Qubit Spin Convention: |0> & |1> Eigenvectors?

In summary, the convention for representing qubits uses the notation |0> = (1,0)^T and |1>=(0,1)^T, with both spin states having equal energy in the absence of an external field. This notation may be misleading as |0> is commonly used to represent the ground state, but it is chosen for binary signaling purposes in communications protocols. The spin up state is typically chosen as the "off" bit.
  • #1
lewis198
96
0
This is a bit embarrassing, but by convention does [itex]|0> = (1,0)^T[/itex] and
[itex]|1>=(0,1)^T[/itex], where we are in the basis of the eigenvectors of [itex]\sigma_{z}[/itex]?
 
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  • #2
The notation is a bit misleading, since [itex]|0\rangle[/itex] is most commonly used to denote the ground state of a system. However, in the absence of an external field, both spin states have the same energy. The justification for using the notation is the convention that in a communications protocol, one state must be chosen to signal binary 0 vs binary 1 for the other state. There's no particular reason to choose one over the other, but indeed the spin up state is conventionally chosen to be the off bit, see http://en.wikipedia.org/wiki/Qubit#Physical_representation
 

Related to Qubit Spin Convention: |0> & |1> Eigenvectors?

1. What is a qubit spin convention?

A qubit spin convention is a way of representing the two possible states of a qubit, 0 and 1, using the eigenvectors of the Pauli spin matrices. These eigenvectors, |0> and |1>, are used to represent the basis states of a qubit in quantum computing.

2. What do |0> and |1> represent in the qubit spin convention?

In the qubit spin convention, |0> and |1> represent the two possible states of a qubit. |0> is the ground state, or the state with spin down, while |1> is the excited state, or the state with spin up.

3. How are the eigenvectors |0> and |1> related to the qubit spin convention?

The eigenvectors |0> and |1> are used to represent the basis states of a qubit in the qubit spin convention. These eigenvectors are used to create a superposition of the two qubit states, which is the basis of quantum computing.

4. Can the qubit spin convention be used for more than two qubit states?

Yes, the qubit spin convention can be extended to represent more than two qubit states. This is done by using multiple qubits and combining their |0> and |1> eigenvectors to create a larger basis state space.

5. How does the qubit spin convention relate to quantum entanglement?

The qubit spin convention is crucial in understanding and manipulating quantum entanglement. By using the |0> and |1> eigenvectors to create a superposition of qubit states, we can create entangled states that exhibit correlations between multiple qubits.

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