Experimental test of robust quantum detection and restoration of a qubit

Macroscopic devices that probe and control elementary quantum systems are subjected to environment-induced decoherence and typically consist of a large number of particles that cannot be precisely controlled and individually accessed. These two factors limit the control of quantum systems by an open macroscopic device. Here, we investigate a faithful and robust implementation of specific elementary quantum operations under such conditions. We propose a procedure for quantum restoration of a single qubit that is resilient to particle loss and decoherence of the macroscopic device and compare it with a similarly robust procedure for indirect quantum detection of the qubit state by measurement on the macroscopic device. Complementary to detection, the restoration recovers the original state of the system qubit by quantum erasing which decouples the system from the device. Perfect restoration is possible even if the particles of the device are only classically correlated. We experimentally witness the robustness of quantum detection and restoration for a two-qubit device represented by the quantum state of photons.

Figure 1

Conceptual scheme of system-device-environment coupling. For details, see the text.

Figure 2

Experimental setup. PPBS, partially polarizing beam splitter with transmittance $T_V=1/3$ and $T_H=1$ for vertical and horizontal polarizations, respectively; PBS, polarizing beam splitter; HWP, half-wave plate; BD, kalcite beam displacer; QWP, quarter-wave plate; APD, single-photon detector.

Figure 3

Dependence of knowledge $K$ on the dephasing strength $p$. The symbols represent experimental data. For a robust detector, we plot $K_1$ (circles) and $K_2$ (diamonds) obtained by accessing only one of the device qubits. For a robust eraser, we plot $K_{D_1{D}_2}$ for decoherence of both qubits (squares) as well as for decoherence of only the first qubit $D_1$ (triangles) and only the second qubit $D_2$ (crosses). The solid and dashed lines indicate the theoretical dependence of $K$ on $p$ for a robust eraser when decoherence affects either both device qubits or only a single qubit, respectively.

Figure 4

Channel fidelity $F_{\chi }$ quantifying performance of system qubit recovery by quantum erasing. For robust quantum erasing device, we plot $F_{\chi }$ obtained by detecting a single device qubit $D_1$ (triangles) or $D_2$ (crosses). For a robust quantum detector both qubits $D_1$ and $D_2$ have to be measured, and the results are shown for decoherence of both qubits (solid diamonds), as well as for decoherence of only qubit $D_1$ (circles) or qubit $D_2$ (open diamonds). The solid and dashed lines represent the corresponding theoretical predictions.