Measuring coherence of quantum measurements

The superposition of quantum states lies at the heart of physics and has been recently found to serve as a versatile resource for quantum information protocols, defining the notion of quantum coherence. In this contribution, we report on the implementation of its complementary concept, coherence from quantum measurements. By devising an accessible criterion which holds true in any classical statistical theory, we demonstrate that noncommutative quantum measurements violate this constraint, rendering it possible to perform an operational assessment of the measurement-based quantum coherence. In particular, we verify that polarization measurements of a single photonic qubit, an essential carrier of one unit of quantum information, are already incompatible with classical, i.e., incoherent, models of a measurement apparatus. Thus, we realize a method that enables us to quantitatively certify which quantum measurements follow fundamentally different statistical laws than expected from classical theories and, at the same time, quantify their usefulness within the modern framework of resources for quantum information technology.

Figure 1

Variance difference, representing the deviation from our classical constraint, $\mathrm{\Delta }V=0$ [Eq. (7)], between the two measurement configurations. (a) The surface depicts the expected theoretical behavior when varying $p$ and $\theta$; the points show the experimental data. (b) Cut of the plot (a) for $p=0.165$. (c) Cut of the plot (a) graph for $p=0.552$. Error bars, typically smaller than the bullet points, are derived from Poissonian statistics of the count rates; the same applies to all following plots.

Figure 2

Variance difference between the two measurement configurations [Eq. (7)]. (a) The surface is the expected theoretical behavior as a function of $\gamma$ and $\theta$; the points depict our data. (b) Cut of the plot (a) along $\theta ={36}^{\circ }$. (c) Cut of the plot (a) along $\theta ={84}^{\circ }$.

Figure 3

Maximal violation of $\mathrm{\Delta }V=0$ for $\theta \approx \pi /2$ as a function of $p$ and $\gamma$ in plots (a) and (b), respectively. Plot (a) is expected to be symmetric with respect to $p=1/2$ in the ideal case.