The discussion revolves around the conditions under which a quantum state can be expressed as a product state for two systems versus when a sum of product states is necessary. Participants explore the implications of these representations in the context of entanglement and quantum state evolution.
Participants express differing views on the relationship between sums of product states and entanglement, with some asserting that a sum indicates entanglement while others argue that it does not necessarily imply entanglement if it can still be factored.
There are unresolved questions regarding the definitions and conditions under which states are considered entangled or separable, as well as the implications of Hamiltonians on state evolution.
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"