Fig. 1. Schematic illustration of quantum positioning based on CV entangled network. (a) Principle of quantum positioning. (b) Structural diagram of PAR network.

Fig. 2. Experimental setup of quantum-enhanced PAR with a CV entangled network. OPA, optical parametric amplifier; HWP, half-wave plate; PBS, polarization beam splitter; BSN, beam splitter network; EOM, electro-optical modulator; HOM, homodyne detection. BPF, bandpass filter.

Fig. 3. Estimation of average field amplitude and normalized noise powers versus applied PAR phases. (a) Estimated average field amplitude. Data points: average displacement from homodyne detection; orange curves: sinusoidal fit; orange shaded area: estimation uncertainties for the entangled (dark color) and classical separable (light color) sensor networks. The blue curve shows the time-domain measurement result of standard quantum limit; the purple, light purple, green, and light green curves represent the measurement results with the entangled sensor network at several PAR phases: π/9, 5π/9, 11π/9, and 13π/9, respectively. (b) Measured noise powers of three phase differences. Black and orange curves show the noise powers based on classical and entangled schemes, respectively. The circular and square data points represent noise powers of three different phase differences with classical and entangled schemes, respectively. All measurement results are normalized to the standard quantum limit.

Fig. 4. Schematic illustration of quantum ranging based on CV entangled network.

Fig. 5. Comparison of the estimated amplitude for the first and second derivatives of the PAR phase under two cases. Data points: means of the measured homodyne signals; curves: sinusoidal fit; shaded area: estimation uncertainties for entangled (dark color) and classical separable (light color) sensor networks. All signals are normalized using the same factor for standard quantum limit normalization.

Fig. 6. Principle of quantum positioning based on quantum-enhanced sensor network.

Fig. 7. Principle of quantum ranging based on quantum-enhanced sensor network.