- #1
Sunny Singh
- 19
- 1
- TL;DR Summary
- I have read in Neilson and chuang that the information represented by a qubit is infinite because the state vector takes values in a continuous space. I have a doubt regarding this statement.
I have just started reading Neilson and chuang's book on quantum computing and two times already have they said that when a qubit is not observed, it can contain infinite information.
"How much information is represented by a qubit? Paradoxically, there are an infinite number of points on the unit sphere, so that in principle one could store an entire text of Shakespeare in the binary expansion of theta"
And again when explaining quantum teleportation, "even if Alice did know the state, describing it precisely takes an infinite amount of classical information since ψ takes values in a continuous space"
Now, doesn't the complete description of the qubit depend only on the two coefficients of its two computational basis states? If Alice did know the state, doesn't it mean that she just knew what these two complex coefficients are? Why will she ever need infinite classical information to explain the state? I understand that we need an ensemble of identically created qubits to determine the coefficients but even if we don't know the exact state of the qubit, we know that there's only two unknown complex numbers. I don't understand what do the authors mean by a qubit having enough space to store an entire book only because those two complex coefficients takes values in a continuous space?
"How much information is represented by a qubit? Paradoxically, there are an infinite number of points on the unit sphere, so that in principle one could store an entire text of Shakespeare in the binary expansion of theta"
And again when explaining quantum teleportation, "even if Alice did know the state, describing it precisely takes an infinite amount of classical information since ψ takes values in a continuous space"
Now, doesn't the complete description of the qubit depend only on the two coefficients of its two computational basis states? If Alice did know the state, doesn't it mean that she just knew what these two complex coefficients are? Why will she ever need infinite classical information to explain the state? I understand that we need an ensemble of identically created qubits to determine the coefficients but even if we don't know the exact state of the qubit, we know that there's only two unknown complex numbers. I don't understand what do the authors mean by a qubit having enough space to store an entire book only because those two complex coefficients takes values in a continuous space?