Distributed quantum sensing in a

continuous-variable entangled network

Xueshi Guo · Casper R. Breum · Shuro Izumi · Mikkel V. Larsen
Tobias Gehring · Jonas S. Neergaard-Nielsen · Ulrik L. Andersen
bigQ - Department of Physics, Technical University of Denmark

Johannes Borregaard · Matthias Christandl
QMATH - Department of Mathematical Science, University of Copenhagen

Nature Physics XX, XXX (2020)

Task:

Simultaneously estimate multiple parameters - perhaps of spatially separated systems

Does entanglement help?

Yes!

- at least when estimating a global property.

First experimental demonstration

\phi_\mathrm{avg} = \frac{1}{M} \sum_{j=1}^{M}\phi_j

Example:

Average of multiple optical phase shifts

Small phase shifts:

Estimate with homodyne detection of phase quadrature

\langle \hat{P}_\mathrm{avg}\rangle \approx \sqrt{2\eta}\alpha \phi_\mathrm{avg}

\sigma_\mathrm{separable} = \frac{1}{2\sqrt{M}N\sqrt{1+\frac{1}{N}}}

\sigma_\mathrm{entangled} = \frac{1}{2MN\sqrt{1+\frac{1}{MN}}}

\sigma_\mathrm{SQL} = \frac{1}{2\sqrt{MN}}

Heisenberg scaling in probe energy and no. of sites/samples

Realistic (lossy) situation:

Heisenberg scaling disappears but sensitivity gain remains

Experiment

\sigma \equiv \frac{1}{SNR} = \frac{\sqrt{\langle\Delta \hat P^2_\mathrm{avg} \rangle}}{|\partial \langle \hat P_\mathrm{avg}\rangle /\partial\phi_\mathrm{avg}|}

Measured sensitivities

Casper R. Breum

Xueshi Guo

Casper R. Breum

Xueshi Guo

Mikkel V. Larsen

Mikkel V. Larsen

Johannes Borregaard