Entanglement Detected in Quantum Systems Without Needing Individual Measurements

Scientists have developed a novel method for detecting multilevel entanglement within systems comprising numerous quantum emitters. Pedro Rosario, from Departamento de Física, Universidade Federal de São Carlos, CNRS and Université de Strasbourg, and Romain Bachelard, also of Departamento de Física, Universidade Federal de São Carlos, alongside et al., present electric-field based inequalities that reveal entanglement, determining that polarisation and detection direction significantly improve the process, a characteristic unique to multilevel systems. This research demonstrates robust detection of genuine multipartite entanglement across states including Dicke, singlet and W-like configurations, even in the presence of noise and with mixed entangled states. Consequently, these findings pave the way for entanglement detection without requiring local measurements in systems utilising multilevel emitters like Rydberg atoms or quantum dots, representing a substantial advancement in quantum information science.

This breakthrough centres on utilising electric-field based inequalities to identify entanglement within systems of N quantum emitters, moving beyond traditional entanglement detection techniques.

The research demonstrates that the polarization of detected light, alongside the direction of observation, significantly enhances the ability to detect these complex quantum correlations, a feature unique to multilevel systems. By applying these newly derived “witnesses” to standard quantum states, including Dicke, singlet, and W-like states, researchers have proven their effectiveness in identifying genuine multipartite entanglement.
This work introduces a set of inequalities capable of detecting entanglement without requiring complete knowledge of the quantum state, a significant advantage for complex, many-body systems. The detection method proves robust against noise and extends to mixed entangled states, broadening its applicability to real-world scenarios.

Crucially, the study establishes a fundamental connection between entanglement and the far-field light emitted from multilevel atoms, revealing how the geometry between detectors and atoms influences entanglement sensing. Each detection direction provides a unique entanglement witness, offering a versatile toolkit for quantum state characterisation.
The theoretical framework builds upon local orthogonal observables and the properties of light emitted from quantum emitters. Researchers demonstrate that the photon creation operator, linked to the electric field in the far field, can be used to formulate entanglement witnesses. These witnesses are derived from electric field quadratures and incorporate the geometry of the detection setup and the polarization of the emitted light.

The resulting inequalities, when violated, definitively indicate the presence of entanglement within the system. This approach allows for the detection of entanglement even when certain atomic transitions are forbidden, expanding the range of detectable states. These findings unlock possibilities for entanglement detection in systems like superconducting qubits, Rydberg atoms, and quantum dots, paving the way for more efficient and scalable quantum information processing.
By circumventing the need for full quantum tomography, a computationally intensive process, this method offers a practical solution for characterising large-scale entangled systems. Ultimately, this research not only advances our ability to detect and quantify entanglement but also deepens our understanding of light as a carrier of quantum information and non-classical correlations.

Construction of local orthogonal observables and entanglement witnessing via atomic radiation

Electric-field based inequalities serve as the foundation for detecting multilevel entanglement within a system of N quantum emitters. The research establishes a connection between entanglement and far-field light emitted from these multilevel atoms, demonstrating that the geometry between the detector and the atoms directly influences entanglement sensing.

Each detection direction provides a unique entanglement witness, a feature not observed in two-level systems. Local orthogonal observables (LOOs) are employed to describe a quantum emitter with d levels and its associated Hilbert space, Hd. These LOOs, comprising d2 Hermitian operators, are constructed using Gell-Mann matrices and Weyl operators, facilitating the decomposition of a quantum state.

Specifically, the set of LOOs includes ladder and population operators of the atom, forming the basis for detecting multipartite entanglement from the radiation of N multilevel emitters. The photon creation operator for a transition α ↔β from a cloud of N multilevel atoms is defined by the positive frequency part of the electric field in the far field, expressed as E+αβ = (E−αβ)†.

This operator incorporates the detection direction, atom positions, dipolar moments, and the transition wavenumber, k0. Electric field quadratures, Xαβ and Yαβ, are then introduced using the electric field and polarization vectors, enabling the quantification of entanglement through the analysis of emitted light.

The study demonstrates the efficiency of these witnesses in detecting genuine multipartite entanglement using paradigmatic quantum states, including Dicke states, singlet states, and W-like states. Detection proves robust to noise and extends to mixed entangled states, opening avenues for entanglement detection without full state tomography in systems like Rydberg atoms or quantum dots. The research highlights the role of light polarization as a key factor in witnessing entanglement in multilevel systems, a departure from observations in two-level systems.

Multilevel atomic systems exhibit geometry-dependent entanglement detectable via electric-field inequalities

Researchers have established a connection between entanglement and far-field light emitted from a system of N multilevel atoms, demonstrating that the geometry between the detector and the atoms directly influences entanglement sensing. The study introduces a set of electric-field based inequalities capable of detecting multilevel entanglement, revealing that the polarization channel and direction of detection can enhance this process, a feature unique to multilevel systems.

Violation of the derived inequality, Wk0, implies entanglement in the quantum state ρ, with the minimum value of Wk0 determining the presence of entanglement. The work details that the inequality Wk0 is calculated using several observables, including w1,k0, wA,B,C 2,k0, and wA,B,C 3,k0, each dependent on variances and modified second moments of electric field quadratures.

Specifically, w1,k0 is determined by the sum of variances of the Xμ+, Yμ−, and Zμz operators, minus a term proportional to the number of atoms N. The observables wA,B,C 2,k0 and wA,B,C 3,k0 incorporate variances and modified second moments related to operators Aμa, Bμb, and Cμc, selected from the set {Xμ+, Yμ−, Zμz}.

These calculations allow for the detection of genuine multipartite entanglement in states such as Dicke, singlet, and W-like states. Furthermore, the research indicates that when measuring linear polarization ez, the entanglement witness Wk0 becomes independent of the measured light polarization, due to the real nature of the associated factor ζα,β.

The study utilizes local orthogonal observables (LOOs) to decompose the quantum state, employing ladder and population operators of the atom as a basis for detecting multipartite entanglement from the emitted radiation. A complete set of d2 LOOs is achieved by including both polarization-dependent and independent terms, ensuring a robust basis for density matrix representation. This framework enables efficient large-scale entanglement detection, circumventing the need for full quantum tomography.

Electric-field inequalities reveal robust multilevel entanglement in extended quantum systems

Scientists have developed a set of electric-field based inequalities to detect multilevel entanglement within systems containing numerous quantum emitters. These inequalities determine that both the polarization channel and the direction of detection can improve the identification of entanglement, a characteristic unique to multilevel systems.

The method’s effectiveness was demonstrated through successful detection of entanglement in standard quantum states including Dicke, singlet, and W-like states, and it remains robust even when quantum noise is present, extending to mixed entangled states. This research introduces a novel approach to entanglement detection, circumventing the need for local measurements in systems such as Rydberg atoms or quantum dots.

The detection process benefits from manipulating the dipole orientation and light polarization, allowing for entanglement identification across different spatial regions. This advancement stems from a direct relationship established between local orthogonal observables and field quadrature operators, offering a new perspective on quantifying entanglement in complex quantum systems.

The authors acknowledge that the current work focuses on specific quantum states and may require further adaptation for broader applicability. Future research could explore transforming these inequalities into parameters for quantifying spin squeezing, potentially enhancing the precision of measurements on probed quantum states. Additionally, the findings pave the way for investigating large, open quantum systems where collective states arise through dipole-dipole interactions, opening avenues for studying more complex quantum phenomena.