# Superposition of 2

• B
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.

## Answers and Replies

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.

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?

PeterDonis
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