Version 3.0

We are thrilled to announce the release of Version 3.0 of "Quantum Entanglement Simulation"! This version builds on our previous releases with exciting new preset experiments and additional enhancements to further your exploration of quantum mechanics.

What's New in Version 3.0

• New Preset Experiments:

  • Entangled Electrons with Stern-Gerlach Magnets:

    • Setup: The detectors are three Stern-Gerlach magnets, one oriented along the z-axis and two in the zx plane with ±120° rotation.
    • Particles: Two entangled electrons in the singlet state.
    • State:

      | Psi > = 1 / sqrt(2) * ( | up down > - | down up > )
      

  • Entangled Photons with Polarizers:

    • Setup: The apparatus consists of two polarizers directing two photons to three photodetectors, one oriented along the z-axis and two in the zx plane with 22.5° and 45° rotation.

    • Particles: Two entangled photons in the second triplet state.

    • State:

      | Psi > = 1 / sqrt(2) * ( | up up > + | down down > )
      

    • Note: In the real world, light polarization is typically measured in degrees, with θ ranging from 0° to 360°. In the Hilbert space, angles are represented by state vectors on the Bloch sphere, with θ ranging from 0 to π. The conversion from real-world polarization angle θ_real to Hilbert space angle θ_Hilbert is given by:

      θ_Hilbert = 2 * θ_real
      

• Improved User Interface: Enhanced visuals and user interactions to make the simulation more intuitive and engaging.

• Performance Optimizations: Faster simulations and reduced computational overhead to provide a smoother user experience.

Upgrade to Version 3.0 today to take advantage of these new features and improvements in your quantum simulations!

Version 2.0

We are excited to announce the release of Version 2.0 of "Quantum Entanglement Simulation"! This version builds upon our initial release, introducing new features and improvements to enhance your quantum simulation experience.

What's New in Version 2.0

• EPR Experiment: Explore the famous Einstein-Podolsky-Rosen (EPR) experiment with our new simulation module. Simulate the violation of Bell's theorem and demonstrate the impossibility of hidden variables using entangled spins.

Key Features

• Dynamic Orientation Controls: Users can input precise coordinates to set the orientation of the measurement apparatus, offering unparalleled control over simulation parameters.
• Enhanced Measurement Capabilities: Our simulation includes options for measuring spins individually or simultaneously, capturing the essence of quantum correlations.
• Statistical Analysis Tools: Gain insights from detailed statistical outputs that describe the probability distributions and correlations between quantum spins.

EPR Experiment

This script simulates two entangled spins following quantum mechanics principles. It can be used to simulate the violation of Bell's theorem and thus demonstrate the impossibility of hidden variables.

Simulation types available:

1. Singlet state:
   • | Psi > = 1 / sqrt(2) * (| ud > - | du >) [DEFAULT]
2. Triplet state I:
   • | Psi > = 1 / sqrt(2) * (| ud > + | du >)
3. Triplet state II:
   • | Psi > = 1 / sqrt(2) * (| uu > + | dd >)
4. Triplet state III:
   • | Psi > = 1 / sqrt(2) * (| uu > - | dd >)

Both apparatus measure at the same time. A button allows random selection of the direction, ensuring statistical measurement in the same direction ⅓ of the time.

Measurement Options:

• Perform 'n' measurements with the number set using the command line option -m, --measurement_number (default = 100).
• Set the color for spin up (| +1 >) with -u, --color_up (default = green) and for spin down (| -1 >) with -d, --color_down (default = red).

Output:

• By default, results are inverted: for the singlet state, if apparatus 1 measures | +1 >, apparatus 2 will agree 100% of the time if oriented in the same direction, otherwise, there will be 0% agreement. This inversion is for convenience in analyzing results and can be overridden with the command line option -n --no-invert.
• The orientation of the apparatus can be set with theta1, theta2, phi1, and phi2 in degrees (default set to 0).
• Equivalent results (100% agreement if in the same direction and 25% otherwise) can be achieved with the following configurations:
  1. invert = True, theta2 = 0° (both apparatus same direction)
  2. invert = False, theta2 = 180° (second apparatus upside down)

We hope you enjoy the new features and improvements in Version 2.0. Your feedback is invaluable as we continue to enhance our simulation tool. Thank you for your support!

Version 1.0

We are excited to announce the release of Version 1.0 of "Quantum Entanglement Simulation"! This initial version marks a major milestone in providing an interactive, user-friendly platform for simulating quantum spin dynamics. Designed for students, educators, and researchers alike, this tool facilitates a deeper understanding of quantum mechanics through computational simulations.

What's New in Version 1.0

• Single Spin Simulation: Simulate the quantum mechanics of a single spin, with customizable apparatus orientations. Experience the quantum world's probabilistic nature with our real-time spin measurement outputs.
• Two Spin Simulation: Dive into the complexities of quantum entanglement with our two-spin simulation module. Explore various predefined quantum states, including product states and entangled states, and measure correlations directly.

Key Features

• Dynamic Orientation Controls: Users can input precise coordinates to set the orientation of the measurement apparatus, offering unparalleled control over simulation parameters.
• Enhanced Measurement Capabilities: Our simulation includes options for measuring spins individually or simultaneously, capturing the essence of quantum correlations.
• Statistical Analysis Tools: Gain insights from detailed statistical outputs that describe the probability distributions and correlations between quantum spins.