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arXiv:1210.4413 · Physical Review Letters

Path Entanglement of Continuous-Variable Quantum Microwaves

E. P. Menzel, Roberto Di Candia, Frank Deppe, Peter Eder, Ling Zhong, Matthias Ihmig, M. Haeberlein, A. Baust, Eric A. Hoffmann, Daniel Ballester, K. Inomata, Tsuyoshi Yamamoto, Yasunobu Nakamura, E. Solano, Achim Marx, R. Gross

Published Dec 18, 2012• 182 citations
arXivHTMLPDF

Abstract

Path entanglement constitutes an essential resource in quantum information and communication protocols. Here, we demonstrate frequency-degenerate entanglement between continuous-variable quantum microwaves propagating along two spatially separated paths. We combine a squeezed and a vacuum state using a microwave beam splitter. Via correlation measurements, we detect and quantify the path entanglement contained in the beam splitter output state. Our experiments open the avenue to quantum teleportation, quantum communication, or quantum radar with continuous variables at microwave frequencies.

DOI
10.1103/physrevlett.109.250502

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Path entanglement constitutes an essential resource in quantum information and communication protocols. Here, we demonstrate frequency-degenerate entanglement between continuous-variable quantum microwaves propagating along two spatially separated paths. We combine a squeezed and a vacuum state using a microwave beam splitter. Via correlation measurements, we detect and quantify the path entanglement contained in the beam splitter output state. Our experiments open the avenue to quantum teleportation, quantum communication, or quantum radar with continuous variables at microwave frequencies.
In recent years, the great progress of studying the quantum entanglement has been made. In the field of optics, the great success has been achieved in quantum entanglement theory and technology. Then researchers concentrate on the microwave frequency band whose frequency is lower than that of optical frequency band. The signal in the microwave frequency band has a longer wavelength, and it has the diffraction capability that the optical signal does not possess. Furthermore, it can spread further in complex environments. Now it is possible to experimentally produce squeezed state of microwave signals and spatially separated path-entangled microwave signals. It is an important issue to judge whether the microwave signals received through dual paths are in entanglement state. In this paper, we firstly introduce the method of using squeezed state of microwave and microwave beam splitter to prepare path-entangled microwave signals. Then we use entanglement witness method to detect entanglement. Through constructing the entanglement witness operator in path-entangled microwave signals, the entanglement of path-entangled microwave signals can be effectively detected. We decompose the expression of the continuous variables path-entangled microwave signals into a large number of 2 2 entangled superposition states, deduce an entangled witness operator of path-entangled microwave signals based on the principle of partial transpose criterion and entanglement witnessing, and prove that the entangled witness can be used to detect the path-entangled microwave signals. Finally, we propose a physical verification of path-entangled microwave signal entanglement. The verification can be realized as follows:firstly, we reverse the phase of a received quantum-state microwave signal by utilizing continuous variable controlled phase gate in a range of 0-, then we send two microwave signals into the two input ports of the microwave beam splitter, and we operate coincidence counting of microwave photons on the two output ports after entanglement microwave signals have passed through the microwave splitter. By analyzing the results of the whole process, we have the following conclusions:if the coincidence rate of two input signals is higher than that of non-entangled microwave signals under the same power, signals can be counted as entanglement. The proposed method can detect the entangled microwave signals more efficiently than the conventional methods, such as quantum state reconstruction, and thus reduce the detection and computational complexity. The entanglement of the two microwave quantum state signals can be observed directly by using this method. This paper provides a new idea for detecting the path-entangled microwave signals.
Two-mode squeezing is a fascinating example of quantum entanglement manifested in cross-correlations of non-commuting 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. Here, we generate propagating microwave TMS states by a beam splitter distributing single mode squeezing emitted from distinct Josephson parametric amplifiers along two output paths. We experimentally study the fundamental dephasing process of quantum cross-correlations in continuous-variable propagating TMS microwave states and accurately describe it with a theory model. In this way, we gain the insight into finite-time entanglement limits and predict high fidelities for benchmark quantum communication protocols such as remote state preparation and quantum teleportation.
Two-mode squeezing is a fascinating example of quantum entanglement manifested in cross-correlations of non-commuting 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. Here, we generate propagating microwave TMS states by a beam splitter distributing single mode squeezing emitted from distinct Josephson parametric amplifiers along two output paths. We experimentally study the fundamental dephasing process of quantum cross-correlations in continuous-variable propagating TMS microwave states and accurately describe it with a theory model. In this way, we gain the insight into finite-time entanglement limits and predict high fidelities for benchmark quantum communication protocols such as remote state preparation and quantum teleportation.
Pairs of entangled electromagnetic beams propagating on physically separated channels, the continuous variable version of Einstein-Podolsky-Rosen (EPR) states, constitute an essential resource in quantum information processing, communication and measurements. We have performed an interference experiment demonstrating the production and measurement of EPR states of microwave light using non-degenerate Josephson mixers. Driven by a pump tone, a first mixer generates a pair entangled beams out of vacuum quantum noise. A second mixer, driven by a phase shifted copy of the first pump tone, recombines and disentangles the two beams. We show that interference fringes of the intensity of the final output noise, referred to the input of the second mixer, pass under the level of vacuum for a range of phase shifts. The minimal measured noise intensity provides a quantitative measure of entanglement and yields a lower bound of 6 Mebits/s on the rate of entangled bits produced by the first mixer.
The thesis establishes a link between theoretical foundations and practical applications in the emerging field of propagating quantum microwaves. Although the concrete focus of the main results lies in specific quantum communication and sensing protocols, the thesis also gives a self-contained introduction to quantum parameter estimation and Gaussian quantum continuous variables, justifying the theoretical results used. Motivated, firstly, by the compatibility between superconducting circuits (a promising quantum computing platform), and the microwave frequency range; and, secondly, by the transparency window of the atmosphere to these frequencies, the work contains two concrete contributions to the fields of microwave quantum sensing and communication: a novel protocol that uses frequency entanglement to measure the first order dependence in frequency of the reflectivity of an object; and a large investigation on different aspects of entanglement degradation due to loss and atmospheric absorption in the context of continuous-variable entanglement distribution for the task of quantum teleportation in open-air. The dissertation includes, as a last chapter, an article that reviews the state-of-the-art in quantum microwave technology, and proposes different research lines, including quantum communication between Earth-based stations and satellites, quantum radar, direct dark matter detection, and exploration of the quantum properties of the cosmic microwave background. This more speculative, yet rigorous chapter closes with a roadmap for possible future research lines in the field of propagating quantum microwaves, that can serve as an outlook of the thesis.