If you have limited resources and want to measure a quantum state in a simple and accessible way, one option is to use a basic qubit system based on polarized photons. Photons are relatively easy to create and manipulate, and measuring their polarization can be done with relatively simple equipment.
Here's a simplified guide to measuring the polarization of a qubit using polarized photons:
Photon source: Start with a photon source that can generate individual photons. This could be a laser pointer or a light-emitting diode (LED) if you have limited resources. Ideally, you would want a photon source that emits photons one at a time to ensure you are working with a single qubit.
Polarization filters: Next, you'll need polarizing filters, which can be inexpensive and readily available. These filters transmit light that has a specific polarization orientation and block light with orthogonal polarization. For example, you can use linear polarizers that transmit light with a specific angle of polarization.
Prepare the qubit: Pass the photons emitted from the source through a polarization filter, which will prepare the qubit in a specific polarization state. For instance, you can set the filter to transmit only vertically polarized photons to prepare a qubit in the state |0⟩ (vertical polarization) or horizontally polarized photons for the state |1⟩ (horizontal polarization).
Measurement setup: Set up a measurement apparatus, which can be as simple as another polarization filter aligned at a specific angle. This filter will serve as the measurement basis. For example, if you use a linear polarizer oriented at 45 degrees, it will measure the qubit in the diagonal basis (|+⟩ and |-⟩ states).
Detection: Finally, detect the photons that pass through the measurement filter. You can use a photodetector or even a smartphone camera to record the photons that reach this stage.
Data analysis: Collect the measurement results and analyze the data to determine the probability of measuring the qubit in a particular state. By repeating the measurements multiple times, you can estimate the probabilities and validate the quantum behavior of the qubit.
While this setup may not provide advanced capabilities for complex quantum experiments, it offers a basic way to prepare and measure the polarization states of qubits using polarized photons. Keep in mind that in more sophisticated quantum laboratories, more precise and controlled setups are used to manipulate and measure qubits, but the simplified approach outlined here can be a starting point for basic quantum state measurements with limited resources.