Programming the Universe: A Quantum Computer Scientist Takes on the Cosmos

by Seth Lloyd

The state |0> + |1> has a definite value of spin along the sideways axis. If you measure which direction it is spinning about that axis, you always find that it is spinning clockwise. But when you take this same spin and try to determine its value of spin about the vertical axis, the result will be completely random; half the time you will find that it is clockwise (that is, you find the state spin-up, or |0>) and half the time you will find that it is counterclockwise (spin-down, or |1>). When the value of spin about the sideways axis is completely certain, the value of spin about the vertical axis is completely uncertain. Similarly, the state |0> has a definite value of spin along the vertical axis. If you measure the spin, you find that it is clockwise (spin-up). But now the value of spin about the sideways axis is completely uncertain; if you measure the spin about the sideways axis, half the time you’ll find it spinning clockwise about this axis and half the time you’ll find it spinning counterclockwise. Now that the value of spin about the vertical axis is certain, the value of spin about the sideways axis is uncertain.