Experimental quantum teleportation of propagating microwaves

  1. K. G. Fedorov,
  2. M. Renger,
  3. S. Pogorzalek,
  4. R. Di Candia,
  5. Q. Chen,
  6. Y. Nojiri,
  7. K. Inomata,
  8. Y. Nakamura,
  9. M. Partanen,
  10. A. Marx,
  11. R. Gross,
  12. and F. Deppe
The modern field of quantum communication thrives on promise to deliver efficient and unconditionally secure ways to exchange information by exploiting quantum laws of physics. Here,
quantum teleportation stands out as an exemplary protocol allowing for the disembodied and safe transfer of unknown quantum states using quantum entanglement and classical communication as resources. The experimental feasibility of quantum teleportation with propagating waves, relevant to communication scenarios, has been demonstrated in various physical settings. However, an analogous implementation of quantum teleportation in the microwave domain was missing so far. At the same time, recent breakthroughs in quantum computation with superconducting circuits have triggered a demand for quantum communication between spatially separated superconducting processors operated at microwave frequencies. Here, we demonstrate a realization of deterministic quantum teleportation of coherent microwave states by exploiting two-mode squeezing and analog feedforward over macroscopic distances d=42cm. We achieve teleportation fidelities F=0.689±0.004 exceeding the no-cloning Fnc=2/3 threshold for coherent states with an average photon number of up to nd=1.1. Our results provide a key ingredient for the teleportation-based quantum gate for modular quantum computing with superconducting circuits and establish a solid foundation for future microwave quantum local area networks.

Beyond the standard quantum limit of parametric amplification

  1. M. Renger,
  2. S. Pogorzalek,
  3. Q. Chen,
  4. Y. Nojiri,
  5. K. Inomata,
  6. Y. Nakamura,
  7. M. Partanen,
  8. A. Marx,
  9. R. Gross,
  10. F. Deppe,
  11. and K. G. Fedorov
The low-noise amplification of weak microwave signals is crucial for countless protocols in quantum information processing. Quantum mechanics sets an ultimate lower limit of half a
photon to the added input noise for phase-preserving amplification of narrowband signals, also known as the standard quantum limit (SQL). This limit, which is equivalent to a maximum quantum efficiency of 0.5, can be overcome by employing nondegenerate parametric amplification of broadband signals. We show that, in principle, a maximum quantum efficiency of 1 can be reached. Experimentally, we find a quantum efficiency of 0.69±0.02, well beyond the SQL, by employing a flux-driven Josephson parametric amplifier and broadband thermal signals. We expect that our results allow for fundamental improvements in the detection of ultraweak microwave signals.

Secure quantum remote state preparation of squeezed microwave states

  1. S. Pogorzalek,
  2. K. G. Fedorov,
  3. M. Xu,
  4. A. Parra-Rodriguez,
  5. M. Sanz,
  6. M. Fischer,
  7. E. Xie,
  8. K. Inomata,
  9. Y. Nakamura,
  10. E. Solano,
  11. A. Marx,
  12. F. Deppe,
  13. and R. Gross
Quantum communication protocols based on nonclassical correlations can be more efficient than known classical methods and offer intrinsic security over direct state transfer. In particular,
remote state preparation aims at the creation of a desired and known quantum state at a remote location using classical communication and quantum entanglement. We present an experimental realization of deterministic continuous-variable remote state preparation in the microwave regime over a distance of 35 cm. By employing propagating two-mode squeezed microwave states and feedforward, we achieve the remote preparation of squeezed states with up to 1.6 dB of squeezing below the vacuum level. We quantify security in our implementation using the concept of the one-time pad. Our results represent a significant step towards microwave quantum networks between superconducting circuits.

Quantum probe of an on-chip broadband interferometer for quantum microwave photonics

  1. P. Eder,
  2. T. Ramos,
  3. J. Goetz,
  4. M. Fischer,
  5. S. Pogorzalek,
  6. J. Puertas Martínez,
  7. E. P. Menzel,
  8. F. Loacker,
  9. E. Xie,
  10. J.J. Garcia-Ripoll,
  11. K. G. Fedorov,
  12. A. Marx,
  13. F. Deppe,
  14. and R. Gross
Quantum microwave photonics aims at generating, routing, and manipulating propagating quantum microwave fields in the spirit of optical photonics. To this end, the strong nonlinearities
of superconducting quantum circuits can be used to either improve or move beyond the implementation of concepts from the optical domain. In this context, the design of a well-controlled broadband environment for the superconducting quantum circuits is a central task. In this work, we place a superconducting transmon qubit in one arm of an on-chip Mach-Zehnder interferometer composed of two superconducting microwave beam splitters. By measuring its relaxation and dephasing rates we use the qubit as a sensitive spectrometer at the quantum level to probe the broadband electromagnetic environment. At high frequencies, this environment can be well described by an ensemble of harmonic oscillators coupled to the transmon qubit. At low frequencies, we find experimental evidence for colored quasi-static Gaussian noise with a high spectral weight, as it is typical for ensembles of two-level fluctuators. Our work paves the way towards possible applications of propagating microwave photons, such as emulating quantum impurity models or a novel architecture for quantum information processing.

Finite-time quantum correlations of propagating squeezed microwaves

  1. Kirill G. Fedorov,
  2. S. Pogorzalek,
  3. U. Las Heras,
  4. M. Sanz,
  5. P. Yard,
  6. P. Eder,
  7. M. Fischer,
  8. J. Goetz,
  9. E. Xie,
  10. K. Inomata,
  11. Y. Nakamura,
  12. R. Di Candia,
  13. E. Solano,
  14. A. Marx,
  15. F. Deppe,
  16. and R. Gross
Two-mode squeezing is a fascinating example of quantum entanglement manifested in cross-correlations of incompatible observables between two subsystems. At the same time, these subsystems
themselves may contain no quantum signatures in their self-correlations. These properties make two-mode squeezed (TMS) states an ideal resource for applications in quantum communication, quantum computation, and quantum illumination. Propagating microwave TMS states can be produced by a beam splitter distributing single mode squeezing emitted from Josephson parametric amplifiers (JPA) into two output paths. In this work, we experimentally quantify the dephasing process of quantum correlations in propagating TMS microwave states and accurately describe it with a theory model. In this way, we gain an insight into quantum entanglement limits and predict high fidelities for benchmark quantum communication protocols such as remote state preparation and quantum teleportation.

Second-order decoherence mechanisms of a transmon qubit probed with thermal microwave states

  1. J. Goetz,
  2. F. Deppe,
  3. P. Eder,
  4. M. Fischer,
  5. M. Müting,
  6. J. P. Martínez,
  7. S. Pogorzalek,
  8. F. Wulschner,
  9. E. Xie,
  10. K. G. Fedorov,
  11. A. Marx,
  12. and R. Gross
Thermal microwave states are omnipresent noise sources in superconducting quantum circuits covering all relevant frequency regimes. We use them as a probe to identify three second-order
decoherence mechanisms of a superconducting transmon. First, we quantify the efficiency of a resonator filter in the dispersive Jaynes-Cummings regime and find evidence for parasitic loss channels. Second, we probe second-order noise in the low-frequency regime and demonstrate the expected T3 temperature dependence of the qubit dephasing rate. Finally, we show that qubit parameter fluctuations due to two-level states are enhanced under the influence of thermal microwave states. In particular, we experimentally confirm the T2-dependence of the fluctuation spectrum expected for noninteracting two-level states.

Photon Statistics of Propagating Thermal Microwaves

  1. J. Goetz,
  2. S. Pogorzalek,
  3. F. Deppe,
  4. K. G. Fedorov,
  5. P. Eder,
  6. M. Fischer,
  7. F. Wulschner,
  8. E. Xie,
  9. A. Marx,
  10. and R. Gross
In experiments with superconducting quantum circuits, characterizing the photon statistics of propagating microwave fields is a fundamental task. We quantify the n2+n photon number
variance of thermal microwave photons emitted from a black-body radiator for mean photon numbers 0.05≲n≲1.5. We probe the fields using either correlation measurements or a transmon qubit coupled to a microwave resonator. Our experiments provide a precise quantitative characterization of weak microwave states and information on the noise emitted by a Josephson parametric amplifier.

Displacement of propagating squeezed microwave states

  1. Kirill G. Fedorov,
  2. L. Zhong,
  3. S. Pogorzalek,
  4. P. Eder,
  5. M. Fischer,
  6. J. Goetz,
  7. E. Xie,
  8. F. Wulschner,
  9. K. Inomata,
  10. T. Yamamoto,
  11. Y. Nakamura,
  12. R. Di Candia,
  13. U. Las Heras,
  14. M. Sanz,
  15. E. Solano,
  16. E. P. Menzel,
  17. F. Deppe,
  18. A. Marx,
  19. and R. Gross
Displacement of propagating quantum states of light is a fundamental operation for quantum communication. It enables fundamental studies on macroscopic quantum coherence and plays an
important role in quantum teleportation protocols with continuous variables. In our experiments we have successfully implemented this operation for propagating squeezed microwave states. We demonstrate that, even for strong displacement amplitudes, there is no degradation of the squeezing level in the reconstructed quantum states. Furthermore, we confirm that path entanglement generated by using displaced squeezed states stays constant over a wide range of the displacement power.