Clarification on what we can consider a qubit to be

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Discussion Overview

The discussion revolves around the definition and conceptual understanding of a qubit within the context of a two-level quantum system. Participants explore whether the individual states |0⟩ and |1⟩ can be considered qubits on their own or if only their superposition represents a qubit.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants question whether the states |0⟩ and |1⟩ can be considered qubits independently or if only their superposition α|0⟩ + β|1⟩ qualifies as a qubit.
  • One participant suggests that if the superposition is regarded as a qubit, then setting α = 1 and β = 0 would also yield a valid qubit state.
  • Another participant argues that the qubit is the two-state system itself, comparing it to a classical bit, and posits that the individual states are not qubits but rather quantum analogues of classical values.
  • Another viewpoint presented is that the pair of states should be considered as forming a qubit, emphasizing that the states alone are not particularly useful without their relationship.
  • A further perspective introduces the idea of a qubit as an anti-commuting pair of observables, linking the states |0⟩ and |1⟩ with specific superpositions.

Areas of Agreement / Disagreement

Participants express differing views on whether individual states can be classified as qubits, indicating that multiple competing perspectives remain without a consensus.

Contextual Notes

Some assumptions about the definitions of qubits and their relationship to classical bits may not be fully articulated, and the discussion does not resolve the implications of these definitions.

eprparadox
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In a 2 level quantum system, should I consider the states

|0>

and

|1|>

to be qubits by themselves?

Or is only the SUPERPOSITION of these two states,

\alpha |0> + \beta |1>

considered to be a qubit?
 
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Nevermind, they have to be qubits as well. If we consider our superposition to be a qubit, then we can set ## \alpha = 1 ## and ## \beta = 0 ## and that should be an appropriate qubit state.
 
eprparadox said:
In a 2 level quantum system, should I consider [...] to be qubits by themselves?
The qubit is the 2-state system, just like a classical bit is a binary variable. The states are not qubits, but the qauntum analogues of the classical values.
 
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You should consider the pair to form a qubit. On their own they're not very useful.

Another useful way to think about what a qubit is is as an anti-commuting pair of observables, such as the observable ##|0\rangle##-vs-##|1\rangle## paired with the observable ##\frac{1}{\sqrt{2}} \left( |0\rangle + |1\rangle \right)##-vs-##\frac{1}{\sqrt{2}} \left( |0\rangle - |1\rangle \right)##.
 
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