Characterizing the multipartite continuous-variable entanglement structure from squeezing coefficients and the Fisher information

Abstract

Understanding the distribution of quantum entanglement over many parties is a fundamental challenge of quantum physics and is of practical relevance for several applications in the field of quantum information. The Fisher information is widely used in quantum metrology since it is related to the quantum gain in metrology measurements. Here we use methods from quantum metrology to microscopically characterize the entanglement structure of multimode continuous-variable states in all possible multi-partitions and in all reduced distributions. From experimentally measured covariance matrices of Gaussian states with 2, 3, and 4 photonic modes with controllable losses, we extract the metrological sensitivity as well as an upper separability bound for each partition. An entanglement witness is constructed by comparing the two quantities. Our analysis demonstrates the usefulness of these methods for continuous-variable systems and provides a detailed geometric understanding of the robustness of cluster-state entanglement under photon losses. arXiv:1804.08296v2 [quant-ph]

Sensitivity Bounds for Multiparameter Quantum Metrology

“…|A L , where the A m describe groups of modes, can be written asρ Λ−sep = γ p γργ,A 1 ⊗ · · · ⊗ρ γ,A L , with density matricesρ γ,A m on A m . Following [47,49], we obtain the state-dependent upper bound…”

“…Our results build the foundation for the development of genuine quantum technological strategies in applications that rely on the precise acquisition of an ensemble of parameters, such as sensing of spatially distributed fields and imaging techniques. Experimental realizations are possible with existing technology in a wide range of atomic and photonic systems that provide coherent access to multiple modes, see, e.g., [5,20,25,26,33,49].…”

Enhancement of the metrological sensitivity limit through knowledge of the average energy

“…The sensitivity thus provides information about the number of entangled atoms [21] and the microscopic entanglement structure in the case of individually addressable subsystems in multi-mode systems [18,24]. Metrological entanglement witnesses have been implemented successfully with Gaussian and non-Gaussian states of cold atoms [5] and multi-mode squeezed states of light [25].…”

k-stretchability of entanglement, and the duality of k-separability and k-producibility

“…k-producibility plays particularly important role in quantum metrology [53]. k-producibly entangled states for larger k lead to higher sensitivity, so better precision in phase estimation, which has been illustrated in experiments [54][55][56], and which also leads to k-producibility entanglement criteria [57].…”