Start with the state ( |00> + |11> ) / √2. Give the first qubit to Alice, the second to Bob, and send them far apart. Consider these hypothetical random variables:
A: what Alice would get by measuring her qubit
B: what Bob would get by measuring his qubit
A’: what Alice would get by rotating her qubit by 30 degrees and then measuring
B’: what Bob would get by rotating his qubit by −30 degrees and then measuring
Each of these variables is a fair coinflip (0 or 1 with probability 1⁄2 each), but they are not independent. Grab a pen and check:
If A and B are measured, they are always equal
If A and B’ are measured, they are equal with probability 3⁄4
If A’ and B are measured, they are equal with probability 3⁄4
If A’ and B’ are measured, they are equal with probability 1⁄4
That’s spooky. From (1)-(3) it follows that A’ and B’ are equal with probability at least 1⁄2, which contradicts (4). But reality still satisfies all four, and you’ll never catch it on a contradiction, because you can’t measure a qubit twice.
(4/?)
EPR paradox.
Start with the state ( |00> + |11> ) / √2. Give the first qubit to Alice, the second to Bob, and send them far apart. Consider these hypothetical random variables:
A: what Alice would get by measuring her qubit
B: what Bob would get by measuring his qubit
A’: what Alice would get by rotating her qubit by 30 degrees and then measuring
B’: what Bob would get by rotating his qubit by −30 degrees and then measuring
Each of these variables is a fair coinflip (0 or 1 with probability 1⁄2 each), but they are not independent. Grab a pen and check:
If A and B are measured, they are always equal
If A and B’ are measured, they are equal with probability 3⁄4
If A’ and B are measured, they are equal with probability 3⁄4
If A’ and B’ are measured, they are equal with probability 1⁄4
That’s spooky. From (1)-(3) it follows that A’ and B’ are equal with probability at least 1⁄2, which contradicts (4). But reality still satisfies all four, and you’ll never catch it on a contradiction, because you can’t measure a qubit twice.