Quantum Computing 2 - Photon as a qubit

In the last post, we discussed the characteristics of a qubit. Then, what kind of physical entity represents a qubit? A photon is one of them, and it shows mysterious phenomena.

Wave-particle duality

Imagine you prepare an illuminant and a detector such as a photomultiplier tube. As you put optical filters between them, electric current in the detector become low. Eventually, it changes to discontinuous. This minimum unit of light is called a photon.

In addition, a photon is electromagnetic wave. If light is traveling in the direction of $z$, the electric field is written as;

$$\begin{equation} \boldsymbol{E} = \mathrm{Re}(E_{x0} \mathrm{e}^{iwt}e_x + E_{y0} \mathrm{e}^{iwt}e_y) \\ |E_{x0}|^2 + |E_{y0}|^2 = 1 \end{equation}$$

Here, $\mathrm{Re}$ means the real part of the complex number. $E_{x0}$ and $E_{y0}$ are complex amplitude. $e_x$ and $e_y$ are unit vectors.

Quantum entanglement

A Ca atom emits two photons that have orthogonal wave (purple and green) each other in opposite direction when it is excited in a particular energy level by a laser. If you set color filters, polarizing filters, and light detectors as below, this system can represent qubits.

If we express a photon polarized $x$ direction as $\vert 0 \rangle$ and $y$ direction as $\vert 1 \rangle$, it is written as;

$$\begin{equation} \vert 0 \rangle_g \otimes \vert 1 \rangle_p \quad {\rm or} \quad \vert 1 \rangle_g \otimes \vert 0 \rangle_p \end{equation}$$

Here, $\vert \rangle_g$ and $\vert \rangle_p$ are the photon conditions detected by each device. It means, if you know one photon condition, you can predict another one. In the other words, if you don’t know one photon condition, you can never predict another one. The phenomenon is called quantum entanglement, and this is a remarkable characteristic in quantum mechanics.

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