Quantum Filtering One Bit at a Time

In this Letter we consider the purification of a quantum state using the information obtained from a continuous measurement record, where the classical measurement record is digitized to a single bit per measurement after the measurements have been made. Analysis indicates that efficient and reliable state purification is achievable for one- and two-qubit systems. We also consider quantum feedback control based on the discrete one-bit measurement sequences.

Figure 1

Average fidelity of one qubit as a function of time with no controls: full record (red dashed line) and OBR (blue solid line). Inset: An example run, showing fidelity for one measurement record.

Figure 2

Average fidelity of one qubit as a function of time with controls applied to rotate the Bloch vector onto the measurement axis: full record (red dashed line) and OBR (blue solid line). Inset: Average fidelity after 50 cycles as a function of the angle to the measurement axis (in $X\mathrm{\text{−}}Z$ plane) for the OBR.

Figure 3

(a) Average fidelity of the two-qubit state as a function of time with single $ZZ$ measurement record and no controls: full record (red dashed line) and OBR (blue solid line), and (b) classical correlations (red crosses) and quantum discord (blue circles) of the two-qubit state as a function of time with single $ZZ$ measurement record and no controls: full record (dotted lines) and OBR (solid lines).