Understanding Quantum Qubits: Up, Down, and Beyond

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SUMMARY

The discussion centers on the representation of qubit states in quantum mechanics, specifically addressing the spin "up" and "down" states as qubit 1 and 0. Participants explore the concept of a state perpendicular to the basis direction, questioning whether it can be expressed as (0+1)/sqrt(2). Additionally, the implications of the phase shift x in the state (0+exp(ix)1)/sqrt(2) are examined. The conversation highlights the non-commutative nature of spin components in quantum systems, particularly in electrons compared to photons.

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Alexandr
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Guys,

I'm stuck with a simple and stupid question...

We have a spin "up" and "down" as a qubit 1 and 0 states.
Now can we consider a state perpendicular to this basis direction as a (0+1)/sqrt(2) state?

If not then what is the sense of the phase shift x in the state (0+exp(ix)1)/sqrt(2)?
 
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Alexandr said:
Guys,

I'm stuck with a simple and stupid question...

We have a spin "up" and "down" as a qubit 1 and 0 states.
Now can we consider a state perpendicular to this basis direction as a (0+1)/sqrt(2) state?

If not then what is the sense of the phase shift x in the state (0+exp(ix)1)/sqrt(2)?

An electron has spin components in the x, y and z directions where x, y and z are mutually perpendicular. These components do not commute, so knowledge of one does not represent knowledge of another.

A photon is different, as the perpendicular component is directly related.
 

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