Certifiable Lower Bounds of Wigner Negativity Volume and Non-Gaussian Entanglement with Conditional Displacement Gates

Abstract

In circuit and cavity quantum electrodynamics devices where control qubits are dispersively coupled to high-quality-factor cavities, characteristic functions of cavity states can be directly probed with conditional displacement (CD) gates. In this Letter, I propose a method to certify non-Gaussian entanglement between cavities using only CD gates and qubit readouts. The CD witness arises from an application of Bochner's theorem to a surprising connection between two negativities: that of the reduced Wigner function, and that of the partial transpose. Non-Gaussian entanglement of some common states, like entangled cats and photon-subtracted two-mode squeezed vacua, can be detected by measuring as few as four points of the characteristic function. Furthermore, the expectation value of the witness is a simultaneous lower bound to the Wigner negativity volume and a geometric measure of entanglement conjectured to be the partial transpose negativity. Both negativities are strong monotones of non-Gaussianity and entanglement, respectively, so the CD witness provides experimentally accessible lower bounds to quantities related to these monotones without the need for tomography on the cavity states.

5+7 pages, 2+3 figures. Final published version

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Cited by in corpus (7)

• Hierarchical Verification of Non-Gaussian Coherence in Bosonic Quantum States
• Quantum entanglement in phase space
• All three-angle variants of Tsirelson's precession protocol, and improved bounds for wedge integrals of Wigner functions
• Even-parity precession protocol for detecting nonclassicality and entanglement
• Sufficient Wigner Negativity Implies Genuine Multipartite Entanglement
• Witnessing genuine multipartite entanglement in phase space with controlled Gaussian unitaries
• Single-shot conditional displacement gate between a trapped atom and traveling light