If you have limited resources and want to measure a quantum state, a good option is to use a qubit based on the principle of photon polarization. Photons can be easily generated using a simple laser and passed through polarization filters to create a qubit. Here's a step-by-step guide to creating and measuring a polarization-based qubit with minimal equipment:
Laser setup: Obtain a low-power laser pointer, preferably in the visible range (such as a red laser). This can be easily found in many stores or online.
Polarization filters: Acquire two linear polarizing filters. These can be inexpensive polarized sunglasses or plastic films that polarize light. Ensure that the filters are perpendicular to each other when oriented correctly.
Photon generation: Point the laser at a beam splitter, which can be a piece of glass or a transparent plastic film. The beam splitter will divide the laser light into two beams.
Polarization preparation: Place one polarizing filter in the path of one beam, and the other filter in the path of the second beam. By adjusting the orientation of the filters, you can control the polarization of each beam.
Qubit creation: The two polarization states of a qubit are typically represented as |0⟩ and |1⟩. You can set up the system so that one polarization state corresponds to |0⟩ and the other to |1⟩. For example, you could set the first filter to pass vertically polarized light (|0⟩) and the second filter to pass horizontally polarized light (|1⟩).
Quantum state preparation: To prepare a specific quantum state, adjust the orientation of the filters accordingly. For example, if you want to create a superposition state like |+⟩ = (|0⟩ + |1⟩)/√2, set the second filter at a 45-degree angle relative to the first filter.
Measurement: To measure the quantum state, you will need a polarization analyzer. This can be as simple as a third polarizing filter. Place the analyzer in the path of the prepared qubit.
Readout: Observe the intensity of the light that passes through the analyzer. If the intensity is maximum, the qubit is in the corresponding state (e.g., vertically polarized light for |0⟩). If the intensity is minimum, the qubit is in the orthogonal state (e.g., horizontally polarized light for |0⟩). Intermediate intensities indicate superposition states.
Keep in mind that this setup provides a basic way to create and measure a quantum state using polarization. It does not offer the same level of precision and control as more advanced laboratory setups. Nonetheless, it can serve as an accessible introduction to quantum measurements.