The recent thread about the delayed choice experiment made me want to understand the experiment as a quantum circuit. I made this:(adsbygoogle = window.adsbygoogle || []).push({});

(contrast with the optical setup diagram from a relevant paper)

The left hand side is the qubit-holding wires and gates to apply, with Alice and Bob each owning one of the top wires and Eve owning the bottom two wires.

The right hand side shows a representation of the final state, with each cell corresponding to an amplitude in the state space. The size and orientation of the circles shows the value of the amplitude for the corresponding basis state (the amplitudes are all +1/sqrt(8) or -1/sqrt(8) in this case).

The "interesting" thing is that:

a) If you trace over Eve's bits in order to measure the entanglement between A and B, you will get a result of "no entanglement".

b) But each individual row, each possible value of Eve's bits, does have entanglement between A and B (but you have to ignore the other rows).

So the whole is unentangled, but it is made up of parts that are entangled. By measuring or conditioning or post-selecting on Eve's bits, you can force yourself into one of the rows and thus, suddenly, de-facto entanglement between A and B!

The main caveat is that A and B need to know which type of entanglement exists between them (same values vs opposite values, same phase vs opposite phase) before they can actually take advantage of it. E.g. that's why quantum teleportation requires sending some classical bits to tell the receiver which case they're in. If they didn't need to be told which type of entanglement they had, you could do FTL signalling and other too-powerful-to-be-allowed things.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Delayed choice as a quantum logic circuit

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**