Quantum Entanglement Wiki

This wikipedia page aims to provide a descriptive basis for quantum mechanics and entanglement for anyone interested in science.

## Introduction to quantum mechanics

Quantum mechanics describes the behaviour of matter and lights on atomic and sub-atomic scales, which differs from the behaviour of larger objects, and as such often appears counter-intuitive.

### Definition of a quantum system

A quantum system is a region of space that obeys the laws of quantum mechanics as opposed to classical mechanics . We say that this system is isolated from all others. And we say that interactions with all other micro or macroscopic systems (the environment of the system) are only there to observe the system, thus by interaction the system collapses from its wavefunction and obeys the laws of classical mechanics again, making the system no longer a quantum one.

### When is something quantum?

.Similarly, a quantum object, unlike a classical object cannot be described by classical physics - therefore its properties such as position in space, energy, velocity, etc., are not well-defined by these deterministic laws, but are instead best described using quantum mechanical methods, e.g. the Schrodinger equation and the Heisenberg Uncertainty Principle, which are discussed below. Quantum mechanics, unlike classical mechanics, therefore deals with probabilistic behaviour and a consequence of that are phenomena such as quantum entanglement. Classical objects are not entangled because classical physics is deterministic, meaning that theoretically we know all the properties of a classical object with no uncertainty.

### The probabilistic nature of quantum systems

In classical Newtonian mechanics, the world is deterministic. This means that if the conditions of a system are known (e.g. mass, velocity, etc.), then we can accurately know the motion of objects at all points in time, and they move in perfectly determined ways. This idea is illustrated by Laplace's demon, a hypothetical creature that knows the position and momentum of every atom in the universe and thus knows the past and future motion of all those atoms.

On the other hand, quantum mechanics is probabilistic. The motion of objects on a quantum scale is not perfectly determined. This is a result of Heisenberg's uncertainty principle, ΔxΔp ≥ ħ/2, which states that the position, x,(whose uncertainty is Δx) and momentum, p,(whose uncertainty is Δp) of a particle cannot both be measured exactly - knowing one automatically leads to high uncertainty in the other.

As such, we can never truly know where a quantum particle is or how fast it is moving at any point in time - we can only know the probability of it having a particular momentum and position at a time. This probability is given by |ψ|2 , when the particle is represented by a wavefunction ψ.

### Measurements in quantum mechanics

Like everything in science, quantum mechanics would be useless if we couldn't use it to make predictions about real life. To see if the predictions it makes are accurate, we have to compare it to what we measure when we observe quantum systems, i.e. systems that we believe can be modeled by quantum mechanics.

The easiest way to visualise this is to think about flipping a coin as a quantum system. After we flick the coin into the air, and before it lands, we can't tell if it's going to be heads or tails, so it might as well be both at once! However, if we could know and describe everything about the coin, we could perfectly predict the outcome, so the probability is due to lacking information that we *could* have**.**

This is very similar to the concept of superposition described above. What we are interested in however is what happens as soon as the coin lands on the table. We say that the state of the coin (either "heads" or "tails") has to be chosen, because you can't have a coin spinning through the table!

In the same way that the table "forces" the coin to become in one of the two "heads" or "tails" states, a measurement in quantum mechanics "collapses" a quantum system into a state that we hope to have predicted. This collapseis actually only specifiv to the Copenhagen interpretation. Other interpretations use alternate ways to explain measurements.

## Introduction to quantum entanglement

Quantum entanglement is an effect that occurs when quantum particles interact, and become 'entangled', meaning that the properties of one of the partcles, e.g. spin, can be determined by observing properties of other particles that are entangled with it. Entanglement has numerous applications in computing and even potentially 'teleportation', which we will discuss.

Please add a link to a separate page on entanglement and hidden variables.

Entanglement:

Hidden Variables; https://quantum-entanglement.wikia.com/wiki/Hidden\_Variables

## Teleportation

One potential application of entanglement is development of technology that could potentially introduce teleportation. The term itself is misleading because as discussed below, the overall effect is similar to teleportation despite the process itself not being 'teleportation' as seen in pop culture. The term 'teleportation' in the context of quantum mechanics refers to a protocol described below.

**Use of Entanglement in Teleportation**

Although quantum entanglement does not itself transfer information, it can be used to aid communication. Suppose we want to teleport a particle A, and that two particles B and C are entangled,C is placed at a different location to A and B. A can then be made to interact with the entangled B and C to form a three-particle entangled system. A measurement of the state of B is taken and this information is sent to the location of C. By entanglement, we now know the state of A, as it is the same as the state of B and this infomation can be used to specify the state of C such that it is identical to the state of A. We have therefore `teleported` A to the location of C, however no matter was actually transferred, only quantum information in the form of qubits at the speed of light.

## Philosophy of quantum theory

While quantum mechanics is an incredibly successful theory of physics in terms of its predictive power, it is in the end only a mathematical theory. This means that while it can let us make incredibly precise measurements of physical properties of particles and relations between them, it does not explain why these values and relations are and behave in the way that they are observed to do. This is actually true of classical mechanics as well, which only gives us ways to calculate the motion of regular objects. Where quantum mechanics becomes much more philosophical than classical mechanics however, is in its probabilistic nature which gives rise to unintuitive behaviour (see previous sections). How we choose to interpret the physical origin and meaning of these probabilistic relationships (and notably the Wave Function) can have drastic repercusions on our conception of reality and causation. Of course, since we have no way of proving such interpretations, the interpretation we finally choose will depend on which conception we personally choose to adopt. The interest of studying these different interpretations is therefore not as much to find an answer as to which conception of reality is actually true, but rather to reflect on the questions brought up by quantum mechanics and the different realities that could give rise to it.

### Ontic vs. epistemic view of quantum theory

When it comes to the Philosophy of Quantum Theory there are two different ways of looking at it. One can take an ontic or epistemic view. One that asks about the true nature of the system in question, and one that merely concerns itself with what knowledge we can glean of the system itself.

### Interpretations of quantum mechanics

Although quantum mechanics is one of the biggest areas of research in science in the last 100 years, it is still not understood properly and as such there are various Interpretations of Quantum Theory that attempt to fully explain quantum behaviour. Although the Copenhagen interpretation is the most widely accepted, it still is not complete, and has not been proven,so there are other interpretations that contend with it, and what is more, some of them theoretically cannot be proven or disproven.

## Quantum computing

For Applied Group

Ever since the first computer was invented, we've been using computers based on laws the average person can understand without any math knowledge. Any information we want to store (numbers, words, phrases) is broken up into the smallest amount of information we could come up with, which happened to be a series of 0s and 1s, which we called binary digits, or bits.

For a while this was the best we could do, with the only advance we could make being making the systems that store either the 0 or the 1 smaller and smaller. However, as our understanding of the physics of small objects grew, we saw that certain properties of physical systems can be used to store information effectively. These were called quantum bits, or qubits.

### Qubits: the building blocks of a quantum computer

Qubits are the direct result of advances in our understanding of quantum mechanics. Like most of quantum mechanics, there isn't really any everyday object that could really describe a qubit, so it's easier to explain the mathematics behind them.

Qubit

### Quantum algorithms

Please add: an overview of the most common quantum algorithms and link to a page about them.

Quantum algorithms

## Quantum cryptography

For Applied Group

Quantum cryptography is the use of qubits for transferring information such that it can't be read by anyone with access to the transferred qubits of information.

### No-cloning theorem

Please add a description of the no-cloning theorem and its importance to quantum cryptography

### Quantum key distribution

Please quickly describe quantum key distribution and link to the page.

## Quantum research and society

For both: Please add your conclusions here from the ethics and societal impacts - misunderstandings.

### Ethical issues in quantum research

In all pages, you should have added ethical aspects and social aspects (e.g. implications of perfect cryptography). Briefly discuss all topics here and link organically to the various pages.

### Misunderstandings of quantum theory

Again, please discuss things people misunderstand here and link organically to the pages. Topics include teleportation, many'worlds, the capacity of quantum comptuers to do research, etc.

### Abstract group research visit

We visited an optomechanics laboratory at UCL with Nathanuel Bullier, a PhD student who works woth Prof. Peter Barker. The focus of their research is to study the behaviour of quantum systems to test and confirm various quantum theories, ranging from quantum gravity to collapse theories. The systems they study are some of the largest that exist today - they consist of silicon and diamond nanospheres which are levitated with electromagnetic fields and cooled with lasers.These spheres need to be cooled to remove the phonons they contain - this ensures that these spheres are quantum, as otherwise they would be too massive to obey quantum mechanical laws. Apart from testing quantum theories, these spheres can be used as sensors to measure external parameters, e.g. gravitational acceleration of the Earth, because they are extremely susceptible to incoming 'noise' from the surroundings.

In the actual lab, they had used several carefully placed lenses in a certain array with light from 2 powerful lasers shining on them (*Figure 1*). These lasers are what cools down the silicon and diamond nano-spheres. They were then shined onto a small box which had the levitating nano-spheres (*Figure 2*) and these nano-spheres were then observed by the Physicists (*Figure 3*).

## Pages

Applied group

Abstract group

Hidden Variables

Quantum Suicide Thought Experiment.

## References

1. ↑ Feynman, R., Leighton, R. and Sands, M. (2011). *Feynman Lectures on Physics, Vol. III*. New York: Perseus (Hachette).
2. ↑ Landau, Lev Davidovich, and Evgenii Mikhailovich Lifshitz. *Quantum mechanics: non-relativistic theory*. Vol. 3. Elsevier, 2013.
3. ↑ Laplace, Pierre-Simon (1902), "A Philosophical Essay on Probabilities”
4. ↑ Heisenberg, W. (1927), "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik", Zeitschrift für Physik (in German), **43** (3–4): 172–198

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