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

摘要

By combining a squeezed propagating microwave field and an unsqueezed vacuumfield on a hybrid (microwave beam-splitter), we generate entanglement betweenthe two output modes. We verify that we have generated entangled states bymaking independent and efficient single-quadrature measurements of the twooutput 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. Thesemeasurements show that the output two-mode state violates the separabilitycriterion and therefore demonstrate entanglement. This shared entanglementbetween propagating microwaves provides an important resource for buildingquantum networks with superconducting microwave systems.