Entanglement Thresholds of Doubly-Parametric Quantum Transducers

TL;DR

This paper derives explicit conditions under which doubly-parametric quantum transducers can generate entanglement between optical and microwave modes, highlighting differences between interaction types and implications for quantum network design.

Contribution

It provides the first explicit entanglement thresholds for these transducers, analyzing both beamsplitter and two-mode squeezing interactions in detail.

Findings

Beamsplitter interaction thresholds distinguish separable, bound entangled, and distillable entangled regimes.

Two-mode squeezing interaction always yields distillable entanglement regardless of temperature or losses.

Entanglement breaking conditions are identified for reduced channels with vacuum inputs.

Abstract

Doubly-parametric quantum transducers, such as electro-opto-mechanical devices, are quickly approaching quantum operation as decoherence mechanisms such as thermal noise, loss, and limited cooperativities are improved. These devices show potential as the critical link between quantum information contained at frequencies as disparate as those in the optical and microwave domains, thus enabling applications such as long distance networking of superconducting quantum computers. However, the requirements on the operating parameters of the transducers necessary to achieve quantum operation have yet to be characterized. In this work we find simple, explicit 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 which 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. Finally, we find the entanglement breaking conditions on the reduced one-mode upconversion and downconversion channels obtained by initializing the unused input with vacuum while ignoring the unused output. These differences between the entanglement thresholds of the beamsplitter-type and two-mode squeezing-type interactions are then important considerations in the construction of larger quantum networks that integrate multiple transducers.