Optimal Randomness Achieved Via Multipartite Bell Inequalities in Quantum Networks

Researchers are continually striving to develop unhackable random number generators, and a new study published today details a significant step forward in certifying device-independent quantum randomness for use in quantum networks. Shuai Zhao, Rong Wang, and Qi Zhao from Hangzhou Dianzi University, along with their colleagues, demonstrate a family of multipartite Bell inequalities inspired by the GHZ state, enabling optimal randomness certification even with non-maximal Bell values , a key limitation of previous methods. This breakthrough offers a more efficient way to verify true randomness from quantum devices without needing to know how they work internally, and importantly, provides a tighter upper bound on the Holevo quantity, outperforming existing inequalities like MABK, Parity-CHSH, and Holz, particularly at values crucial for practical network applications.

Due to the straightforward representation of the stabilizer group, these inequalities can be readily expanded to accommodate a larger number of parties, enhancing their applicability in complex quantum networks. Compared to established Mermin-type inequalities, the presented approach yields a more efficient certification of randomness under these conditions. This improvement is particularly significant for experimental investigations focused on DI Quantum cryptography within quantum network architectures.

Experiments reveal that this new approach allows for the certification of optimal quantum randomness, effectively extracting true random numbers from observed correlations without requiring detailed characterization of the Quantum state preparation and measurement devices. The simplicity of the inequalities’ structure facilitates their implementation in practical quantum systems, paving the way for more robust and efficient DI random number generators. This work opens exciting possibilities for enhancing the security and reliability of quantum cryptographic protocols and other applications reliant on verifiable randomness, such as secure communication and computation. By addressing the limitations of existing strategies, this study significantly advances the field and promises to accelerate the development of practical DI quantum random number generators for a wide range of applications, from secure key distribution to advanced scientific simulations.

Multipartite Bell Inequalities for GHZ State Certification offer

This approach leverages the simple representation of the stabilizer group to construct inequalities easily expandable to multiple parties, offering a significant advantage over existing methods. The research team developed these inequalities to address limitations in current device-independent (DI) randomness certification strategies, particularly when dealing with non-maximal Bell values. To construct these inequalities, the study pioneered an expansion from the α-CHSH expression, a technique previously used for global randomness certification, but refined for optimal DI quantum randomness. Specifically, the N-party Bell expression takes the form BN = (A10 + A11)A20···AN0 + N∑i=2 (αA10 − A11)Ai1, where Ai0 and Ai1 represent measurement settings for each party and α is an adjustable parameter.

This stabilizer-type construction ensures the number of correlators increases polynomially with N, simplifying expansion to larger systems. Experiments employed the NPA hierarchy method to analyse the robustness performance for N = 3 and N = 4 parties, comparing the new inequalities with the Mermin inequality. Analysis revealed that, at its maximal Bell values, the new inequalities can certify optimal quantum randomness for arbitrary N parties by taking α →∞. Furthermore, the study established that the inequalities can certify optimal N bits of global randomness when α approaches infinity, with the optimized observables aligning with the GHZ state |GHZ⟩= 1/√2 (|00···0⟩+|11···1⟩). Calculations show that for N = 3, the guessing probability in measurement settings A10A20A30 approaches 1/8, indicating the certification of 3 bits of randomness, optimal for a three-party quantum system. This innovative methodology not only advances DI quantum randomness certification but also provides a generalizable framework applicable to other multipartite entanglement states with stabilizer representations.

Optimal randomness from multipartite Bell inequalities

The research team meticulously constructed these inequalities to facilitate investigations into device-independent (DI) quantum randomness certifications, paving the way for more robust and reliable random number generation. These measurements confirm a substantial advancement in the ability to extract truly random numbers from quantum systems without needing detailed characterization of the devices used. Results demonstrate that this approach can certify optimal N bits of global randomness for N parties when α approaches infinity, effectively maximizing the potential for secure communication and computation. Robustness analysis, conducted for N = 3 and N = 4 parties using the NPA hierarchy method, revealed that the new inequality family is more efficient than the Mermin inequality across most ranges of non-maximal Bell violation.

Tests prove that the complexity of these inequalities increases polynomially with the number of parties, allowing for easy scaling to larger systems. The simple structure of these inequalities, involving primarily two-party correlations, simplifies implementation and expands the possibilities for DI quantum randomness amplification, which considers weak randomness in measurement setting choices.