simple particle entanglement example

We can use our BKO scheme to encode a simplified version of particle entanglement. In this example, 2 particles, with spin either up or down. The idea is we don't know what state the particles are in until we measure. Makes use of weighted-pick-elt which has some similarities to wave-function collapse.

Here is some BKO:

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|context> => |context: simple entanglement example>

entanglement-1 |particles> => |particle 1: spin up> + |particle 2: spin down>
entanglement-2 |particles> => |particle 1: spin down> + |particle 2: spin up>
the-list-of-possible-entanglements |particles> => |op: entanglement-1> + |op: entanglement-2>
measure |particles> #=> apply(weighted-pick-elt the-list-of-possible-entanglements|_self>,|_self>)
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Now, let's measure our particles:

sa: measure |particles>
|particle 1: spin down> + |particle 2: spin up>

It's random, so let's try again:

sa: measure |particles>
|particle 1: spin down> + |particle 2: spin up>

And again:

sa: measure |particles>
|particle 1: spin up> + |particle 2: spin down>

I guess that is simple enough. And if we want to encode the idea that the particles take a fix state on measurement, then we should use memoizing rules instead of stored rules:

wave-fn-collapse-measure |particles> !=> apply(weighted-pick-elt the-list-of-possible-entanglements|_self>,|_self>)

Now, see what we have:

sa: dump
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|context> => |context: simple entanglement example>

entanglement-1 |particles> => |particle 1: spin up> + |particle 2: spin down>
entanglement-2 |particles> => |particle 1: spin down> + |particle 2: spin up>
the-list-of-possible-entanglements |particles> => |op: entanglement-1> + |op: entanglement-2>
measure |particles> #=> apply(weighted-pick-elt the-list-of-possible-entanglements|_self>,|_self>)
wave-fn-collapse-measure |particles> !=> apply(weighted-pick-elt the-list-of-possible-entanglements|_self>,|_self>)
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Now measure our particles and then see what we know:

sa: wave-fn-collapse-measure |particles>
|particle 1: spin up> + |particle 2: spin down>

sa: dump
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|context> => |context: simple entanglement example>

entanglement-1 |particles> => |particle 1: spin up> + |particle 2: spin down>
entanglement-2 |particles> => |particle 1: spin down> + |particle 2: spin up>
the-list-of-possible-entanglements |particles> => |op: entanglement-1> + |op: entanglement-2>
measure |particles> #=> apply(weighted-pick-elt the-list-of-possible-entanglements|_self>,|_self>)
wave-fn-collapse-measure |particles> => |particle 1: spin up> + |particle 2: spin down>
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Anyway, hope that is clear.