All posts by Bobby

Information is Physical (?)

If you know anything about computers, then you probably have some idea of the way it stores and processes information. It is all about the 1’s and 0’s right? You write the 1’s and 0’s somewhere, the computer somehow reads it and BAM! It does what you want. Well, that is perhaps oversimplifying things just a little, but life is too short to care for the details. In any case, you have to store those 1’s and 0’s somewhere, perhaps on a microSD card or a hard disk drive or a compact disc or any one of the whole multitude of devices meant to store your digital information. In this sense, you probably already have an intuitive idea that information is physical because you always have to write them down on physical objects.

In 1961, Rolf Landauer took this (admittedly obvious) observation to another level by demonstrating a physical principle using it. It essentially states the following: the erasure of a single bit of information has to cost a minimum amount of energy called the Landauer limit (it has a numerical value of KTln2, see  Details aside, the essential argument revolves around a theoretical engine, named the Szilard Engine (Figure 1) after the scientist who studied it.  The engine appears to be able to do physical work without actually requiring any input of energy. This violates the 2nd law of thermodynamics, which says that this engine is giving us too good a deal and that a free lunch is impossible. The Szilard engine, however, does require you to make a measurement that gives you a single bit of information about the system in order to do work. Since the information has to be written down somewhere, and the actual writing on information appears to be doable without costing any energy, it should cost energy to erase this bit of information. In this way, there is no free lunch since you will eventually run out of space to write down the measurement and erasure of information has to be performed.

Figure 1: A rough Schematic of the Szilard Engine. You initially have a box containing a single particle in a heat bath. At first, you don’t know where the particle is inside the box. You then insert a movable partition inside the box and perform a measurement to find out if the particle is on the left or right of the partition. After this measurement, you know which direction the partition will move when the gas expands, therefore performing useful work.

These arguments are fairly convincing, and Landauer’s principle is accepted by many in the scientific community today. However, the issue of its validity is far from completely settled. One may for instance argue that the assumptions underlying the Szilard engine cannot be valid. Using the same set of assumptions, you can actually design a separate engine that does work without even performing a measurement (See Figure 2), also a clear violation of the 2nd Law of Thermodynamics. Is there a flaw in such a design

Figure 2: An engine design similar to the Szilard engine that performs work without measurement. For details see Mind, Matter and Methods by Paul K Feyerabend

So this casts some doubt as to whether Landauer’s principle is actually valid or not. Needless to say, this is an issue that is still being debated today, decades after the principle was proposed. Whatever your stand is on the issue, information remains physical, so keep that hard disk drive handy.

Looking Through the Looking Glass

‘Well! I’ve often seen a cat without a grin,’ thought Alice, ‘but a grin without a cat! It’s the most curious thing I ever saw in my life!’ – Alice in Wonderland


The Cheshire cat. Its smile is in the top right.

Pictured: The infamous Cheshire Cat. Its smile is in the top right but the rest of the cat is elsewhere! How does that work?


The Cheshire Cat may seem like the product of a mind descending into madness, but then so is Quantum Mechanics. It will therefore surprise absolutely no one that a quantum version of the Cheshire Cat story exists. The Quantum Cheshire Cat also continues the ongoing fascination that physicists have with cute fluffy cats (see Schrodinger’s cat for another example). I am a dog person myself, but I digress.

Let us break down the Cheshire cat into its parts. The cat has a large toothy grin, you see, but a cat grinning is not the weirdest part. The weirdness comes along when the body of the Cheshire disappears and then reappears somewhere else, but the grin stays behind, floating suspiciously without a body attached.

Inspired by this, Aharanov et al. presented a way to translate this previously fictional weirdness into Quantum Mechanics. Unable to perform experiments on actual cats, they proposed an experiment using photons instead. Photons have an intrinsic property called polarization, which basically tells you the direction that the electromagnetic waves are oscillating. In Aharanov’s experiment, the photons are set up such that they can move along on 2 possible paths – Left and Right, and the polarizations are along 2 possible directions – Horizontal and Vertical. The polarization is a part of the photon, since it doesn’t make much sense to speak of which direction a photon is oscillating in when the photon is not there.

In Aharanov’s experiment, however, it is possible to have the photon in the left path but the polarization on the right! Suppose we implement Aharanov’s experiment and we prepare the photons in exactly the same manner many times in a row. If we were to make a measurement to see if the photon travelled the left path, the detector will always click, 100% of the time. We will therefore conclude that the photon is travelling the left path, not a difficult conclusion to make. However, if we were to make a polarization measurement on the right path, that detector will start giving us clicks! This means there is photon polarization on the right path! We have previously ascertained, with 100% confidence that a photon prepared in the same manner will always travel the left path, so the photon must have performed a “Cheshire Cat”, by moving in the left path, but having its polarization appear on the right.

The above argument is called counterfactual reasoning. Counterfactual reasoning basically refers to arguments made on the following basis: we didn’t do this, but if we did, this would have happened instead. In the previous paragraph, we are measured the polarization on the right path, but suppose we didn’t and measured the path of the photon instead, then we will conclude that the photon is always on the left, but this somehow contradicts our polarization experiment. The apparent weirdness, or paradox, therefore arises because we employed counterfactual logic, since we didn’t (and couldn’t) measure the path of the photon on the same photon we are measuring the polarization, but made our conclusion supposing that we did.

Aharanov et al. of course realized this, and thinking that may be an avenue for criticism, also devised an alternative reasoning based off of weak measurements that does not rely on counterfactual reasoning. I personally don’t think it is a problem per se, but instead perfectly illustrates how our everyday ‘common sense logic’ simply does not apply to quantum mechanics. In any case, it is fun to ponder why counterfactual reasoning does not work in quantum mechanics. 


Link to Aharanov et al.’s paper : [1202.0631] Quantum Cheshire 

How to cool your (quantum) beer

Everybody has a fridge. Maybe not an Eskimo, but I have heard that Eskimos actually use fridges to make sure that their foodstuffs are not always completely frozen. I have never personally met an Eskimo to verify this, but anyway everybody has a fridge, and everybody enjoys a nice cold beverage every now and then. Including physicists.

Now, as physicists are wont to do, they start to think: What if you have a quantum beer?

Suppose said beer is a qubit. This is the smallest possible beer since a qubit only has 2 discrete energy states. What is the smallest self contained refrigerator that, in principle, can be constructed?

This was a question that was tackled by Linden et. al. (See link). Their answer: a single atom that can occupy at least 3 discrete energy states. Or alternatively, if you construct your fridge out of qubits, then the answer is 2 qubits which collectively occupy a grand total of 4 possible energy states.

How does it work? Well, technicalities aside, it really is pretty simple. Consider the case where the fridge is made out of 2 qubits. Suppose when a qubit is occupying its lowest energy (ground) state, we label the state 0 and say the qubit is in the state 0. If the qubit is occupying its excited state (the only other energy level), then we say it is in state 1.If you have 3 qubits, then we can describe them compactly in the following way: 000 means all 3 qubits are in the lowest energy state, 001 means only the 3rd qubit is excited, and so on.

All you then need to do is to arrange an interaction between the qubits (or in physics nomenclature, introduce an interacting Hamiltonian) which transfers a 3 qubit state from an energy configuration of 101 to 010. If your quantum beer is the first qubit, then if you start at state 1, you will end in state 0. This means basically that the qubit becomes less energetic and therefore cooler. The problem is that such an interaction between 101<–>010 typically go both ways, which causes the state of your beer to go from 1->0 (cooling) and from 0->1 (heating) with equal measure, messing up the cooling process. This is where a little bit of ingenuity becomes necessary. By putting part of the fridge at a different (higher) temperature, and tweaking the energy levels of the qubits appropriately, you can make the beer and fridge system more likely to find itself in the 101 configuration than the 010 configuration. This means that your beer is more likely to go from 1->0 than from 0->1, and wala! you have a 2 qubit fridge and a nice chill qubit beer.

And that’s pretty cool.




In Douglas Adam’s Hitchhikers guide to the Galaxy, the author describes a race of hyper-intelligent beings who built a super-computer whose purpose is to compute the Answer to the Ultimate Question of Life, the Universe, and Everything. The computer, christened Deep Thought by its architects, famously gave the answer to be 42. The creators now have a huge problem: they have the answer, but what does the answer really mean?

Now, I am not writing this because I have secret aspirations of being a philosopher. In fact, I tend to run away in uncontrolled panic as soon as a philosopher steps into my peripheral vision. No, the real reason why I thought of Hitchhiker’s Guide is because some scientists right now have a similar problem right now. Except we are not hyper-intelligent beings.  And the computer is not really that super.

On May 2011, a company called D-Wave Systems announced a device called the D-Wave One, declaring it the world’s first commercially available quantum computer. Quantum computing has long been touted as one of the next big revolution in computing technology.  The basic promise of a quantum computer is easy to understand: Problems that may take years or decades using a classical computer may potentially be solved in hours or days using a quantum computer. A closer look will tell you that this does not necessarily apply to every problem you would like to solve, but hey, nobody ever reads the fine print anyway.

In any case, D-Wave may claim that they are selling a quantum computer, but can we really know for sure it is really quantum? If you are purchasing a multimillion dollar device, it kind of makes sense to do some checks to make sure you are not blowing all that cash on snake oil. As it stands, the ‘quantum computer’ in question does give out an answer if you give it the right kinds of questions, but what does that answer really mean? That is what scientists like Sergio Boixo et al.  (arXiv:1304.4595) are trying to find out. So far the results appear to support D-Wave’s claims in that it does indeed appear to be quantum, but skepticism remains. Still, ignoring the controversy a little bit, it is perhaps interesting to discuss a little bit about the science behind how the D-Wave One is supposed to work.

The basic idea behind D-Wave’s system is Quantum Annealing. Annealing takes its name from a process with the same name in metallurgy. When you cast steel, a sudden temperature change can lead to internal irregularities that stresses and weaken the material. By heating the steel at an intermediate temperature and cooling it, it allows to metal to rearrange itself in the atomic level so that it becomes more homogeneous, and stronger.

The same idea goes behind Quantum Annealing. The idea is to have lots of tiny little magnets called spins that possibly interacts with each other. Ordinarily, this configuration of spins may occupy a high energy state instead of the lowest energy state called the ground state. Classically, spins can get stuck in this higher energy state because they don’t have enough energy to get out of it. This is where the annealing portion comes in. To make sure that the spins occupy the ground state, one can heat up the system, giving the spins enough energy to reconfigure themselves such that they can enter a lower energy state, and then slowly decreasing the energy of the system. The quantum part of the process comes from the fact that the spins can occupy a superposition of states or be entangled with one another, in addition to being able to tunnel between energy states which are classically not allowed. The process ends when the spins occupy the lowest energy configuration, the ground state.

Now, this appears to have nothing to do with computation. Where is the answer to the computations? What is the problem being computed? Well, both the question and the answer turn out to be the ground state of the system.  It just so happens that when the number of spins get large, it becomes computationally very difficult to find out the ground state, but relatively simple to perform the Quantum Annealing process and just measure the ground state coming  out of it. So D-Wave’s system can only solve computational problems that can be modeled by a system of interacting spins, and where the desired answer is the ground state configuration of such a system of spins. This sounds a bit restrictive, and indeed it is, but that’s the device D-Wave is selling, and the only such device on the market, if it is not a complete fake of course.

One thing’s for sure though:  it isn’t going to give us the the Answer to the Ultimate Question of Life, the Universe, and Everything anytime soon.


How procrastinating is sometimes a good thing

Having worked with Quantum Mechanics for a couple of years, and getting comfortable with playing around with the rules and mathematics involved, a person may sometimes fall into the trap and say to himself: “Yeah, I think I understand Quantum Mechanics now.” But being a scientist, one is skeptical of everything, even the things you say to yourself, so he may go on further to ask “But do I really?” At times like these, I like to think of my favorite thought experiment – Wheeler’s Delayed Choice Experiment, following which I go back to thinking that quantum mechanics is this crazy thing, and all is right with the world again.

A good starting point to understand the delayed choice experiment is the (in)famous double slit experiment, which is basically present in any popular science book or textbook trying to explain what a weird thing quantum mechanics actually is. It has a simple enough setup: (i) you need a light source (ii) you shine said light source onto a thin plate with 2 slits (iii) you place a screen after that to see what comes out of the slits. Many people have tried this before, and what comes out of the slit is a wavelike pattern on the screen, with alternating light and dark spots. There is nothing inherently strange about this. We already know that light is a wave, and a wave will lead to a wavelike pattern on the screen on the other side of the double slit, big deal.

But wait. We also know that light can be thought of as being made up of tiny little nuggets called photons, so how does this explain the wavelike pattern on the screen? Well, light is typically made up of many, many photons right? Maybe all these photons passing through the slits are interacting amongst themselves and this results in an overall, collective wavelike pattern. This is a bit contrived, but still somewhat reasonable.

The problem comes about when the you have a light source that emits photons slowly, one at a time. If only one photon is passing through the slits at a time, then there isn’t anything it can possibly interact with. The logical end point of this is that if only one photon passes through the slits at a time, the wavelike pattern will disappear. However, countless experiments have been done to verify this, and all of them agree on one point: If you wait long enough and collect enough photons one at a time, the wavelike pattern persists. The only explanation for this is that the photon, although it is particulate in nature, nonetheless went through both slits at the same time and interacted with itself. Strange, but true. Funnily enough, if you observe which slit the photon actually passes through, and thus exclude the photon from ever passing through the other slit, then the wavelike pattern disappears. The photon behaves like a particle again.

The experiment could have just ended there – the conclusions to be drawn from it are strange enough. By this point, an experimenter could have relented and concluded “Okay, a photon is both a wave and a particle, strange, but at least I know that if the photon decides to go through both slits, it behaves like a wave coming out of it, and if it only went through a single slit, it behaves like a particle. I can accept that.” Nature, however, is relentless in trying to confound the experimentalist. This is where John Archibald Wheeler’s famous Delayed Choice Experiment comes in.

The delayed choice experiment is a simple variant of the classic double slit experiment, except performed by a lazy college student. The college student has one job: decide whether to put a screen and collect the overall pattern, or look at both of the slits to see which slit the photon went through (he may use a telescope to look at the slit, if that helps). Being ever the procrastinator, the college student decides what to do only at the last minute, long after the photon passes through the slits, and just before the photon reaches the college student. Now, since the photon had already passed through the slits, it must have decided to pass through either both slits, or a single slit, so you get a wavelike pattern for the former, and particle like behavior for the latter, regardless of what the student chooses to do. But no. For some reason, when the student puts up a screen, he gets a wave pattern, and if he looks at the slits to observe the photons, the wave pattern disappears. The conclusion? The you cannot even say that the photon went through a single slit or went through both slits. Somehow, the photon behaves like it went through both slits when the student puts up the screen, and behaves like it went through a single slit when the student observes which slit the photon went through, despite the fact that the photon already went through the slits long before the student even made his decision. The future influenced what happen in the past! Thus the experimenter was not even right to assume that the photons either went through both slits or a single slit. The most accurate answer we have is perhaps that the photon did both at the same time. And that’s just crazy if you think about it.