# The heart of all of quantum physics is superposition

I am going to teach an introductory course on quantum information and I thought about this statement that I want to give at the very beginning.

Would you agree on that? From my perspective, every quantum notion has something to do with superposition at the end, right? Be it entanglement, computing, interference. Even exotic notions like the Aharonov-Bohm has in its heart something to do with superposition. If you are looking for quantum gravity, the notion of superposition is the first that raises a problem (a solvable problem, but still), because it is that elementary and different of classical physics.

Can I state superposition as the heart of all of quantum physics?

• Commented Apr 18 at 14:37

I've answered a related question (What is the role of entanglement in quantum-computational speed-up?) in the past, where I argue that superposition is merely derivative of the more fundamental "heart" - that quantum mechanics as we know it operates within those mathematical spaces known as Hilbert spaces. So I wouldn't precisely agree with your statement that "superposition is the heart of all quantum physics".

But, from a pedagogical perspective, I think a statement like that is nice and provocative, and it sets a nice, concrete, consistent framework with which to frame each unit. (If you haven't already, I recommend going through each unit you plan to cover and think about how you can relate it to this statement, and if you have trouble with any, consider how you might revise the statement so that you can.) In fact I kinda love this idea and might steal it someday. :P

If you can pull this off, I think the prompt "Do you agree with the statement?" would be an awesome end-of-term writing prompt for your students. Especially with a topic like quantum mechanics, which has such a rich philosophical significance, you as a teacher can afford to make statements not everyone would agree with, as long as your students understand they too are allowed to not agree with you. ;)

• Classical electrodynamics also works in Hilbert space, then what is the advantage that qc gives ? Commented Apr 20 at 1:29

@relativeentropy, since you are interested in knowing from a pedagogical perspective, It would be great to look at superposition from purely mathematical ground.

Superposition is not an exclusive feature of Quantum theory. Any linear theory incorporates superposition. (see wiki link on superposition)

It doesn't undermine the importance of superposition in Quantum mechanics (QM). It gives us a clue that certain other features in QM make it more successful than other physics theories in explaining certain physical phenomena.

A highly informal rule of thumb would be:- Superposition is necessary but insufficient to capture the essence of quantum theory. [Please take it with a pinch of salt:) ]

In his famous lectures on quantum mechanics, Richard Feynman described superposition as "the heart of quantum mechanics". He also stated that "no one has ever been able to define the difference between interference and superposition satisfactorily."

Repeated time and again with unimaginably more sophisticated and sensitive apparatus than Young's, the double-slit experiment encapsulates, said the physicist Richard Feynman, the "heart of quantum mechanics," its "only mystery."

~Robinson

When a state is formed by the superposition of two other states, it will have properties that are in some vague way intermediate between those of the original states and that approach more or less closely to those of either of them according to the greater or less 'weight' attached to this state in the superposition process. The new state is completely defined by the two original states when their relative weights in the superposition process are known, together with a certain phase difference, the exact meaning of weights

~Dirac

To monochromatic light corresponds in the acoustic domain the simple tone. Out of different kinds of monochromatic light composite light may be mixed, just as tones combine to a composite sound. This takes place by superposing simple oscillations of different frequency with definite intensities.

~Weyl

In my presentation on application of quantum computation in finance, I put emphasize naturaly on superposition as very imporant concept. Take for example Toffoli gate. It can be used as a classical NAND gate, hence it is universal for classical computing. Just by adding Hadamard gate, which only function is to prepare equally distributed superposition of single-qubit states $$|0\rangle$$ and $$|1\rangle$$, we get a universal gate set for quantum computation (see article by D. Aharanov for details). So, yes, superposition is really important.

However, besides superposition, quantum computers would be definitely less powerful without entanglement. In other words, only once you are able to put two or more qubit to communicate each other, your can do a meaningful computations. Because of this, I also put another emphasize on entanglement.

What is more, concept of interference of wave functions is equally important as it allows you to explain where speed-up comes from. See article Quantum Complexity Theory by Bernstein and Vazirani. On page 4, second column, last paragraph, they very nicely explain how interference of states gives quantum computers something that is not witnessed within classical computation.

And finally, we would not be able to extract any useful information about our calculation without a measurement. Therefore, I consider measurement to be another important pillar of quantum computing.

Overall, I would discuss all these phenomena as to be at heart of quantum computing despite as you mentioned the superposition is omnipresent. From pedagogical point of view, it could be tricky to describe something really complex like quantum computing with only one sentence. It can lead to oversimplification and false thinking of students that they understand the concept perfectly.

Superposition on its own seems a bit reductive. Because the concept does not enclose every mechanics. I am especially thinking at (1) entanglement, (2) non-locality and (3) tunnelling.

A quantum system is in superposition to an observer. But we also have

1. entanglement: a correlation of different systems;

2. non-locality: the correlation of systems stays independent from their position in space;

3. tunnelling: a property of particles violating classical mechanics.

Indeterminism sounds more appropriate to me.