Yes, exactly. And that symbol is a tensor product.StevieTNZ said:Okay so if we have two pairs of entangled photons:
We'd write the whole state of both pairs as the sum of the product state (which would be two photons TENSOR two photons)?
I don't even know if tensor is the right word (circle with x in it?)?
If we write a quantum state as a sum of products of arbitrary states (they could be linearly dependent, for instance), then we may still be able to factor this state as a product of states, so there's not entanglement. If, however, it cannot be factored into a single product, then it's entangled.StevieTNZ said:And when we write a sum of product states, they're entangled?
That's the point, when you have to use a sum, then it's entanglement. But if it's merely possible to write it using a sum, that need not be entanglement.StevieTNZ said:Now I'm confused, because Erich Joos is saying "When you have to use a sum of product terms, you have an entangled state"
The sum notation should be used when the state of a system can be described as a combination of two or more separate states. This is often the case in quantum mechanics, where a system can exist in multiple states simultaneously.
To write a product state using a sum, you first need to identify the separate states that make up the system. Then, use the sum notation to combine these states into one expression. For example, if a system can exist in two states, A and B, the product state can be written as A + B.
Yes, a product state can also be written using a tensor product, denoted by the symbol ⊗. This is often used when the separate states are not independent of each other, but rather interact with each other.
Yes, using a sum to write product states can make calculations and equations simpler and more intuitive. It also allows for a more elegant representation of a system's state, especially in quantum mechanics where states can be complex and abstract.
There are certain cases where a sum may not be the most appropriate notation for writing product states. For example, if the states are not discrete and can take on continuous values, other mathematical operations such as integration may be more suitable.