Andrew Clough wrote:
> As I've always understood it, the spin of the entangled particle can't be
> forced into either of the possible states. So though you may examine it,
> and affect the other particle X distance away, you still can't use it to
> transmit information.
Can Alice and Bob, space-like separated, use a shared entangled state
in order to communicate? No, because Bob describes the system by the
same density matrix, independently of Alice's measurements or actions.
No signaling, between Alice and Bob.
What about if Alice chooses to measure the system in many different bases?
Alice projects Bob's (entangled) system in many different states!
Different quantum states are distinguishable, in general. But different
quantum states generated from a single entangled state are not
distinguishable (i.e. by Bob).
Thus, no signaling, again, between Alice and Bob.
If Alice chooses to measure the system in many different bases,
Alice projects Bob's (entangled) system in many different states.
Now if If Bob could copy (clone) his system many times, those
different quantum states (prepared by Alice) could be distinguished.
But the so called "cloning theorem" (1982, Zurek & Wooters) states that
a quantum state cannot be "cloned" perfectly, due to linearity of QM.
So, no signaling, again, between Alice and Bob.
Just one more chance is left. Can Alice and Bob use several shared
entangled states in order to communicate by means of some _string_?
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