Previously, I argued for principles rather than postulates. Usually, principles are added to a field of study only after some progress have been made with the theories in that field. However, sometimes these principles are required ahead of the time to make progress in a field. That may be the case in fundamental physics where such principles can be used as guiding principles. However, in the latter case such principles may be just guess-work. They may turn out to be wrong.
Quantum physics has been around for a long enough time to justify having its own set of principles. There are postulates for quantum mechanics, but as I explained, they are like a set of axioms for the mathematical formalism and therefore don’t qualify as principles. Principles are statements phrased in terms of physical concepts and not in terms of mathematical concepts.
Here, I want to propose such principles. They are a work in progress. Those that I can state are not extremely surprising. They shouldn’t be because quantum physics has been investigated in so many different ways. However, there are some subtleties that need special attention.
The first principle is simply a statement of Planck’s discovery: fundamental interactions are quantized. Note that it does not say that “fields” or “particles” are quantized, because we don’t know that. All we do know is what happens at interactions because all our observations involve interactions. Here, the word “quantized” implies that the interacting entities exchange quantized amounts of energy and momentum.
What are these interacting entities? Usually we would refer to them as particles, but that already makes an assumption about their existence. Whenever we make an observation that would suggest that there are particles, we actually see an interaction. So we cannot conclude that we saw a particle, but we can conclude that the interaction is localized. Unless there is some fundamental distance scale that sets a lower limit, the interaction is point-like – it happens at a dimensionless point. The most successful theories treat these entities as fields with point-like interactions. We can therefore add another principle: fundamental interactions are localized. However, we can combine it with the previous principle and see it as another side of one and the same principle: fundamental interactions are quantized and localized.
The next principle is a statement about the consequences of such interactions. However, it is so important that it needs to be stated as a separate principle. I am still struggling with the exact wording, so I’ll just call it the superposition principle. Now, superposition is something that already exists in classical field theory. In that case, the superposition entails the coherent additions of different fields. The generalization that is introduced by quantum physics is the fact that such superpositions can involved multiple entities. In other words, the superposition is the coherent addition of multiple fields. The notion of multiple entities is introduced due to the interactions. It allows a single entity to split up into multiple entities, each of which can carry a full compliment of all the degrees of freedom that can be associated with such an entity. However, due to conservation principles, the interaction sets up constraints on the relationship among the degrees of freedom of the different entities. As a result, the degrees of freedom of these entities are entangled, which manifests as a superposition of multiple entities.
We need another principle to deal with the complexities of fermionic entities, but here I am still very much in the dark. I do not want to refer to the anti-commuting nature of fermionic operators because that is a mathematical statement. Perhaps, it just shows how little we really know about fermions. We have a successful mathematical formulation, but still do not understand the physical implications of this formulation.
Flippiefanus 
Thank you the discussion. Historically the concept of quantization was first introduced by Planck to explain black body radiation and later Einstein used that same concept of quantization to explain the photo electric effect. These cases are not associated atomic transitions. So the concept really has to do with the fact that light is emitted and absorbed in lumps. Hence quantization. It does not have anything to do with compact spaces. Although you do get a natural form of quantization in such cases that is not what quantum mechanics is about.
As for the outcomes of measurements in quantum mechanics, it is determined by what you are measuring, which is determined by the observable. If your observable has two possible outcomes a and b with associated probabilities, then there can be another observable that can give outcomes in terms of linear combinations of a and b. So in this respect it is not so different from the classical case.
Anyway, I’m glad we at least agree that the superposition principle should be one of the fundamental principles of quantum physics.
First of all, I’m very much in favor of your program of principles over axioms. However, I don’t find myself agreeing with all your principles, and I really don’t agree with your ordering of them. First of all, I don’t think that quantization is all that central to quantum mechanics, and I think it only gets that name for historical reasons. You only get quantization when you have a compact configuration space, which then has a discrete Fourier transform. This is not true in general quantum systems. Angular momentum is quantized, but that’s because the configuration space is a sphere which is compact. Regular momentum, and energy, are not necessarily quantized in most quantum mechanical systems. Most particle interactions in qft can transfer any amount of momentum, (bearing in mind mass thresholds). The historical centrality of quantization comes from the fact that the first place quantum mechanics really came into play was in studying atomic transitions, and these are in fact quantized since the energy gained or lost is energy coming from angular momentum.
I think the central physical principle in quantum mechanics is superposition. That is to say if you can measure a system and get values a and b, then any (properly normalized) complex linear combination of a and b is a valid configuration of your system. Crucially though, the allowed outcomes of measurements is still only a and b.
This differs from the kind of superposition you see in classical mechanics. In classical mechanics, if your equations of motion are linear, and you have two solutions a and b, then any linear combination of a and b, call it c, is also a valid configuration of your system. But unlike quantum mechanics, you can also measure and find c.
To the best that I can tell, this is the defining physical principle of quantum systems that makes them different from classical systems.
I think that, with the probability interpretation of quantum states let’s you to the introduction of Brown’s QFT textbook where he states (and I’m paraphrasing) quantum mechanics only answers one question; suppose I measured my system and found it to be in state a, what’s the probability of finding it in state b if I measure it at some later time