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 \(E_\mathrm{W}=-0.263^{+0.001}_{-0.036}\) and the negativity \(N=0.0824^{+0.01}_{-0.0004}\) 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.