Since the modern communications revolution got into full swing with the advent of the telegraph, people have always wondered just how much information can be sent down that line. In classical communication, this is governed by Shannon's law, which looks at the correlation between input and output signals. Once the noise in the channel reaches a particular level, the output and the input are no longer correlated and you have to slow the bit rate down. If the noise is high enough, there is a point where no communication is possible. Recently, researchers have been asking the same question about quantum communications channels and it turns out that the answer isn't really that clear.

Quantum channel capacity cannot be defined the same as classical information due to entanglement. Entanglement is the phenomena where the states of two quantum objects are correlated and cannot be described independently. The paper's authors put it elegantly, writing: "The whole of a quantum system can be in a definite state while the states of its parts are uncertain." Taking into account entanglement has allowed researchers to define a channel capacity, but not in a useful sense (e.g., it requires a weighted average of an infinite number of communication attempts).

In an attempt to shed light on the problem, a pair of researchers has investigated the properties of channels that are known to have zero capacity. In the classical case, channel capacity is additive, so two zero-capacity channels still have zero combined capacity. However, it seems that quantum communications channels behave a bit differently. The researchers discovered that two channels that have zero capacity can have a non-zero channel capacity, provided one condition is met: the two channels must have zero capacity for different reasons.

Why would this be the case? The researchers do not offer much in the way of speculation (as is entirely appropriate in a scientific paper), but I am happy to speculate. In the channels that they chose, one contains the information that cannot be retrieved without destroying it. In the second channel, the entanglement is such that the states of the entangled pair cannot be separated, making the information unobtainable. However, the output of both channels are correlated (in the classical sense), meaning that joint measurements on the output of both channels probably resolves the issues with the first channel, allowing the information to be retrieved. This may well be true of any mixed set of zero-capacity channels, where measurements from one channel can be used to obtain information from the second.

This is not a trivial result for several reasons. First, it tells us that, for quantum communications, channel capacity will actually depend on the details of the implementation rather than just the amount of noise in the channel. Second, the presence of a supposedly zero-capacity channel that actually has a non-zero capacity shows that existing methods for estimating the channel error are incorrect. In fact, the researchers show that there can be an arbitrarily large error between the estimated capacity and the actual capacity. Since most error correction routines are based on the estimated channel capacity, those calculations will also be wrong. Wrong in a good way, because if this work is correct, less error correction will be required.

This research has not been through peer review yet, but I expect that it will find its way into one of the Physical Review journals in the next few months.

ArXiv.org, 2008