A Thermometer for Measuring Quantumness
A modern variant of Maxwell’s demon can act as a kind of catalyst, boosting a flow of heat from cold to hot quantum objects.
Daniel Garcia for Quanta Magazine
Introduction
If there’s one law of physics that seems easy to grasp, it’s the second law of thermodynamics: Heat flows spontaneously from hotter bodies to colder ones. But now, gently and almost casually, Alexssandre de Oliveira Jr. has just shown me I didn’t truly understand it at all.
Take this hot cup of coffee and this cold jug of milk, the Brazilian physicist said as we sat in a café in Copenhagen. Bring them into contact and, sure enough, heat will flow from the hot object to the cold one, just as the German scientist Rudolf Clausius first stated formally in 1850. However, in some cases, de Oliveira explained, physicists have learned that the laws of quantum mechanics can drive heat flow the opposite way: from cold to hot.
This doesn’t really mean that the second law fails, he added as his coffee reassuringly cooled. It’s just that Clausius’ expression is the “classical limit” of a more complete formulation demanded by quantum physics.
Physicists began to appreciate the subtlety of this situation more than two decades ago and have been exploring the quantum mechanical version of the second law ever since. Now, de Oliveira, a postdoctoral researcher at the Technical University of Denmark, and colleagues have shown that the kind of “anomalous heat flow” that’s enabled at the quantum scale could have a convenient and ingenious use.
It can serve, they say, as an easy method for detecting “quantumness” — sensing, for instance, that an object is in a quantum “superposition” of multiple possible observable states, or that two such objects are entangled, with states that are interdependent — without destroying those delicate quantum phenomena. Such a diagnostic tool could be used to ensure that a quantum computer is truly using quantum resources to perform calculations. It might even help to sense quantum aspects of the force of gravity, one of the stretch goals of modern physics. All that’s needed, the researchers say, is to connect a quantum system to a second system that can store information about it, and to a heat sink: a body that’s able to absorb a lot of energy. With this setup, you can boost the transfer of heat to the heat sink, exceeding what would be permitted classically. Simply by measuring how hot the sink is, you could then detect the presence of superposition or entanglement in the quantum system.
Practical benefits aside, the research demonstrates a new aspect of a deep truth about thermodynamics: How heat and energy can be transformed and moved in physical systems is intimately bound up with information — what is or can be known about those systems. In this case, we “pay for” the anomalous heat flow by sacrificing stored information about the quantum system.
“I love the idea that thermodynamic quantities can signal quantum phenomena,” said the physicist Nicole Yunger Halpern of the University of Maryland. “The topic is fundamental and deep.”
Knowledge Is Power
The connection between the second law of thermodynamics and information was first explored in the 19th century by the Scottish physicist James Clerk Maxwell. To Maxwell’s distress, Clausius’ second law seemed to imply that pockets of heat will dissipate throughout the universe until all temperature differences disappear. In the process, the total entropy of the universe — crudely, a measure of how disordered and featureless it is — will inexorably increase. Maxwell realized that this trend would eventually remove all possibility of harnessing heat flows to do useful work, and the universe would settle into a sterile equilibrium pervaded by a uniform buzz of thermal motion: a “heat death.” That forecast would be troubling enough to anyone. It was anathema to the devoutly Christian Maxwell. But in a letter to his friend Peter Guthrie Tait in 1867, Maxwell claimed to have found a way to “pick a hole” in the second law.
He imagined a tiny being (later dubbed a demon) who could see the motions of individual molecules in a gas. The gas would fill a box that was divided in two by a wall with a trapdoor. By opening and closing the trapdoor selectively, the demon could sequester the faster-moving molecules in one compartment and the slower-moving ones in the other, making a hot gas and a cold one, respectively. By acting on the information it gathered about molecules’ motions, the demon thus reduced the entropy of the gas, creating a temperature gradient that could be used to do mechanical work, such as pushing a piston.
Scientists felt sure that Maxwell’s demon couldn’t really violate the second law, but it took nearly 100 years to figure out why not. The answer is that the information the demon collects and stores about the molecular motions will eventually fill up its finite memory. Its memory must then be erased and reset for it to keep working. The physicist Rolf Landauer showed in 1961 that this erasure burns energy and produces entropy — more entropy than is reduced by the demon’s sorting actions. Landauer’s analysis established an equivalence between information and entropy, implying that information itself can act as a thermodynamic resource: It can be transformed into work. Physicists experimentally demonstrated this information-to-energy conversion in 2010.
Unsettled by the second law of thermodynamics, the Scottish physicist James Clerk Maxwell invented a thought experiment about an all-knowing demon that is still yielding insights today.
The Print Collector/Heritage Images
But quantum phenomena allow information to be processed in ways that classical physics does not permit — that’s the entire basis of technologies such as quantum computing and quantum cryptography. And that’s why quantum theory messes with the conventional second law.
Exploiting Correlations
Entangled quantum objects have mutual information: They are correlated, so we can discover properties of one by looking at the other. That in itself is not so strange; if you look at one of a pair of gloves and find it’s left-handed, you know the other is right-handed. But a pair of entangled quantum particles differs from gloves in a particular way: Whereas the handedness of gloves is already fixed before you look, this isn’t the case for the particles, according to quantum mechanics. Before we measure them, it’s undecided which value of the observable property each particle in the entangled pair has. At that stage the only things we can know are the probabilities of the possible combinations of values, such as 50% left-right and 50% right-left. Only when we measure the state of one of the particles do these possibilities resolve themselves into a definite outcome. In that measurement process, the entanglement is destroyed.
If gas molecules are entangled in this way, then a Maxwell’s demon can manipulate them more efficiently than if all the molecules are moving independently. If, say, the demon knows that any fast-moving molecule it sees coming is correlated in such a way that it will be trailed by another fast one just a moment later, the demon doesn’t have to bother observing the second particle before opening the trapdoor to admit it. The thermodynamic cost of (temporarily) foiling the second law is lowered.
In 2004, the quantum theorists Časlav Brukner of the University of Vienna and Vlatko Vedral, then at Imperial College London, pointed out that this means macroscopic thermodynamic measurements can be used as a “witness” to reveal the presence of quantum entanglement between particles. Under certain conditions, they showed, a system’s heat capacity or its response to an applied magnetic field should carry an imprint of entanglement, if it is present.
In a similar vein, other physicists calculated that you can extract more work from a warm body when there is quantum entanglement in the system than when it is purely classical.
And in 2008, the physicist Hossein Partovi of California State University identified a particularly dramatic implication of the way quantum entanglement can undermine preconceptions derived from classical thermodynamics. He realized that the presence of entanglement can actually reverse the spontaneous flow of heat from a hot object to a cold one, seemingly upending the second law itself.
That reversal is a special kind of refrigeration, Halpern said. And as usual with refrigeration, it doesn’t come for free (and so doesn’t truly subvert the second law). Classically, refrigerating an object takes work: We have to pump the heat the “wrong” way by consuming fuel, thereby repaying the entropy that’s lost by making the cold object colder and the hot object hotter. But in the quantum case, Halpern said, instead of burning fuel to achieve refrigeration, “you burn the correlations.” In other words, as the anomalous heat flow proceeds, the entanglement gets destroyed: Particles that initially had correlated properties become independent. “We can use the correlations as a resource to push heat in the opposite direction,” Halpern said.
Vlatko Vedral is one of the originators of the idea of using thermodynamic measurements as a “witness” to reveal the presence of quantum entanglement between particles.
Courtesy of Vlatko Vedral
In effect, the fuel here is information itself: specifically the mutual information of the entangled hot and cold bodies.
Two years later, David Jennings and Terry Rudolph of Imperial College London clarified what’s going on. They showed how the second law of thermodynamics can be reformulated to include the case where mutual information is present, and they calculated the limits on how much the classical heat flow can be altered and even reversed by the consumption of quantum correlations.
The Demon Knows
When quantum effects are in play, then, the second law isn’t so simple. But can we do anything useful with the way quantum physics loosens the bounds of thermodynamic laws? That’s one of the goals of the discipline called quantum thermodynamics, in which some researchers seek to make quantum engines that run more efficiently than classical ones, or quantum batteries that charge more quickly.
Patryk Lipka-Bartosik of the Center for Theoretical Physics at the Polish Academy of Sciences has sought practical applications in the other direction: using thermodynamics as a tool for probing quantum physics. Last year, he and his co-workers saw how to realize Brukner and Vedral’s 2004 idea to use thermodynamic properties as a witness of quantum entanglement. Their scheme involves hot and cold quantum systems that are correlated with each other, and a third system to mediate the heat flow between the two. We can think of this third system as a Maxwell’s demon, except now it has a “quantum memory” that can itself be entangled with the systems it is manipulating. Being entangled with the demon’s memory effectively links the hot and cold systems so that the demon can infer something about one from the properties of the other.
Patryk Lipka-Bartosik has explored how to use thermodynamic measurements to detect quantum effects.
Alicja Lipka-Bartosik
Such a quantum demon can act as a kind of catalyst, helping heat transfer happen by accessing correlations that are inaccessible otherwise. That is, because it is entangled with the hot and cold objects, the demon can divine and exploit all their correlations systematically. And, again like a catalyst, this third system returns to its original state once the heat exchange between the objects is completed. In this way, the process can boost the anomalous heat flow beyond what can be achieved without such a catalyst.
The paper this year by de Oliveira, co-authored by Lipka-Bartosik and Jonatan Bohr Brask of the Technical University of Denmark, uses some of these same ideas but with a crucial difference that turns the setup into a kind of thermometer for measuring quantumness. In the earlier work, the demonlike quantum memory interacted with a correlated pair of quantum systems, one hot and one cold. But in the latest work, it sits between a quantum system (say, an array of entangled quantum bits, or qubits, in a quantum computer) and a simple heat sink with which the quantum system is not directly entangled.
Because the memory is entangled with both the quantum system and the sink, it can again catalyze heat flow between them beyond what is possible classically. In that process, entanglement within the quantum system converts into extra heat that enters the sink. So measuring the energy stored in the heat sink (akin to reading its “temperature”) reveals the presence of entanglement in the quantum system. But since the system and sink aren’t themselves entangled, the measurement doesn’t affect the state of the quantum system. This gambit circumvents the notorious way that measurements destroy quantumness. “If you simply tried to make a measurement on the [quantum] system directly, you’d destroy its entanglement before the process could even unfold,” de Oliveira said.
The physicists Alexssandre de Oliveira Jr. (left) and Jonatan Bohr Brask (right) collaborated with Patryk Lipka-Bartosik on a new scheme for detecting quantumness without destroying it.
Jonas Schou Neergaard-Nielsen
The new scheme has the advantage of being simple and general, said Vedral, who is now at the University of Oxford. “These verification protocols are very important,” he said: Whenever some quantum computer company makes a new announcement about the performance of its latest device, he said the question always arises of how (or if) they really know that entanglement among the qubits is helping with the computation. A heat sink could serve as a detector of such quantum phenomena purely via its energy change. To implement the idea, you might designate one quantum bit as the memory whose state reveals that of other qubits, and then couple this memory qubit to a set of particles that will serve as the sink, whose energy you can measure. (One proviso, Vedral added, is that you need to have very good control over your system to be sure there aren’t other sources of heat flow contaminating the measurements. Another is that the method will not detect all entangled states.)
De Oliveira thinks that a system already exists for testing their idea experimentally. He and his colleagues are discussing that goal with Roberto Serra’s research group at the Federal University of ABC in São Paulo, Brazil. In 2016, Serra and colleagues used the magnetic orientations, or spins, of carbon and hydrogen atoms in molecules of chloroform as quantum bits between which they could transfer heat.
Using this setup, de Oliveira says it should be possible to exploit a quantum behavior — in this case coherence, meaning that the properties of two or more spins are evolving in phase with one another — to change the heat flow between the atoms. Coherence of qubits is essential for quantum computing, so being able to verify it by detecting anomalous heat exchange could be helpful.
The stakes could be even higher. Several research groups are trying to design experiments to determine whether gravity is a quantum force like the other three fundamental forces. Some of these efforts involve looking for quantum entanglement between two objects generated purely by their mutual gravitational attraction. Perhaps researchers could probe such gravity-induced entanglement by making simple thermodynamic measurements on them — thereby verifying (or not) that gravity really is quantized.
To study one of the deepest questions in physics, Vedral said, “wouldn’t it be lovely if you could do something as easy and macroscopic as this?”
