Why does the Bloch sphere have a radius of 1?

Thank you so much! I am a quantum newbie, so forgive me if this is basic.

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    $\begingroup$ Downvotes: why? It seems to be an earnestly asked question. $\endgroup$ Commented Apr 22 at 20:57
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    $\begingroup$ To the question itself: the radius of a point on or in the Bloch sphere serves as a measure of the fidelity, which is bounded between 0 and 1. A points on the surface of the sphere corresponds to a pure qubit with fidelity = 1, while a point inside corresponds to a qubit in some mixed state, with fidelity <1 (but $\ge$ 0.) $\endgroup$ Commented Apr 22 at 21:00
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    $\begingroup$ Just to add, a pure single qubit state has to be described by a unit vector so that sum of probabilities of measurement of states 0 and 1 is 1. This may be helpful to understand Bloch sphere better: quantumcomputing.stackexchange.com/questions/37905/…, quantumcomputing.stackexchange.com/questions/9404/…, quantumcomputing.stackexchange.com/questions/10303/… $\endgroup$ Commented Apr 23 at 6:14
  • $\begingroup$ @MarkSpinelli: Absolutely agree, no point in downvoting. Everybody has to start learn from beginning. $\endgroup$ Commented Apr 23 at 6:19
  • $\begingroup$ Thank you so much for the help!! $\endgroup$ Commented Apr 23 at 20:35


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