Circuit analysis of quantum measurement

We develop a circuit theory that enables us to analyze quantum measurements on a two-level system and on a continuous-variable system on an equal footing. As a measurement scheme applicable to both systems, we discuss a swapping state measurement that exchanges quantum states between the system and the measuring apparatus before the apparatus meter is read out. This swapping state measurement has an advantage in gravitational-wave detection over contractive state measurement in that the postmeasurement state of the system can be set to a prescribed one, regardless of the outcome of the measurement.

Figure 1

CNOT circuit.

Figure 2

Double CNOT (DCNOT) circuit.

Figure 3

SWAP circuit.

Figure 4

Circuit representation of general unitary transformation $U$ in Eq. (20) in terms of three basic quantum gates ${\widehat{V}}_{y{p}_x}$, ${\widehat{V}}_{x{p}_y}$, and ${\widehat{\Pi }}_y$ [see Eq. (29) for the mathematical expression].

Figure 5

Circuit representation of a generalized von Neumann’s position measurement.

Figure 6

Circuit representation of generalized contractive state measurement.

Figure 7

Circuit representation of swapping state measurement.