Generating and verifying entangled itinerant microwave fields with efficient and independent measurements

Abstract

By combining a squeezed propagating microwave field and an unsqueezed vacuum field on a hybrid (microwave beam-splitter), we generate entanglement between the two output modes. We verify that we have generated entangled states by making independent and efficient single-quadrature measurements of the two output modes. We observe the entanglement witness $E_{\mathrm{W}}=-0.263_{-0.036}^{+0.001}$ and the negativity $N=0.0824_{-0.0004}^{+0.01}$ with measurement efficiencies at least $26\pm 0.1\%$ and $41\pm 0.2\%$ for channel~1 and 2 respectively. These measurements show that the output two-mode state violates the separability criterion and therefore demonstrate entanglement. This shared entanglement between propagating microwaves provides an important resource for building quantum networks with superconducting microwave systems.