Using a superconducting circuit, the Josephson mixer, we demonstrate the first experimental realization of spatially separated two-mode squeezed states of microwave light. Driven by a pump tone, a first Josephson mixer generates, out of quantum vacuum, a pair of entangled fields at different frequencies on separate transmission lines. A second mixer, driven by a π-phase shifted copy of the first pump tone, recombines and disentangles the two fields. The resulting output noise level is measured to be lower than for the vacuum state at the input of the second mixer, an unambiguous proof of entanglement. Moreover, the output noise level provides a direct, quantitative measure of entanglement, leading here to the demonstration of 6 Mebit · s(-1) (mega entangled bits per second) generated by the first mixer.

In quantum mechanics, measurements cause wavefunction collapse that yields precise outcomes, whereas for non-commuting observables such as position and momentum Heisenbergs uncertainty principle limits the intrinsic precision of a state.Although theoretical work 1 has demonstrated that it should be possible to perform simultaneous non-commuting measurements and has revealed the limits on measurement outcomes, only recently 2,3 has the dynamics of the quantum state been discussed. To realize this unexplored regime, we simultaneously apply two continuous quantum non-demolition probes of non-commuting observables to a superconducting qubit. We implement multiple readout channels by coupling the qubit to multiple modes of a cavity. To control the measurement observables, we implement a single quadrature measurement by driving the qubit and applying cavity sidebands with a relative phase that sets the observable. Here, we use this approach to show that the uncertainty principle governs the dynamics of the wavefunction by enforcing a lower bound on the measurement-induced disturbance. Consequently, as we transition from measuring identical to measuring non-commuting observables, the dynamics make a smooth transition from standard wavefunction collapse to localized persistent diffusion and then to isotropic persistent diffusion. Although the evolution of the state differs markedly from that of a conventional measurement, information about both non-commuting observables is extracted by keeping track of the time ordering of the measurement record, enabling quantum state tomography without alternating measurements. Our work creates novel capabilities for quantum control, including rapid state purification 4 , adaptive measurement 5,6 , measurement-based state steering and continuous quantum error correction 7 . As physical systems often interact continuously with their environment via non-commuting degrees of freedom, our work offers a way 8,9 to * shayhh@berkeley.edushayhh@berkeley.edu study how notions of contemporary quantum foundations 10-14 arise in such settings.In this work, we implement two high quantum efficiency readouts of the angular momenta about two different axes of an artificial spin-1/2 system and observe in real-time the resulting dynamics. Importantly, our measurements are designed to be individually quantum non-demolition, which ensures that the back-action arises only from the competition between incompatible observables.Our experiment utilizes a single superconducting transmon qubit coupled dispersively to a multimode waveguide cavity 15 . This results in a qubit-state dependent shift of the cavity mode frequency. By applying a microwave tone to a single cavity mode, one can infer the qubit state from the phase of the reflected signal 16 ; this readout scheme has been used extensively with superconducting qubits for quantum information processing, and also to perform weak measurements 17 and track quantum trajectories of a single qubit 18 . In our configuration, each cavity mode constitutes a measure...

We present the first experimental realization of a widely frequency tunable, nondegenerate three-wave mixing device for quantum signals at gigahertz frequency. It is based on a new superconducting building block consisting of a ring of four Josephson junctions shunted by a cross of four linear inductances. The phase configuration of the ring remains unique over a wide range of magnetic fluxes threading the loop. It is thus possible to vary the inductance of the ring with flux while retaining a strong, dissipation-free, and noiseless nonlinearity. The device has been operated in amplifier mode, and its noise performance has been evaluated by using the noise spectrum emitted by a voltage-biased tunnel junction at finite frequency as a test signal. The unprecedented accuracy with which the crossover between zero-point fluctuations and shot noise has been measured provides an upper bound for the noise and dissipation intrinsic to the device.