Undoing a Quantum Measurement

In general, a quantum measurement yields an undetermined answer and alters the system to be consistent with the measurement result. This process maps multiple initial states into a single state and thus cannot be reversed. This has important implications in quantum information processing, where errors can be interpreted as measurements. Therefore, it seems that it is impossible to correct errors in a quantum information processor, but protocols exist that are capable of eliminating them if they affect only part of the system. In this work we present the deterministic reversal of a fully projective measurement on a single particle, enabled by a quantum error-correction protocol in a trapped ion quantum information processor. We further introduce an in-sequence, single-species recooling procedure to counteract the motional heating of the ion string due to the measurement.

Figure 1

(a) Schematic circuit for undoing a quantum measurement. ${\rho }_{\mathrm{enc}}$ is the encoded state of the register, ${\rho }_{\mathrm{meas}}$ is the state after the measurement, ${\rho }_{\mathrm{sys}}$ is the corrected state of the system qubit after the QEC cycle, and ${\rho }_{\mathrm{rec}}$ is the state of the register after the full correction. (b) Circuit representation of the error correction algorithm. $D$ is a unitary operation that commutes with phase flips. $U$ is an arbitrary unitary operation. These operations do not affect the error correction functionality.

Figure 2

(a) Schematic of the measurement process on the $S_{1/2}\leftrightarrow P_{1/2}$ transition. The auxiliary qubits are hidden from the measurement by transferring the population to the $m=-5/2$ substate of the $D_{5/2}$ level. (b) Schematic of the Raman recooling procedure. This scheme utilizes two 1.5 GHz detuned Raman beams that remove one phonon upon transition from the Zeeman substates $m=-1/2$ to $m=+1/2$ and an additional resonant beam that is used to optically pump from $m=+1/2$ to $m=-1/2$ via the $P_{1/2}$ state.

Figure 3

(a) Absolute value of the reconstructed three qubit density matrices before the measurement ${\rho }_{\mathrm{enc}}$. (b) Histogram of the measured photon counts for a measurement time of $200\mu \mathrm{s}$. Absolute value of three qubit density matrices after the measurement ${\rho }_{\mathrm{meas}}$ for outcome (c) $|0⟩$ and (d) $|1⟩$. Density matrices after the measurement reversal ${\rho }_{\mathrm{rec}}$ for outcome (e) $|0⟩$ and (f) $|1⟩$.