4 ms·

So why does the Hadamard+CNOT acting on two qubits give an entangled state, but a Hadamard acting on a single qubit does not give an entangled state?

nonsapreiche 8y ago
I think you need 2 qbit to have them entangled
- onorton 8y ago
  Exactly. The point of quantum entanglement is that the state of two (or more) qubits cannot be separated. To entangle a single qubit is meaningless. For two qubits, the simplest entangled states are the Bell States[0] (generated from a CNOT and Hadamard gate). The article gives an example of one of them. [0] https://en.wikipedia.org/wiki/Bell_state https://en.wikipedia.org/wiki/Bell_state
  - Yajirobe 8y ago
    What's the difference between an entangled state and a mixed state?
    - onorton 8y ago
      Knowledge is a bit rusty (took a module in Uni) but I'll try to answer. A mixed state is that which is a linear combination of pure states e.g. a|0> + b|1> What determines an entangled state is that qubit values will correlate exactly with each other. |00> + |11> would be an example of an entangled state as measuring one qubit determines the value of the other with certainty. If you measure |0> for the first qubit, the second will definitely be |0> and vice versa. They are also not mutually exclusive as mixed entangled states exist.
      - Yajirobe 8y ago
        > A mixed state is that which is a linear combination of pure states e.g. a|0> + b|1> Here https://en.wikipedia.org/wiki/Qubit#Mixed_state https://en.wikipedia.org/wiki/Qubit#Mixed_state it says that 'Mixed states can be represented by points inside the Bloch sphere'. However, points ON the sphere correspond to linear combinations of the pure states. How to reconcile this?
        onorton 8y ago
        Like I said, my knowledge is rusty. I've gotten pure states mixed up with |0>, |1> I believe what it's saying is that with a mixed state |a|^2 + |b|^2 does not need to equal 1. So pure states are a|0> + b|1> where |a|^2 + |b|^2 = 1

nonsapreiche 8y ago

I think you need 2 qbit to have them entangled

onorton 8y ago
Exactly. The point of quantum entanglement is that the state of two (or more) qubits cannot be separated. To entangle a single qubit is meaningless. For two qubits, the simplest entangled states are the Bell States[0] (generated from a CNOT and Hadamard gate). The article gives an example of one of them. [0] https://en.wikipedia.org/wiki/Bell_state https://en.wikipedia.org/wiki/Bell_state
- Yajirobe 8y ago
  What's the difference between an entangled state and a mixed state?
  - onorton 8y ago
    Knowledge is a bit rusty (took a module in Uni) but I'll try to answer. A mixed state is that which is a linear combination of pure states e.g. a|0> + b|1> What determines an entangled state is that qubit values will correlate exactly with each other. |00> + |11> would be an example of an entangled state as measuring one qubit determines the value of the other with certainty. If you measure |0> for the first qubit, the second will definitely be |0> and vice versa. They are also not mutually exclusive as mixed entangled states exist.
    - Yajirobe 8y ago
      > A mixed state is that which is a linear combination of pure states e.g. a|0> + b|1> Here https://en.wikipedia.org/wiki/Qubit#Mixed_state https://en.wikipedia.org/wiki/Qubit#Mixed_state it says that 'Mixed states can be represented by points inside the Bloch sphere'. However, points ON the sphere correspond to linear combinations of the pure states. How to reconcile this?
      - onorton 8y ago
        Like I said, my knowledge is rusty. I've gotten pure states mixed up with |0>, |1> I believe what it's saying is that with a mixed state |a|^2 + |b|^2 does not need to equal 1. So pure states are a|0> + b|1> where |a|^2 + |b|^2 = 1