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**This simulation is under construction!!!**. There are most likely
bugs and computational errors in the code. Please keep this in mind.

This simulation demonstrates entanglement of spins.

Choose one or two spins with the "One Spin" and "Two Spins" buttons at the top of the panel.

Drag the head of the arrow of either spin to arrange it in any orientation. (The circle shown is a slice of the sphere in the YZ plane. That is, the vertical axis represents the Z-axis of the sphere and the horizontal axis representing the Y-axis).

Drag either end of the green measurement vector to set the direction that in which the spin measurement operation will occur.

The gray arrows show the position of the spins before the measurement occurred.

The parameter table shows the Spin and Measurement angles in degrees. Also shown is the expectation value of the probability that the spin will be aligned with the measurement vector CLOSEST to the spin angle.

The spins can be entangled in the **Spin-Singlet** state
by clicking on the "Singlet" button. In this state, the spins cannot
be controlled independently. The position of the individual spins is
unknown. Measuring the spins in any direction
will put the spins into a definite
state, with the inevitable result that
this measurement will destroy the entanglement.

The "Triplet" button is not yet implemented.

Clicking on the "Measure" button will measure the spins. This will mandate that each spin lie in a direction parallel to each measurement vector.

Note that if the spins are in the entangled singlet state, they are inherently coupled together. However, once their spin directions have been measured, the entanglement is lost, and the spins can be manipulated and controlled independently. This is an important quality which is vital for quantum computation.

To Do :

- Add axes on graphs, and possibly a general XYZ set of axes
- Format floats in the table to display fewer decimal digits
- Add Quantum Encryption Demonstration
- Allow value entry from parameter table
- Possibly allow entanglement in the Triplet state
- Possibly allow other values of spin besides S=1/2

December 27, 2003