Optimal experimental demonstration of error-tolerant quantum witnesses

Testing quantum theory on macroscopic scales is a longstanding challenge whose solution could have a significant impact on physics. For example, laboratory tests (such as those anticipated in nanomechanical or biological systems) may look to rule out macroscopic realism: the idea that the properties of macroscopic objects exist objectively and can be noninvasively measured. Such investigations are likely to suffer from (i) stringent experimental requirements, (ii) marginal statistical significance, and (iii) logical loopholes. We address all of these problems by refining two tests of macroscopic realism, or “quantum witnesses”, and implementing them in a microscopic test on a photonic qubit and qutrit. The first witness heralds the invasiveness of a blind measurement; its maximum violation has been shown to grow with the dimensionality of the system under study. The second witness heralds the invasiveness of a generic quantum channel and can achieve its maximum violation in any dimension; it therefore allows for the highest quantum signal-to-noise ratio and most significant refutation of the classical point of view.

Figure 1

(a) Generic procedure for testing our two quantum witnesses. We need four processes, including state preparation, state evolution [e.g., $\mathrm{\Phi }\left(\rho \right)=U_1\rho U_1^{†}]$, and projective measurement (PM) of $B$. We also require the optional application of either (i) blind measurement (BM) of $A$ (for testing witness $W$) or (ii) some generic channel $\mathcal{E}\left(\rho \right)$, here chosen as a phase modulation $U_0\rho U_0^{†}$ (for testing witness $V$). (b) Experimental setup. The heralded single photons are created via type-I SPDC in a BBO crystal and are injected into the optical network. Qubit states are prepared via a polarizing beam splitter (PBS) and half-wave plates (HWPs). The phase channel $U_0^{2D}$ can be implemented by a set of wave plates (not shown), while a quartz crystal (QC) is used to realize a blind measurement of $A$. For the qutrit, the polarizing beam splitter, half-wave plate, and beam displacer are used for state preparation. $U_0^{3D}$ is implemented with half-wave plates and quarter-wave plates (QWPs), the blind measurement is again implemented with the quartz crystal (not shown), and $U_1^{3D}$ can be implemented with a cascaded interferometer network. The projective measurement of $B$ is realized via a beam displacer which maps the basis states of the qubit or qutrit to distinct spatial modes.

Figure 2

(a) Experimentally determined values for our two quantum witnesses $W$ and $V$ for the fixed-point preparations 0 and 1 (also 2) and for the superposition preparation $\sigma$ of a photonic qubit (and qutrit). Theoretical predictions are represented by dashed and dotted lines. Error bars indicate the statistical uncertainty which is obtained based on assuming Poissonian statistics. (b) Experimental results showing maximum violations of both quantum witness conditions for two-level and three-level photonic systems. The blue (red) dashed (dashed-dotted) line represents the theoretical predictions of the maximum violations of the first (second) quantum witness condition.

Figure 3

Experimental setup with cascaded interferometers which is able to implement any unitary operator. In this diagram, $N$ is assumed to be an even number.