Certifying Bipartite Entangled States with Few Local Measurements Enables Fidelity Bounds for Multipartite Systems

Certifying that quantum states are genuinely entangled remains a fundamental challenge in quantum information science, and researchers continually seek methods requiring fewer measurements. Jennifer Ahiable from Universitat Autònoma de Barcelona, alongside Andreas Winter from Universität zu Köln, now demonstrate a streamlined approach to verify bipartite entanglement using only a few locally measurable quantities. Their work establishes a clear link between the probability of detecting specific quantum properties and the confidence with which a state’s entanglement can be confirmed, offering a practical tool for quantum technologies. Importantly, this method extends to systems involving multiple parties, providing a way to assess the quality of complex quantum states and paving the way for more robust quantum communication and computation.

Efficient Certification of High-Dimensional Entanglement

This research addresses the challenge of certifying quantum entanglement, particularly in systems with many possible states. Certification means proving that a quantum state is genuinely entangled, a crucial step for developing quantum technologies like computers, communication networks, and sensors. The team investigates methods for efficient certification, requiring a minimal number of measurements to confirm entanglement and considering how much noise a system can tolerate before it becomes indistinguishable from a non-entangled state. Ultimately, this work aims to optimize resource use and improve the reliability of quantum experiments by providing efficient strategies for proving entanglement and understanding its limitations.

Certifying Quantum States with Separable Projectors

Scientists have pioneered a technique for certifying quantum states, both for two-particle and multi-particle systems, by identifying them as unique joint eigenstates of separable projectors. These projectors, measurable through local operations on individual particles, provide a robust way to verify the authenticity of a quantum state. Measurements of these projectors directly yield a lower bound on the fidelity, a measure of accuracy, between a prepared state and its target, and also provide a lower bound on the entanglement fidelity of a quantum channel. The team constructed fully separable projectors, allowing for measurements requiring only the distribution of information regarding which projector to measure on each subsystem. They extended this approach to multi-particle systems through a recursive process, treating the system as a cascade of two-particle certifications. This iterative method generates a set of projectors that uniquely stabilize the multi-particle state, preserving the experimental robustness of the original two-particle method, and allows the fidelity of the multi-particle state to be directly estimated from the outcomes of these simple, sequential tests.

Entangled State Certification Via Local Measurements

Researchers have developed a method to definitively certify the state of a quantum system using only a small number of local measurements, even for complex, multi-particle entangled states. This work establishes a strong connection between the properties of quantum states and the simplicity of verifying their authenticity. The core of this achievement lies in identifying two separable projectors that uniquely define any two-particle entangled state, acting as a “fingerprint” for the state. The team constructed these projectors using a Schmidt decomposition of the entangled state, allowing them to express the state in a specific basis.

Crucially, the entangled state is the only one that yields a positive result when measured against both projectors, providing a robust certification process. Mathematical analysis confirms that the product of these two projectors precisely reproduces the original entangled state, solidifying the method’s accuracy. This approach extends beyond two-particle systems, generalizing to arbitrarily large numbers of particles through a recursive procedure, treating the system as a cascade of two-particle certifications.

Local Projectors Uniquely Verify Quantum States

This research establishes a novel method for verifying quantum states, demonstrating that any pure, multi-particle state can be uniquely identified through measurements of separable projectors. The team proved that these projectors directly relate to the fidelity of the certification process, offering a more general approach applicable to a wider range of quantum states and systems. The researchers extended this principle to multi-particle systems, showing that the infidelity can be bounded by the infidelities of the individual, locally measured projectors, providing a practical way to assess the quality of complex quantum states using relatively simple measurements. They acknowledge that extending the method to mixed states presents a significant challenge for future investigation, and suggest exploring the potential of this certification technique within the context of quantum error correction and fault-tolerant quantum computation.