Quantum-enhanced sensing from hyperentanglement

Hyperentanglement—simultaneous entanglement between multiple degrees of freedom of two or more systems—has been used to enhance quantum information tasks such as quantum communication and photonic quantum computing. Here we show that hyperentanglement can lead to increased quantum advantage in metrology, with contributions from the entanglement in each degree of freedom, allowing for Heisenberg scaling in the precision of parameter estimation. Our experiment employs photon pairs entangled in polarization and spatial degrees of freedom to estimate a small tilt angle of a mirror. Precision limits beyond shot noise are saturated through a simple binary measurement of the polarization state. The dynamics considered here have broad applicability, implying that similar strategies based on hyperentanglement can offer improvement in a wide variety of physical scenarios and metrological tasks.

Figure 1

(a) Experimental setup (see text). (b) One quadrant of the equatorial plane of the Bloch sphere. Tilt of mirror M2 causes the Bloch vector of the initial polarization state $|{\varphi }^{+}\rangle$ to shrink and rotate.

Figure 2

Experimental probability $p^{\left(\ell \right)}\left(\theta \right)$ and corresponding Fisher Information $F^{\left(\ell \right)}\left(\theta \right)$ (blue curves) as a function of $\theta$ for different values of the initial displacement $d$. Black squares in (a) and (c) correspond to independent photons ($\ell =1$), while the red circles in (b) and (d) correspond to hyperentangled photon pairs ($\ell =2$). The red and black curves are fits to Eq. (8). From the fit parameters we plotted the theoretical curves (in blue) for the Fisher information, given by Eq. (2).

Figure 3

Experimentally determined Fisher information $F^{\left(2\right)}\left(\theta \right)$ as a function of $\theta$ for the input state $|{\mathrm{\Phi }}^{+}\rangle$ for different values of the initial spatial correlation, and displacement $d=0$. The blue solid curve corresponds to larger correlation $C=0.84\pm 0.14$, while the orange dashed curve corresponds to $C=0.18\pm 0.10$ (see text).

Figure 4

Experimental probability $p^{\left(2\right)}\left({\varphi }^{+}\right)$ (red circles) and corresponding Fisher Information $F_2$ (blue curve) as a function of $\theta$ for $d=6\mathrm{mm}$. The red curve is a fit using Eq. (8) for $\ell =2$, which yields the detection probability for the two-photon polarization state. From the fit parameters the Fisher information is plotted, using Eq. (2). Precision beyond shot noise, given by the horizontal dashed line, is clearly displayed.