Today we submitted a paper on quantum filtering using a digitized weak measurement record:
“Quantum filtering one bit at a time”
Jason F. Ralph and Neil P. Oxtoby
(read the abstract and download from arXiv:1108.0823)
The classical analogue signal originating from diffusive weak measurement of a qubit (or two) is digitized into a single bit based on its sign (+/-). We show that such a one-bit record (OBR) can be used to purify a single- or double-qubit, both with and without feedback control. Quantum discord and classical correlations between a pair of qubits are also very well reproduced by the OBR.
The bottom line:
we have made a significant reduction in the data required to accurately reconstruct a quantum state with only minor reduction in the filter performance.