Quantum Mechanics: Superposition of 2 States?

In summary, the conversation discusses the possibility of superpositions in quantum mechanics and whether they are limited to only two states. The quick answer is that for some quantum systems, there can be more than two states as part of the superposition. However, there is a disagreement on this topic and further clarification is needed. This conversation also brings up the question of whether the Born rule is violated or just misunderstood.
  • #1
kurt101
284
35
Assuming Quantum mechanics is a probability theory that describes something real (which should be our first presumption), is there ever only a superposition of 2 states?

The reason I ask this is because:

For calculating the probability of an outcome you square the sum of the probability amplitudes.

If you have outcomes with probability amplitudes a, b, c; then you would get a probability of aa + ab + ac + bb + ba + bc + cc + ca + cb. You don't ever see a term like abc or aab for example.

So assuming QM is a realistic probability theory, you are multiplying all of the ways A can happen plus all of the ways B can happen plus all of the ways C can happen. Assuming these different terms are treated as actual realistic instance possibilities, doesn't this imply that when considering one instance a superposition of only aa or ab or ac or ba or bb or bc or ca or cb or cc is actually possible? In other words you don't actually see superpositions beyond two states at a time.
 
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  • #2
kurt101 said:
Assuming Quantum mechanics is a probability theory that describes something real (which should be our first presumption), is there ever only a superposition of 2 states?

The quick answer, for some quantum systems, no -- there can be more than 2 states as part of the superposition.
 
  • #3
StevieTNZ said:
The quick answer, for some quantum systems, no -- there can be more than 2 states as part of the superposition.
Can you provide a reference, example, or anything that might me be able to understand the longer answer? And are you implying that the Born rule is violated or just my interpretation of it is?
 
  • #4
kurt101 said:
If you have outcomes with probability amplitudes a, b, c; then you would get a probability of aa + ab + ac + bb + ba + bc + cc + ca + cb.

No, you don't. I've already corrected you on this in the other thread where you made this claim; see here:

https://www.physicsforums.com/threa...y-qm-is-incomplete.956222/page-3#post-6064334

Since your OP is based on a mistaken premise, I am closing this thread.
 

1. What is superposition in quantum mechanics?

Superposition in quantum mechanics refers to the ability of a quantum system to exist in multiple states at the same time. This means that the system can be in two or more states simultaneously, rather than being confined to just one state like in classical mechanics.

2. How does superposition work?

Superposition is a fundamental principle of quantum mechanics that arises from the wave-like nature of particles at the quantum level. The state of a quantum system is described by a wave function, which is a mathematical representation of all the possible states that the system can exist in. When a measurement is made, the wave function collapses to a single state, but until then, the system exists in a superposition of all possible states.

3. What are examples of superposition in everyday life?

Superposition is a concept that is not easily observed in everyday life, as it primarily applies to the microscopic world. However, one example that is often used to explain superposition is the famous thought experiment known as Schrödinger's cat. In this scenario, a cat is placed in a box with a vial of poison that will be released if a radioactive atom decays. According to quantum mechanics, until the box is opened and the cat is observed, it exists in a superposition of both alive and dead states.

4. What is the significance of superposition in quantum computing?

Superposition is a key principle in quantum computing, which utilizes the quantum states of particles to perform calculations. By allowing a quantum computer to exist in a superposition of states, it can perform multiple calculations simultaneously, making it potentially much faster than classical computers for certain tasks.

5. Can superposition be observed directly?

No, superposition cannot be directly observed, as it is a quantum phenomenon that occurs at the microscopic level. The effects of superposition can only be observed indirectly through the results of experiments and measurements.

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