single photon to Alice in one of four polarization states (two reference frames and two polarization states per reference frame). Alice does not know any of Bob's choices, so she chooses at random a reference frame, measures the polarization, and notes the result. If Alice and Bob choose different reference frames, then the results of Alice's measurement is entirely random. But, if they choose the same reference, then the result of Alice's measurement is not random, and Bob knows what her result should be.

After sending a long string of photons, Bob and Alice both have two lists: each has a list of reference frames, Alice has a list of measurement results, and Bob has a list of sent states. They share their list of reference frames. Where they both happened to choose the same reference frame, Alice will accurately measure the photon Bob sent. That means they can share the list of reference frames in an insecure manner and use that to choose the common entries.

Ideally, they should agree half of the time. If someone chooses to interfere by intercepting and resending single photons, that can be detected by examining the statistics of the measurement and seeing if this isn't the case. Hence, the key-generation process gives away the presence of an eavesdropper.

In the last paragraph, I state that they should agree half the time. But this is only true if no photons are lost or intercepted. A typical 50km optical fiber link might result in 90 percent of the photons being lost, so agreement is expected just five percent of the time. Now, imagine that Eve intercepts one percent of the photons, so we go from agreeing 5 percent of the time to agreeing 4.5 percent of the time.

This presents two problems: first, you have to send enough photons to have sufficient statistical power to determine that the rate of agreement has changed by 0.5 percent. And, to make matters worse, you have to know the rate at which photons are lost to an accuracy of one percent. Only then can you say with certainty that Eve is present (or not—she probably gets annual leave and a pension plan).

A protocol that avoided this need for statistical power would have the potential of simplifying things considerably.

Let’s conjugate

In our description of QKD, we almost always use polarization because it is easier to visualise. But, in real implementations, it is easier to use the phase of the light. Essentially, each photon gets passed through a piece of material with a refractive index that can be varied via an applied voltage. Depending on the voltage, the photon will be ever so slightly delayed with respect to some reference photon.

To measure this, both the manipulated and reference photons pass through a partially reflecting mirror. The photons then follow two possible paths to another partially reflecting mirror, where they recombine and are either transmitted or reflected to one of two detectors. When there's no phase shift, one detector will click; a phase shift of 180 degrees, the other detector will click.

A necessary extra requirement is that the vast majority of photon time-slots are empty. Reference photons interfere with these empty time-slots and provide results that are truly random, revealing the presence of Eve, even when she tries to mask her presence by faking the photons she has detected.

The new development is that the researchers have shown that, instead of using a separate reference beam of photons, or using adjacent pulses as a reference, you can randomize your reference choice. The idea is that you have a string of, say ten photons time-slots, and a random number generator chooses which photons are interfered with each other. Again, the photons enter the interferometer, but now one path is set by this random choice to a length that will synchronize the correct photon pairs.

For each time slot, one of the detectors may go bing and Bob records the time slots and bit value for every bing. Bob throws away the pair combinations that did not generate a bing. To generate a key, Alice gets sent the random choices that Bob made, so she know which time slots were paired and generated data. She can then compute what Bob must have measured, which becomes a secret key.

This is complicated, so why do it? In standard QKD, the number of bits required to generate a secure key grows with the amount of noise added by Eve. However, in this protocol, Eve does not impact the data rate—assuming she doesn't actively block the channel. So, although the absolute data rate for a low-noise channel is lower, in noisy channels, the researchers show that their implementation outperforms many of the standard protocols.

The most interesting part, however, is the security. There are at least two methods by which the photon pairs can be chosen. In the paper, the authors present two, one of which results in Bob measuring the photon's temporal position, which destroys the phase state (thanks to quantum mechanics, knowledge of one destroys knowledge of the other). If Bob should choose this method, neither he, nor Alice, nor Eve can derive a key. The researchers claim that the mere existence of this choice eliminates the possibility of Eve obtaining the key. Unfortunately, the proof is given in such a scanty form—thank you journal page limits—that the utility of this is difficult to judge.

This is a very nice idea. And, it is not too difficult to implement. But, I will await an actual experiment before being convinced.

Nature, 2014, DOI: 10.1038/nature13303

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