Comments on Measurement

Measurement

Some issues regarding measurement in quantum circuits are to be noted

here, which you can prove for yourself with some thought:

1. Deferred measurement: when measurements are made in a circuit

and after that further gates are implemented (whether controlled by the

measurement or no), it can always be assumed that the measurement is

made at the very end of the circuit. This is saying that measurement can

always be assumed to have been deferred to the end of the computation

without any eﬀect on the results.

2. Implicit measurement: any quantum wires that are left at the end

of the circuit can be assumed to have been measured: their states will

anyway have collapsed when other wires are measured for the purpose

of readout.

3. Irreversibility: quantum measurement is in general an irreversible pro-

cess, and if included in a circuit, will make it irreversible. However, if

the measurement reveals no information about the state being measured

(refer for instance to the teleportation protocol of Example 7.2) then the

circuit is still reversible!

Many of the results in this chapter are discussed in the paper by Barenco

et al. [3], and in the book by Mermin [48].

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