Do you play cards? Be it bridge or poker, all such games are built from a set of rules which you have to know and learn to turn to your favour, if you wish to play well and win.
Entering the world of quantum physics is very similar to starting a game of cards. Get acquainted with a few guiding principles and tricks, and quantum mechanics will appear less quirky than you may think.
“Quantum phenomena do not occur in a Hilbert space. They occur in a laboratory”, in the words of physicist Asher Peres. Very well then – let us visit a quantum optics laboratory populated of variously coloured beams of light together with all sorts of mirrors and lenses. Here our deck of cards is made out of nothing else but light.
Quantum optics describes phenomena which involve light quanta, also called photons, and their interactions with matter. Such physical phenomena obey the laws of quantum mechanics. For this reason, quantum optical experiments can lead into insights into the very foundations of quantum mechanics – a theory about a century old with a few mysteries yet to be explained. We shall thus identify our quantum cards with light quanta.
In the laboratory we can prepare our deck of photons with different features; we may let photons interact with other light quanta as well as with matter. We can also interrogate them by performing some measurements. The aim of the game is to ask questions and gain insights into the composition of our deck of experimentally produced cards.
By the way – this laboratory is dark. This is because we wish to harness the elusive photons that we carefully crafted, not the million billions light particles emitted by your kitchen lamp. If the darkness annoys you, you should not worry – you will not be using your naked eye here. If you are then wondering how we are supposed to play this game, here comes the first rule:
There Are No Yes-Or-No Answers To Questions. Measuring a given property of light quanta is similar to asking the other player to tell us something about the cards on the table. When the game starts, all cards are blank. Yes, blank – each of them can be any and every card. As soon as we pick up one, it takes on a value. So far so good. However, this is not all. If asked to show us one card, our fellow player who keeps the deck will say ‘Sure, this is the card you asked for with a probability of 60%.’ Sometimes we will know the outcome of a measurement with certainty. More often we will have to cope with probabilities.
We could perhaps try to rephrase our question in order to obtain additional information. But this would not work, as the second rule explains:
Questions May Be Only Asked Once. This sounds worse than it really is. What it means is that we can measure, say, the position of a photon and find a value. However, if we were to ask again the same question the photon would simply repeat its previous answer. The card was played and it is now discarded until the end of the game.
What if it were possible to ask questions differently, and overcome the bounds imposed by the first two rules? Here is the good news:
You May Use Special Cards. Do you remember that we produced our own deck of photons? As a matter of fact, we may decide to generate light quanta in pairs. The reason why these pairs are special is that you can measure one photon from the pair and learn something about both. To follow our analogy, if you call for a special card (which is in fact a pair of cards) and enquire ‘Is the special card over here red?’ you may be positively surprised in being told ‘Yes, this card is red while the special card over there is white.’ This rather astonishing aspect of quantum mechanical systems is known as entanglement, and it is a most powerful property.
On this note, we have reached the end of the first class on the game of quantum cards. To go back to the classical world, please ring the bell for assistance. ‘How do I know that quantum rules do not apply anymore?’ you may wonder. This is a sensible and delicate question; if misinterpreted it can lead to confusions and rather troublesome situations. Famous physicist Erwin Schrödinger thought of a cat trapped in a box with a radioactive substance in order to illustrate this conundrum.
Did you ring the bell? Good – you should not play quantum cards for too long, you may get lost…
** The image “A studio image of a hand of playing cards” was taken from the Wikimedia Commons