# Quantum games inspiration

Keen to enter Quantum Games, but not sure where to start? Below you will find some short summaries of key themes in quantum physics, including:

###### Superposition

In the classical world, we are pretty confident that things can only be in one state at a time − even if we don’t *know* which one. For example, after a coin is flipped, we may not know yet if came up heads or tails, but we are sure that it is definitely one or the other. Likewise, a ball hidden behind under one of two hats is definitely under one hat or under the other. In these examples, it wouldn’t make sense for both possible outcomes to be simultaneously represented in reality: the coin isn’t “partially-heads” and "partially-tails" at once.

In quantum mechanics this logic turns out not to be true. A quantum coin can be in a state which is partially heads and tails, simultaneously. There is one way to imagine this, using the polarisation of light. Light can be polarised, e.g. vertically or horizontally − think of polaroid sun-glasses.  Light also comes in particles called photons. The polarisation of a single photon could be horizontal or it could be vertical, and it can be anywhere in between: think of polaroid sunglasses tilted at an angle − the light coming through is diagonally polarised. If we think of horizontal polarisation as “heads” and vertical polarisation as “tails” then a diagonally polarised photon is a bit of “heads” and a bit of “tails”. We say that the photon is in a “superposition” of horizontal/heads and vertical/tails.

The same is true for any quantum system: it can simultaneously be in two different states at once. A quantum “ball” may not be localised under a single “hat”.

This is the origin of Schrodinger’s cat, which could in principle be put into a superposition of being alive and being dead.

###### Interference

We are familiar with interference when we think of waves in water: the combination of ripples and troughs from different wavefronts can cancel out (destructive interference) or add up (constructive interference). In our experience, this is not a property that particles have: a stone thrown at a pond doesn’t “interfere” with itself. It turns out the quantum particles do.  If a stream of particles is roughly aimed at a screen with two holes, then classically, the particles individually go through one or the other of the holes and predictably end up in one or other of two piles on the other side of the holes. A wave incident on the same screen (e.g. a sound wave) will go through both holes, leading to interference of the waves on the other side of the screen: the sound energy ends up distributed in a ripple pattern after passing through the screen. A quantum particle (e.g a photon or an electron) does both of these things: the particles arrive at the other side of the screen as indivisible object, but with a characteristic ripple pattern of wave interference in the typical areas where they land!

###### Quantum Tunnelling

When a classical particle encounters an energetic barrier − think of a marble rolling up a large hill − it slows down, and eventually reverses its course. It cannot surmount the obstacle unless it has sufficient energy. In quantum mechanics, this is not certain. It is possible for a particle to “tunnel” through the barrier and emerge on the other side, even though it was energetically forbidden.  The probability of the particle tunnelling depends on the energetic mismatch: the higher the barrier, the less likely that the particle can tunnel. This has been demonstrated in many experiments, and is responsible for radioactive decay.

###### Heisenberg Uncertainty Principle

Classically, we think of position and momentum (speed) as completely independent properties of an object, which we could know to arbitrary accuracy, at least in principle. For instance, we believe that we can know the position and speed of a car travelling along the road − as determined by the speedometer and the GPS coordinates, for instance. It turns out that in quantum mechanics, this is not true: the uncertainty in position Δx, and the uncertainty in momentum Δp cannot both be arbitrarily small.  In fact, the product ΔxΔp must be larger than a certain small number related to Planck’s constant ħ: ΔxΔp>ħ/2. So if the position of a particle is very well known, it’s momentum must have some minimum uncertainty. For everyday objects, this is not a practical problem, but it does for microscopic particles.

###### Wave−Particle Duality / Photons

We tend to think of light and sound as waves, and atoms and electrons as particles. But light and sound come in “lumps” (or particles) of energy generically called “quanta”. For light, the quanta are “photons”, and for sound the quanta are called “phonons”. Conversely, particles like electrons can cause interference fringes, and so have a definite wave-like character. So waves come as particles, and particles exhibit wavy behaviour. In quantum mechanics, these two characteristics are embodied in all objects.

###### Entanglement

Two classical particles can be correlated with each other: think of two coins that are hidden from view by a trickster, but who promises they are both heads or both tails. Observing one coin “reveals” the state of the other coin. It is obvious through that the coins were in one state or the other (since the trickster knows; see Superposition). In quantum mechanics, it is possible for two quantum “coins” to be correlated even when the state of each coin is unknowable: measuring one coin forces the other to take on the same value. This is called “entanglement”.

###### EPR Paradox / Bell Inequality

If two quantum particles are entangled, it is possible to produce statistical correlations between them that are stronger than shared classical randomness (a one-time pad) would allow. Einstein, Podolski and Rosen used this fact to argue that quantum mechanics was “incomplete” and showed “spooky action at a distance”, since the state of one particle depends on the outcome of a measurement on a very distant partner with which it is entangled. John Bell later proposed an experimental test to establish this empirically.  We now know that quantum mechanics is not incomplete in the sense that Einstein meant!

If two people share a entangled pairs of particles, they can use them to do unbreakable encryption, and they can also fool people into believing they have (partial) telepathic powers in some tests! They cannot, however, communicate faster than light.

###### Black Hole Evaporation

Black holes may sound like they boringly absorb everything they come into contact with.  However Stephen Hawking showed that this is not entirely true: Black holes can evaporate. The mechanism for this is “pair production”. In a vacuum, rather than a complete absence of activity, there are “quantum fluctuations" of particles that transiently appear and disappear. To conserve charge etc, particles appear and disappear in pairs, but very close to the surface of a black hole (the event horizon), a pair of particles can spontaneously appear, and one of the falls into the black hole, while the other moves away from it. This combination of processes leads to a small rate of emission of particles from the black hole: it not only absorbs particles, but also emits them in the form of “Hawking Radiation”; a form of evaporation.

###### Spin

We are familiar with the idea of “angular momentum”, which captures the idea that spinning bodies tend to keep spinning, just as moving bodies tend to keep moving. A child’s spinning top is a good example: a body with some spatial extent can obviously be set spinning, but what about a “point particle”, that has no extent? It turns out that electrons and quarks are really point-like (they are immeasurably small), yet they do possess “intrinsic spin”, and carry angular momentum!  It arises from a combination of quantum physics and Einstein’s theory of relativity.

###### Interpretations of Quantum Mechanics

Quantum mechanics is described by a set of mathematical rules to manipulate “wavefunctions” − mathematical objects that describe the state of matter. However there is still a question as to how we interpret these objects: are they “real” or just mathematical artefacts. In the 19th Century, a similar argument was had about atoms: did they really exist, or were they a convenient mathematical concept to help get physics calculations right. We now know atoms do exist… but how about the wavefunction?

A number of different approaches to this problem have been described, none of which have universal appeal!

###### Coherent states of matter

When matter becomes very cold, its properties change dramatically.  Ordinary metals, that have electrical resistance, can become a “superconductor” in which the resistance goes to zero, leading to perpetual electrical currents with no external power supply. Liquid helium goes from having some viscosity (like honey or treacle, but much less so!) to having exactly zero viscosity, so that fluid can flow in a vortex forever as a "superfluid”. These phenomena happen because most of the particles in question (electrons in a metal for a superconductor, helium atoms in a bucket for a superfluid) all collapse into the same quantum state.  In this situation, they all take on a collective identity, and behave is if they were a single “macroscopic” quantum particle which can flow through barriers (see tunnelling) and levitate magnets perpetually.

###### Interaction-free measurement

Imagine you are a bomb-disposal expert, and you have to defuse a black box which *may* contain an extremely sensitive bomb. You guess that the chance of a bomb being inside the box is 50%. The box has a window (initially closed), and bomb is so sensitive that if even a single particle of light (a photon) enters the open window, then the bomb will explode!  You’ve been asked to deal with the bomb, but if it explodes it will cause terrible damage.

Your challenge is to first figure out if there is in fact a bomb in the black box: if not then you can just remove the box and go home.  Of course, the obvious thing to do is to open the window and look inside − but if you do that, you let light in, and the bomb explodes… You certainly learn if there had been a bomb, but you can no longer do much with the information if it was there!

In the classical world, this is the only thing you can do: open the window, let light in and see if the box explodes or not.

In the quantum world, it turns out that you can *partially* let a photon in − this is called “superposition” − and learn partial, incomplete information about whether there was a bomb in the box. As you learn partial information, you change the probability of there being a bomb in there or not. If you do this many times, it turns out you can learn about whether the box contains a bomb, but without it ever exploding!

This phenomenon is called “interaction-free measurement”, in which we are able to learn about something without seemingly having ever interacted with it directly.

###### No cloning

From dolly the sheep to your computer backup, it appears as though we can clone one thing into many replicas. But in quantum mechanics, this not generally true. If an eavesdropper tried to replicate a quantumly encoded song or document, they couldn’t succeed; instead they will necessarily produce a slightly noisy copy. These are not the clones you are looking for!

###### Teleportation

While you can’t clone anything perfectly, it can be teleported using pure light alone.  All you need is a convenient source of entangled photon pairs − send one to the destination, and keep the other locally − and a way to decompose your precious object into its constituent quantum parts.  Measuring each part alongside one of photon from each entangled pair produces a string of bits.  This information is sent to the destination, and the receiver uses the other photon from the pair to reconstruct a perfect replica of the original object.  Be careful though, if the information is scrambled on the way, then “Beam me up Scotty” might just come out as “Pet cat obeys Mum”.

###### Casimir effect

In quantum mechanics, a vacuum isn’t a vacuum: even in empty space all the fundamental fields of nature fluctuate, with ephemeral “virtual” particles flitting in and out of existence. This principle is responsible for black-hole evaporation, and in (slightly) less extreme situations, the Casimir pressure. Matter affects quantum vacuum fluctuations, and vice-versa. If you put two conducting metal plates in free space they subtly change the density of vacuum fluctuations in between the plates.  As a consequence, the vacuum energy in the space between the plates is smaller than the vacuum energy in the surrounding space, leading to a pressure on the plates − vacuum fluctuations cause a measurable force on objects!

Last updated 15 April 2020
Last reviewed 2 May 2017

## Major funding support

The Australian Research Council Centre of Excellence for Engineered Quantum Systems (EQUS) acknowledges the Traditional Owners of Country throughout Australia and their continuing connection to lands, waters and communities. We pay our respects to Aboriginal and Torres Strait Islander cultures and to Elders past and present.