Quantum mechanics is the most successful description of nature known to humans, yet it has many bizarre implications for our understanding of the world. There are phenomena of superposition (objects being in two places at the same time), entanglement (correlations that exceed any classical correlations) and nonlocality (apparent ability for information to travel instantaneously across vast distances). As my cover story in the June issue of *Scientific American* discusses, these oddities are not just limited to subatomic realms, but challenge our conception of the everyday world, too. Now, in a paper published in *Nature*, together with my colleagues from Switzerland and Singapore, I have discovered yet another counterintuitive consequence of quantum physics.

Everyone who has ever worked with a computer knows that they get hotter the more we use them. Physicist Rolf Landauer argued that this needs to be so, elevating the observation to the level of a principle. The principle states that in order to erase one bit of information, we need to increase the entropy of the environment by at least as much. In other words we need to dissipate at least one bit of heat into the environment (which is just equal to the bit of entropy times the temperature of the environment).

Landauer's erasure principle has been considered controversial in physics ever since he proposed it in the early '60s. Was it a new law of physics or just a consequence of some already existing laws? Our new paper argues that in quantum physics, you can, in fact, erase information and cool the environment at the same time. For many physicists, this is tantamount to saying that perpetual motion is possible! What makes it possible is entanglement, but let me not get too far ahead of myself. I will first set the scene by giving you a bit more background on Landauer.

Landauer always emphasized that there is no disembodied information. Bits of information need to be encoded into real physical systems and will therefore have to conform to the laws of physics that these systems obey. In the case of Landauer's erasure, the law we are talking about is the in(famous) second law of thermodynamics. The second law states that the disorder in a closed system mostly increases and at best stays the same. Landauer argued that the link between erasing information and generating heat is a consequence of the second law. That sounds reasonable and, in fact, his colleague Charles Bennett showed in the late '70s that if you could erase information without generating heat you could construct a perpetual machine of the second kind. Bennett thus showed that negating Landauer's principle implies negating the second law, which (for those who are familiar with the basic laws of logic) is the same as saying that the second law implies Landauer's erasure. Bennett and Landauer wrote a classic article for *Scientific American* on this subject.

So where's the controversy? It comes from asking whether it also true that Landauer's principle implies the second law. If this were so, then the two would be equivalent, as each implies the other. Some authors have even talked about the possibility of Landauer's principle being *stronger* than the second law.

Now my colleagues and I have discovered an additional twist in the Landauer tale. As I said earlier, in quantum physics, you can erase information, but rather than adding heat to the environment you can actually take it away! This sounds like it contradicts Landauer's principle. Even more worryingly, since we argued the equivalence with the second law, this would mean that quantum physics contradicts the second law. Quantum physics seems to allow us to have a cake and eat it, in that it allows us to erase information and cool the environment too.

But this, luckily for the second law (though not for would-be inventors of perpetual motion machines), is not the case. Landauer's insight is still fine, and erasing information adds entropy to the environment. What saves the second law is that, in quantum physics, entropy can actually be negative. Adding negative entropy is the same as taking entropy away. The key phenomenon behind it is the spookiest of all quantum phenomena, entanglement.

To understand the connection between entanglement and negative entropy we have to go back to Schrödinger's view of entanglement. When two systems are entangled, we have complete information about their joint state, but have no information about their individual states. If we are erasing the state, as a whole we need not generate entropy (since the state has zero entropy), but if we erase subsystems individually, then each will contribute to entropy generation. The difference between the global and local erasing is negative entropy. To rephrase, if we have to erase some information, it helps to know whether this information arises from the entanglement with another system. Then, by invoking the other system in the erasure, we can actually erase and the environment can lose entropy.

Landauer's erasure therefore acquires a new dimension when entanglement is allowed, but even then it still remains fully compliant with the second law. For better or for worse, the entropy of the whole universe still cannot be decreased even with the full assistance of the quantum magic of entanglement and negative entropies of quantum objects.

If all this seems confusing, it is! This is very subtle physics and few people, even eminent physicists, understand it straight away. If you pose your questions below, I'll do my best to answer them.

The implications of our result could be important for superfast and superefficient computers. Current computers waste about 10,000 units of heat per computational step. If we can somehow control and manipulate entanglement between the microprocessor and the computer memory, then we could erase computations to make room for new ones, but keep the environment cool—we'd be right at the boundary of what is physically allowed. At present, this is admittedly very difficult to do, but who can foretell the already rapid progress of quantum technologies?

*Photo courtesy of Jenny Hogan, Centre for Quantum Technologies *