[math-fun] Stupid QM question (EPR, B-E statistics)
Bose-Einstein statistics apply to bosons, correct? If I have a number N of these bosons, *all in the "same" state*, then these are all maximally entangled, correct? If I "measure" one of these bosons (is this even possible -- to measure just one?), this measurement necessarily puts *all* of my bosons into the same state ? I.e., the usual EPR experiment works with 2 entangled qubits; measure one and the same measurement on the other will produce the same result. Now, I'd like to have N entangled qubits, so that measuring any one will guarantee the same measurement on *all* of the other qubits. Does this work in theory? Does this work in practise?
On Fri, Jan 29, 2016 at 12:09 PM, Henry Baker <hbaker1@pipeline.com> wrote:
Bose-Einstein statistics apply to bosons, correct?
If I have a number N of these bosons, *all in the "same" state*, then these are all maximally entangled, correct?
No; in fact they're completely disentangled: you've just said that each particle is in the same state, so we can write the total state as (tensor_{i=1}^{n} |psi_i>) // S_n The superpositions involved only involve the order of the particles, not their spin. Read the wiki article on Fock space.
If I "measure" one of these bosons (is this even possible -- to measure just one?),
Yes, that's possible.
this measurement necessarily puts *all* of my bosons into the same state ?
They're already all in the same state, by assumption.
Now, I'd like to have N entangled qubits, so that measuring any one will guarantee the same measurement on *all* of the other qubits.
It sounds like you want a GHZ state. The measurement still only occurs on one of the qubits, but the measuring device gets entangled with them, so you get |Device 0>(|000> + |111>)/sqrt(2) | XOR the state of the first GHZ qubit into the state of the device | V (|Device 0>|000> + |Device 1>|111>)/sqrt(2) So if YOU are the measurement device and you do subsequent measurements on the second and third GHZ qubits, you'll either see the qubits all being 0 or all being 1. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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