Researchers Achieve Robust Self-testing of N-qubit GHZ Basis Measurements Without Shared Entanglement

Entangled basis measurements are fundamental to building quantum networks, allowing for the secure distribution of information and enabling powerful computational capabilities, but verifying the accuracy of these measurements across multiple parties presents a significant challenge. Barnik Bhaumik, Sagnik Ray, and Debashis Saha, from institutions including the Indian Institute of Science Education and Research Thiruvananthapuram and the Indian Institute of Technology Bhubaneswar, now demonstrate a new method for rigorously testing these measurements without the need for pre-shared entanglement. Their approach involves a communication scenario where multiple senders each provide input, and a single receiver assesses the results, allowing for a robust self-test of multi-qubit measurements. This advancement represents a crucial step towards building practical and trustworthy quantum communication systems, as it provides a way to verify the integrity of measurements without relying on assumptions about the devices involved.

This research advances the ability to robustly verify these measurements, a significant step towards building practical quantum networks. Directly verifying entanglement becomes increasingly challenging as the number of parties involved grows, so the team focuses on developing a practical method to confirm successful implementation of multipartite entanglement protocols without relying on pre-certified devices or making strong assumptions about the internal workings of the quantum systems. This work addresses the need for reliable entanglement verification, which is essential for secure quantum communication and distributed quantum computation.

In this work, the researchers adopt a semi-device-independent approach that enables the self-testing of n-qubit Greenberger, Horne, Zeilinger (GHZ) basis measurements without requiring shared entanglement between distant parties. The method relies solely on analysing input-output statistics from a communication scenario involving n spatially separated senders, each receiving two bits of input, and a single receiver with no input. The robustness of the proposed self-testing protocol receives careful analysis, and a protocol for robust self-testing of the three-outcome partial Bell basis measurement is introduced, which is easily implementable in an optical setup.

Pure Antipodal States Maximise Communication Success

This research demonstrates that using specific quantum states, known as ‘pure antipodal’ states, optimises the success of a communication protocol involving multiple senders and a single receiver. Pure states represent a definite quantum condition, while antipodal states are orthogonal, meaning they are completely distinguishable from one another. The team mathematically proves that employing these states maximises a key metric, which quantifies the effectiveness of the communication process.

The analysis defines the success metric and then proceeds to show, through mathematical manipulation, that it reaches its maximum value when the senders use pure, orthogonal states. This derivation involves expanding relevant equations and demonstrating that the maximum value is achieved under these specific conditions. The research builds upon the concept of the Bloch vector, a representation of a quantum state, to show that the optimal states lie at opposite ends of the Bloch sphere.

Self-testing Entanglement Distribution Measurement Quality

This research introduces a method for verifying the quality of quantum measurements used to distribute entanglement across a network, without requiring pre-shared entanglement between parties. The team demonstrates a way to ‘self-test’ these measurements by analysing input-output statistics from multiple senders and a single receiver, effectively assessing the measurement’s accuracy based on the data received. Importantly, the analysis reveals that focusing on ‘antipodal’ messages, those representing opposite quantum states, simplifies the process of determining a lower bound on measurement fidelity.

The findings establish a connection between the observed statistics and the actual quality of the measurements, providing a robust way to ensure reliable entanglement distribution. The researchers derive a mathematical relationship that links the observed signal strength to a lower bound on the measurement’s fidelity, offering a quantifiable metric for assessment. While the study focuses on theoretical foundations and mathematical proofs, it paves the way for practical applications in quantum communication networks, where verifying the integrity of measurements is crucial for secure and efficient data transmission.