Quantum Metrological Power of Continuous-Variable Quantum Networks

We investigate the quantum metrological power of typical continuous-variable (CV) quantum networks. Particularly, we show that most CV quantum networks provide an entanglement to quantum states in distant nodes that enables one to achieve the Heisenberg scaling in the number of modes for distributed quantum displacement sensing, which cannot be attained using an unentangled probe state. Notably, our scheme only requires local operations and measurements after generating an entangled probe using the quantum network. In addition, we find a tolerable photon-loss rate that maintains the quantum enhancement. Finally, we numerically demonstrate that even when CV quantum networks are composed of local beam splitters, the quantum enhancement can be attained when the depth is sufficiently large.

Figure 1

Schematic diagram of distributed quantum displacement sensing (see the main text).

Figure 2

QFI averaged over 20 000 different Haar-random BSNs with a squeezed state input (inset: log-log scale). The error bars represent 3 times of the standard deviation of QFIs.

Figure 3

(a) CV quantum network composed of depth $D$ local beam splitters with a squeezed vacuum input. (b) Average QFIs over 1000 different local Haar-random beam splitters with ($H_{\mathrm{MLO}}$) and without ($H_{\mathrm{LO}}$) optimizing the input mode. The error bars represent the standard deviation of QFIs over samples. Black dashed (solid) line represents the asymptotic average (maximum) QFI divided by $M^2$, obtained by a random (balanced) BSN, which is equal to $2\pi \overline{n}$ ($8\overline{n}$).