# How to get $\theta$ and $\phi$ in a Bloch sphere for individual qubits in a quantum register?

I have a quantum register with some qubits (I'm just new to all of this). Is there a way to achieve $$\theta$$ and $$\phi$$ angle values in the Bloch sphere for each qubit separately? If I do a circuit with only one qubit, everything is ok, but when I have more, the statevector contains all the possible states that can come up with a measurement $$(2^N)$$, but I need to know, before measurement, what are such values for every single qubit. Is it possible?

• Nov 3, 2023 at 16:42
• The short answer is, no, it is not possible, unless your quantum circuit does not entangle any of your qubits. This is a feature of quantum information, not a bug. Nov 3, 2023 at 16:44

I have a quantum register with some qubits (I'm just new to all of this). Is there a way to achieve $$\theta$$ and $$\phi$$ angle values in the Bloch sphere for each qubit separately?

If I do a circuit with only one qubit, everything is ok,

Yes, for one qubit, the most general state is, well, one qubit. There are $$2^1=2$$ complex coefficients needed to specify the state vector of a qubit. The 2 complex coefficients are subject to one normalization condition, and the physical state is only meaningful up to an overall phase. So, for one qubit, you can specify the state using two real coefficients $$\theta$$ and $$\phi$$.

but when I have more, the statevector contains all the possible states that can come up with a measurement $$(2^N)$$, but I need to know, before measurement, what are such values for every single qubit.

A direct product state of N-qubits only has $$2N$$ complex coefficients, but in general a state needs $$2^N$$ complex coefficients. So, it seems that at least for $$N>2$$ there is no way to specify a general N-qubit state in terms of a direct product of N qubits. In fact, even for $$N=2$$ you can't specify a general state in terms of a direct product of 2 qubits. For example, it is impossible to write the state $$(|00\rangle + |11\rangle)/\sqrt{2}$$ as a direct product of 2 qubits.

Therefore, generally, when $$N\ge 2$$, it is not possible to describe an $$N$$-qubit state in terms of a direct product of $$N$$ qubits. That is, you can't generally specify an N-qubit state in terms of $$2N$$ parameters $$\theta_1$$, $$\phi_1$$, $$\ldots$$, $$\theta_N$$, $$\phi_N$$.

Is it possible?

No.