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arXiv:2008.11733 · Physical Review A

Gaussian state entanglement witnessing through lossy compression

Waldemar Kłobus, Paweł Cieśliński, Lukas Knips, Paweł Kurzyński, Wiesław Laskowski

Published Mar 12, 2021• 1 citation
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Abstract

We study the possibility of witnessing Gaussian entanglement between two continuous-variable systems with the help of two spatially separated qubits. Its key ingredient is a local lossy state transfer from the original systems onto local qubits. The qubits are initially in a pure product state, therefore by detecting entanglement between the qubits we witness entanglement between the two original systems.

DOI
10.1103/physreva.103.032412

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We use quantum entanglement witnesses derived from Gaussian operators to study the separable criteria of continuous variable states. We transform the validity of a Gaussian witness to a Bosonic Gaussian channel problem. It follows that the maximal means of two-mode and some four-mode Gaussian operators over product pure states are achieved by vacuum (or coherent states and squeezed states) according to the properties of Bosonic Gaussian channels. Then we have necessary and sufficient criteria of separability not only for Gaussian quantum states, but also for non-Gaussian states prepared by photon adding to or/and subtracting from Gaussian states. The criterion can be further explicitly expressed with covariance matrix of the Gaussian state or covariance matrix of Gaussian kernel of the non-Gaussian state. This opens a way for precise detection of non-Gaussian entanglement.
We investigate how entanglement can be transferred between qubits and continuous-variable (CV) systems. We find that one ebit borne in maximally entangled qubits can be fully transferred to two CV systems which are initially prepared in a pure separable Gaussian field with high excitation. We show that it is possible to retrieve the entanglement back to qubits from the entangled CV systems. The deposition of multiple ebits from qubits to the initially separable CV systems is also pointed out. We show that the entanglement transfer and retrieval are done at a quasisteady state.
Entangling two systems at distant locations using a separable mediating ancilla is a counterintuitive phenomenon proposed for qubits by T. Cubitt et al. [Phys. Rev. Lett. 91, 037902 (2003)]. We show that such entanglement distribution is possible with Gaussian states, using a certain three-mode fully separable mixed Gaussian state and linear optics elements readily available in experiments. Two modes of the state become entangled by sequentially mixing them on two beam splitters, while the third one remains separable in all stages of the protocol.
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