Measuring a Photonic Qubit without Destroying It

Measuring the polarization of a single photon typically results in its destruction. We propose, demonstrate, and completely characterize a quantum nondemolition (QND) scheme for realizing such a measurement nondestructively. This scheme uses only linear optics and photodetection of ancillary modes to induce a strong nonlinearity at the single-photon level, nondeterministically. We vary this QND measurement continuously into the weak regime and use it to perform a nondestructive test of complementarity in quantum mechanics. Our scheme realizes the most advanced general measurement of a qubit to date: it is nondestructive, can be made in any basis, and with arbitrary strength.

Figure 1

A QND measurement of a polarization encoded single photon qubit. (a) A linear optics scheme, as explained in the text. The $\frac{2}{3}\mathrm{BS}$ is used only for weak operation. (b) A schematic of the experimental setup. Pairs of photons were generated through spontaneous parametric down-conversion in a $\beta$-barium-borate crystal cut for beamlike [19, 20] type-II phase matching and coupled [21] into single mode optical fibers (details are given in 10). The output of each fiber was collimated and wave plates in each input beam allow preparation of the required signal and meter states. The tilted HWP corrects a systematic phase shift between the meter modes. A standard polarization analyzer—a half wave plate (HWP), quarter wave plate (QWP), and polarizing beam splitter (PBS)—is used in each output before a SPCM. A coincidence window of 5 ns was used with coincident counts of $\sim 100{\mathrm{s}}^{-1}$, and we do not subtract accidental counts.

Figure 2

Nondestructive weak measurement of a polarization qubit in an equal superposition state, demonstrating the principle of complementarity. (a) When $\theta =0°$, the meter makes no measurement and the signal output state is quite pure, as seen in the real part of the reduced density matrix ${\rho }_s$: the one-qubit linear entropy $S_L=2(1-\mathrm{Tr}[{\rho }_s^2])=0.22$. (b) When $\theta =33°$ the meter makes a strong measurement and the signal output state ${\rho }_s$ is highly mixed: $S_L=0.98$. (Note that all the imaginary components (not shown) are $<0.08$.) (c) Weak measurement and complementarity: Plots of $K$, $V$, and $K^2+V^2$ for a number of different values of $\theta$. The error bars take into account the count statistics and the input wave plate angle setting, respectively.