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I have been reading the book by Michael A Nielsen and Isaac Chuang and came across the principle of deferred measurement. They showed using this principle how the circuit for quantum teleportation can be changed and measurements taken at last. But wouldn't this imply that we don't need to pass classical information that would make the receiver take the necessary action for transportation of the circuit as it has already happened no matter the outcome of measurement of the first two qubits? Wouldn't that imply that information can be transferred faster than light as there is no need for passing of classical information?

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I think faster than light communication is more stubborn than that :-)

The principle of deferred measurement, to quote Nielsen and Chuang, page 186, is

Measurements can always be moved from an intermediate stage of a quantum circuit to the end of the circuit; if the measurement results are used at any stage of the circuit then the classically controlled operations can be replaced by conditional quantum operations.

To convert teleportation circuit to a measurement-free version, you need to replace fixups applied by Bob based on Alice's measurement results by controlled X and Z gates applied to his qubit with Alice's qubits as controls (as shown in a circuit on page 187). I believe an implementation of controlled gates acting on qubits separated by a significant physical distance (which is a premise of teleportation when discussed in the context of faster-than-light communication) is going to involve some kind of information transfer. If the qubits are close enough to allow applying two-qubit gates to them, we could have just done a SWAP between message qubit and Bob's qubit, without going through all the trouble.

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  • $\begingroup$ Aah that makes a lot sense thank you :) $\endgroup$ – Rishabh Kothary Apr 7 at 18:11

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