6 ms·

No. A state is entangled when it isn’t a product state. Two spin (1/2) particles in a singlet state have the kind of “they have opposite states” thing going o

by drdeca 1mo ago

No. A state is entangled when it isn’t a product state. Two spin (1/2) particles in a singlet state have the kind of “they have opposite states” thing going on that you describe, and is a specific way that two particles can be entangled.

tauwauwau 1mo ago
OK, so instead of having all states (00, 01, 10, 11) available in entangled state they only have 01 and 10 available because they have to be opposite of each other, but even with that these particles individually are able to have both states right? I'm not knowledgeable in this field, I just have interest.
- fasterik 1mo ago
  00, 01, 10, 11 are separable states, meaning that a pair of particles in one of those states can be described as two separate one-particle systems. For example, 01 means that the first particle is in the state 0 and the second particle is is in the state 1. A state like (01 + 10) is not separable, so by definition it's an entangled state. "Separability" is a straightforward algebraic fact that follows from the definition of a vector and the tensor product. You can see what this means in the following Google answer https://share.google/aimode/13jNpR7bmpPMo1pn3 https://share.google/aimode/13jNpR7bmpPMo1pn3 (01 + 10) means that if I measure the first particle and get 0, then the second particle is now in the state 1. If I measure the first particle and get 1, then the second particle is now in the state 0.
- drdeca 1mo ago
  The state you describe, sqrt(1/2) ( |01> + |10>) is an entangled state, but not all entangled states are like that. The state sqrt(1/2) ( |00> + |11> ) is also possible, and is also an entangled state, but doesn’t have the two particles in opposite states. By contrast, the state (1/2) (|00> - |01> + |10> - |11>) is (while a valid state) not an entangled state, because it is equal to (1/2) (|0> + |1>) (|0> - |1>) .

by drdeca 1mo ago

tauwauwau 1mo ago

OK, so instead of having all states (00, 01, 10, 11) available in entangled state they only have 01 and 10 available because they have to be opposite of each other, but even with that these particles individually are able to have both states right? I'm not knowledgeable in this field, I just have interest.

fasterik 1mo ago
00, 01, 10, 11 are separable states, meaning that a pair of particles in one of those states can be described as two separate one-particle systems. For example, 01 means that the first particle is in the state 0 and the second particle is is in the state 1. A state like (01 + 10) is not separable, so by definition it's an entangled state. "Separability" is a straightforward algebraic fact that follows from the definition of a vector and the tensor product. You can see what this means in the following Google answer https://share.google/aimode/13jNpR7bmpPMo1pn3 https://share.google/aimode/13jNpR7bmpPMo1pn3 (01 + 10) means that if I measure the first particle and get 0, then the second particle is now in the state 1. If I measure the first particle and get 1, then the second particle is now in the state 0.
drdeca 1mo ago
The state you describe, sqrt(1/2) ( |01> + |10>) is an entangled state, but not all entangled states are like that. The state sqrt(1/2) ( |00> + |11> ) is also possible, and is also an entangled state, but doesn’t have the two particles in opposite states. By contrast, the state (1/2) (|00> - |01> + |10> - |11>) is (while a valid state) not an entangled state, because it is equal to (1/2) (|0> + |1>) (|0> - |1>) .