Fisher Information and entanglement of non-Gaussian spin states (1507.03782v1)

Abstract: Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian statistics. Here we report on the creation and characterization of non-Gaussian many-body entangled states. We develop a general method to extract the Fisher information, which reveals that the quantum dynamics of a classically unstable system creates quantum states that are not spin squeezed but nevertheless entangled. The extracted Fisher information quantifies metrologically useful entanglement which we confirm by Bayesian phase estimation with sub shot-noise sensitivity. These methods are scalable to large particle numbers and applicable directly to other quantum systems.

• The paper shows that non-Gaussian spin states generated in a BEC exhibit metrologically useful entanglement that exceeds what spin squeezing alone can reveal.
• It introduces a novel method for extracting Fisher information using the Hellinger distance in combination with Bayesian phase estimation to quantify measurement sensitivity.
• The experimental setup with interacting binary condensates highlights significant advances for precision quantum measurements and potential applications in atom interferometry.

Fisher Information and Entanglement of Non-Gaussian Spin States

The paper "Fisher Information and entanglement of non-Gaussian spin states" presents a significant advancement in the characterization of entangled states, particularly within the domain of quantum metrology. The research focuses on the generation and evaluation of non-Gaussian many-body entangled states, thereby extending the potential for quantum-enhanced measurement sensitivities beyond the conventional squeezed states described by Gaussian statistics.

The authors detail the creation of non-Gaussian entangled states in a Bose-Einstein condensate (BEC) setting. Through the interplay between nonlinear interaction and weak Rabi coupling within an optical lattice, they explore the quantum dynamics rooted at a classically unstable fixed point. This setup enables the formation of entangled states that, although not spin-squeezed, exhibit metrologically useful entanglement as quantified by Fisher information.

Remarkably, the paper demonstrates that these non-Gaussian states can surpass shot-noise limited measurement sensitivity. Fisher information, derived from Bayesian phase estimation, indicates significant entanglement at a level where conventional spin squeezing fails to detect it. Specifically, the authors report a maximum spin squeezing of -4.5±0.2 dB at an evolution time of 15 ms, whereas the Fisher information continues to reveal entanglement even when spin squeezing diminishes, achieving an experimental Fisher information greater than one, i.e., $F/N > 1$.

The implementation of their experimental system involves an array of interacting binary BECs of $^{87}$Rb, combined with precise microwave and radio frequency coupling. The non-Gaussian states generated are analyzed through tomographic reconstruction, exploiting the statistical distinguishability of probability distributions obtained from high-repeatability experiments. This technique circumvents the impractical full reconstruction of the density matrix.

A salient highlight from the research is the novel method for extracting Fisher information using the Hellinger distance, circumventing the limitations posed by large system sizes. This statistical approach connects Fisher information directly to measurement sensitivity, corroborated by a Bayesian analysis which verified sub-shot-noise phase sensitivity for the non-Gaussian states.

The implications of these findings are profound for both practical applications and theoretical developments in quantum physics. Practically, the results pave the way for enhanced precision in quantum measurements and atom interferometry, essential for competitive quantum technologies. Theoretically, this work points to the potential advantages of utilizing non-Gaussianity in quantum state preparation for achieving the ultimate Heisenberg limit of metrological precision.

Future research endeavors might further explore the scalability and robustness of these methods in more complex quantum systems. Additionally, extending these experimental techniques to other platforms, such as ion traps or solid-state systems, could provide broader applicability in quantum information science and technology.

In summary, this paper delivers a comprehensive paper on non-Gaussian spin states, demonstrating their utility in quantum-enhanced measurement contexts. The rigorous extraction and validation of Fisher information stand as a cornerstone for future advancements in precision quantum measurements.