An EPR circuit diagram

It has occurred to me that the cartoon I drew two days ago will appear to most people as absurd: Alice measures one half of an entangled pair and instantly splits into two versions of herself!  Bob measures the other half and also splits, but each Alice is paired with one of the Bobs in such a way that, should they meet later to discuss their results, everything remains consistent.

Yet if you replace Alice and Bob with two qubits - to get a quantum circuit like the one below - no quantum computing expert would find this outcome absurd.

from left to right and leaving out normalizers for brevity: the R's reset the state to |0000>; X flips a bit giving |0100>; H puts a bit in a superposition giving |01>(|0>+|1>)|0>, or |0100> + |0110>; the 1st 2-qubit CNOT gate entangles the middle qubits to give |0100> + |0010>; and the last two CNOTs entangle the observers to give |1100> + |0011>
The Einstein Podolsky Rosen experiment in circuit form with non-classical Alice and Bob

Alice is qubit q0 and Bob is q3.  Qubits q1 and q2 are entangled into the Bell state $(\lvert 01 \rangle + \lvert 10 \rangle)/\sqrt 2$ and then q1 is shared with Alice, and q2 with Bob.  In the standard (collapse-based, non-multiversal) description Alice and Bob measure q1 and q2, collapse the q1q2 wavefunction, and find that one gets 0 while the other gets 1.  But in the multiversal picture, Alice and Bob do not have - by virtue of being human, large, or by having a soul - some innate ability to collapse wavefunctions.  Instead of causing the wavefunction to change in a discontinuous manner, measurement is just another unitary transformation applied to the system as a whole.  In fact it performs the same role as the last two CNOTs in the diagram above.

In the circuit shown, the final state is $(\lvert 0011 \rangle + \lvert 1100 \rangle) /\sqrt 2$.  Remember, the top qubit is Alice (or more precisely the value she measures) and the bottom qubit is Bob.  So this says we end up in a superposition of two classical states: the first in which Alice has measured 0 and Bob has measured 1 and the second in which Alice has measured 1 and Bob 0.

The most convincing argument that this is not what happens - when humans are involved - relates to the size of humans.  (At least, to my mind.  I feel justified in writing off any argument that claims humans in particular have a special relationship to Physics that other machines of a similar scale don't.)  It goes a bit like this: Alice and Bob are large objects and cannot sustain being in a superposition as a result.  However, what is really being claimed here is that by virtue of being large we humans are constantly interacting with our surroundings.  But there is no need invoke "collapse" to explain this given that physics already supplies us with the much better understood phenomenon of "entanglement".

For example, suppose Alice and Bob are 10 meters apart when they receive their qubits, and suppose that only Alice measures her qubit.  Then, approximately 30 nanoseconds after the measurement, information about the measurement from Alice will have reached Bob.  And as a result of the scale of information arriving, Bob could not - in principle at least - avoid being able to infer what result Alice got.  Bob will have become entangled with post-measurement Alice and by extension with the original Bell State qubits.  The whole system is then in a superposition of two terms where each  represents a classical state (of two qubits and two humans).  But, subjectively, each human can remain perfectly happy modelling the macroscopic world as purely classical.


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