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arXiv:2110.10235 · Physical Review Applied

Entanglement Thresholds of Doubly Parametric Quantum Transducers

Curtis L. Rau, Akira Kyle, Alex Kwiatkowski, Ezad Shojaee, John D. Teufel, Konrad W. Lehnert, Tasshi Dennis

Published Apr 29, 2022• 7 citations
arXivHTMLPDF

Abstract

Doubly parametric quantum transducers, such as electro-optomechanical devices, show promise for providing the critical link between quantum information encoded in highly disparate frequencies such as in the optical and microwave domains. This technology would enable long-distance networking of superconducting quantum computers. Rapid experimental progress has resulted in impressive reductions in decoherence from mechanisms such as thermal noise, loss, and limited cooperativities. However, the fundamental requirements on transducer parameters necessary to achieve quantum operation have yet to be characterized. In this work we find simple, protocol-independent expressions for the necessary and sufficient conditions under which doubly parametric transducers in the resolved-sideband, steady-state limit are capable of entangling optical and microwave modes. Our analysis treats the transducer as a two-mode bosonic Gaussian channel capable of both beamsplitter-type and two-mode squeezing-type interactions between optical and microwave modes. For the beamsplitter-type interaction, we find parameter thresholds that distinguish regions of the channel's separability, capacity for bound entanglement, and capacity for distillable entanglement. By contrast, the two-mode squeezing-type interaction always produces distillable entanglement with no restrictions on temperature, cooperativities, or losses. Counterintuitively, for both interactions, we find that achieving quantum operation does not require either a quantum cooperativity exceeding one, or ground-state cooling of the mediating mode. Finally, we discuss where two state-of-the-art implementations are relative to these thresholds and show that current devices operating in either mode of operation are in principle capable of entangling optical and microwave modes.

DOI
10.1103/physrevapplied.17.044057

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Doubly parametric quantum transducers, such as electro-optomechanical devices, show promise for providing the critical link between quantum information encoded in highly disparate frequencies such as in the optical and microwave domains. This technology would enable long-distance networking of superconducting quantum computers. Rapid experimental progress has resulted in impressive reductions in decoherence from mechanisms such as thermal noise, loss, and limited cooperativities. However, the fundamental requirements on transducer parameters necessary to achieve quantum operation have yet to be characterized. In this work we find simple, protocol-independent expressions for the necessary and sufficient conditions under which doubly parametric transducers in the resolved-sideband, steady-state limit are capable of entangling optical and microwave modes. Our analysis treats the transducer as a two-mode bosonic Gaussian channel capable of both beamsplitter-type and two-mode squeezing-type interactions between optical and microwave modes. For the beamsplitter-type interaction, we find parameter thresholds that distinguish regions of the channel's separability, capacity for bound entanglement, and capacity for distillable entanglement. By contrast, the two-mode squeezing-type interaction always produces distillable entanglement with no restrictions on temperature, cooperativities, or losses. Counterintuitively, for both interactions, we find that achieving quantum operation does not require either a quantum cooperativity exceeding one, or ground-state cooling of the mediating mode. Finally, we discuss where two state-of-the-art implementations are relative to these thresholds and show that current devices operating in either mode of operation are in principle capable of entangling optical and microwave modes.
Doubly parametric quantum transducers (DPTs), such as electro-optomechanical devices, show promise as quantum interconnects between the optical and microwave domains, thereby enabling long-distance quantum networks between superconducting qubit systems. However, any transducer will inevitably introduce loss and noise that will degrade the performance of a quantum network. We explore how DPTs can be used to construct a network capable of distributing remote two-mode microwave entanglement over an optical link by comparing 14 different network topologies. The 14 topologies we analyze consist of combinations of different transducer operations, entangled resources, and entanglement-swapping measurements. For each topology, we derive a necessary and sufficient analytic threshold on DPT parameters that must be exceeded in order to distribute microwave-microwave entanglement. We find that the thresholds are dependent on the given network topology, along with the available entanglement resources and measurement capabilities. In the high-optical-loss limit, which is relevant to realistic networks, we find that down-conversion of each half of an optical two-mode squeezed vacuum state is the most robust topology. Finally, using currently achievable experimental capabilities, we find the encouraging result that several of these topologies could produce microwave-microwave entanglement. However, most of these topologies cannot work given current transducer performance, which demonstrates the importance of thoroughly analyzing all possible networks.
A quantum network linking superconducting quantum computers would enable highly sought-after applications such as distributed quantum computing. Optical photons are the natural way of encoding information for long distance communication; however, exchanging quantum information between optical and microwave domains requires a quantum transducer. There are many ways transducers could be integrated into a network which leads to the question: Which network is most tolerant of current transducers which are far from perfect? A logical metric for optimizing the first quantum networks is the entanglement threshold which is necessary and sufficient condition on network parameters for microwave-microwave entanglement. Here we first address the problem of finding the network with the least restrictive entanglement threshold on physical parameters. For tractability we restrict our study to networks containing only gaussian states, operations, and measurements which are among the most readily experimentally accessible options. Within this vast space of possible network configurations, we identify a small set of topologies which we believe to be optimal. We find that with previously reported technology some of these topologies are capable of entangling remote microwave modes, despite imperfections in current transduction technology. Finally, progress towards a physical implementation of one of these topologies is discussed.
Quantum networks linking quantum computers are predicted to be extremely useful for a wide range of applications. At the hardware level, superconducting quantum computers have emerged as one of the most promising scalable platforms for general quantum computation, and optical networks are clearly the best choice for long distance communication due to their minimal loss. To leverage the strengths of these two dissimilar platforms, quantum transducers, which are reachingquantum-enabled operation, are needed. This thesis presents progress towards designing a long distance optical network which will entangle two superconducting qubits and the implementation of the optical portion of this network. We have found simple, application independent, necessary and sufficient conditions for transducers to work in quantum networks, and we conclude that some previously demonstrated devices are ready for integration into a quantum network. Optimizing the integration of two transducers into a network is explored and it is found that the most robust topology to transmission loss consists of generating optical Gaussian entanglement and then using the two transducers to down-convert this entanglement to the microwave domain. To implement this topology we have constructed a tunable source of optical two-mode squeezing and two ultra-low noise photodetectors. Finally a new method for transferring and distilling Gaussian entanglement to qubits using the dispersive Jaynes-Cummings interaction is presented. This proof-of-principle two-node network should be able to entangle superconducting qubits at a rate of 5 ebits/second over 4 km of optical fiber using currently available technology.
A quantum transducer converts an input signal to an output probe at a distant frequency band while maintaining the quantum information with high fidelity, which is crucial for quantum networking and distributed quantum sensing and computing. In terms of microwave–optical quantum transduction, the state-of-the-art quantum transducers suffer low transduction efficiency from weak nonlinear coupling, wherein increasing pump power to enhance efficiency inevitably leads to thermal noise from heating. Moreover, we reveal that the efficiency-bandwidth product of a cavity electro-optical or electro-optomechanical transducer is fundamentally limited by pump power and nonlinear coupling coefficient, irrespective of cavity engineering efforts. To overcome this fundamental limit, we propose to noiselessly boost the transduction efficiency by consuming intraband entanglement (e.g., microwave–microwave or optical–optical entanglement in the case of microwave–optical transduction). Via a squeezer–coupler–antisqueezer sandwich structure, the protocol enhances the transduction efficiency to unity in the ideal lossless case, given an arbitrarily weak pump and nonlinear coupling. In practical cavity systems, our entanglement-assisted protocol surpasses the non-assisted fundamental limit of the efficiency-bandwidth product and reduces the threshold cooperativity for positive quantum capacity by a factor proportional to two-mode squeezing gain. Given a fixed cooperativity, our approach increases the broadband quantum capacity by orders of magnitude. The entanglement-assisted advantage is robust to ancilla loss and cavity detuning.
State transfer between light and microwaves is a key challenge in quantum networks. Promising transducers use a mechanical intermediary that couples to both fields via radiation pressure. Such electro-optomechanical devices have achieved high efficiencies, yet require resolved-sideband cavities, and generally compromise in scalability and noise performance. Here, we relax this constraint by extending the protocol of Navarathna et al. that transfers optical quantum information onto a mechanical resonator using a broadband, sideband-unresolved cavity and feedback. Combining this with parametric mechanical-to-microwave conversion, we show that continuous optical-to-microwave quantum state transfer is possible using measurement-based feedback, while all-optical coherent feedback enables bidirectional transfer. To assess the transfer, we introduce the quantum transfer witness WT\mathcal{W}_TWT​, which -- though similar to the input-referred added noise -- also identifies whether a channel is capable of both preserving Gaussian entanglement and outperforming classical transduction schemes. Finally, we show that quantum-compatible noise performance is within reach of current experimental capabilities. Our results unlock a new design space for electro-optomechanical transducers and strengthens their candidacy as scalable quantum links between distant nodes.
The first quantum revolution has brought us the classical Internet and information technology. Today, as technology advances rapidly, the second quantum revolution quietly arrives, with a crucial moment for quantum technology to establish large-scale quantum networks. However, solid-state quantum bits (such as superconducting and semiconductor qubits) typically operate in the microwave frequency range, making it challenging to transmit signals over long distances. Therefore, there is an urgent need to develop quantum transducer chips capable of converting microwaves into optical photons in the communication band, since the thermal noise of optical photons at room temperature is negligible, rendering them an ideal information carrier for large-scale spatial communication. Such devices are important for connecting different physical platforms and efficiently transmitting quantum information. This paper focuses on the fast-developing field of optomechanical quantum transducers, which has flourished over the past decade, yielding numerous advanced achievements. We categorize transducers based on various mechanical resonators and discuss their principles of operation and their achievements. Based on existing research on optomechanical transducers, we compare the parameters of several mechanical resonators and analyze their advantages and limitations, as well as provide prospects for the future development of quantum transducers.