Quantum Entanglement’s ‘no Signalling’ Rule Bends, but Doesn’t Break

Scientists are increasingly scrutinising the no-signalling principle, a cornerstone of Bell inequality and steering experiments, as experimental flaws can mimic violations beyond statistical fluctuations. Lucas Maquedano (Federal University of Paraná), Sophie Egelhaaf (University of Geneva), and Amro Abou-Hachem (Lund University, with et al. including Jef Pauwels and Armin Tavakoli) present extensions to local hidden variable and local hidden state theories, accommodating quantifiable signalling. Their research develops non-classicality tests applicable to these extended models, utilising both complete statistical analysis and corrections to established Bell and steering inequalities. This work is significant because it addresses apparent signalling in realistic scenarios, specifically demonstrating its applicability to data arising from processor imperfections and inefficient detectors.

These violations, previously attributed to statistical fluctuations, can arise from subtle systematic effects present in realistic experimental setups.

The work introduces extensions to local hidden variable and local hidden state theories, allowing for bounded and quantifiable amounts of signalling between entangled particles. This approach moves beyond simply enforcing no-signalling through data post-processing, instead explicitly relaxing classical models to incorporate a measurable signalling parameter.
The study establishes methods for developing non-classicality tests applicable to these extended models, utilising both exact calculations based on complete statistical data and corrections to standard Bell and steering inequalities. These techniques were demonstrated using two scenarios known to exhibit apparent signalling: data obtained from an IBM quantum processor and post-selected data originating from inefficient detectors.

By quantifying the permissible signalling, the research provides a means to distinguish genuine quantum non-classicality from artefacts introduced by experimental imperfections. This geometric and operational approach defines a “signalling budget” directly from observed data, quantifying deviations from the no-signalling subspace.

Specifically, the researchers expanded the classical local hidden variable polytope to create a signalling LHV model, enabling the reproduction of any probability distribution unless constrained by ontological considerations. In the context of EPR steering, the unsteerable set of assemblages was similarly enlarged, allowing for a more accurate assessment of steering phenomena in the presence of signalling.

The framework was successfully applied to analyse data from both the IBM quantum processor and experiments employing post-selection with inefficient detectors, revealing how residual signalling can lead to false positives in steering tests and spurious violations of quantum bounds. This work offers a robust methodology for analysing data from quantum experiments, addressing a critical challenge in the field of quantum information science.

By explicitly accounting for bounded signalling, the research paves the way for more reliable tests of fundamental quantum theory and the development of secure quantum technologies, such as device-independent randomness and quantum key distribution. The ability to accurately characterise and mitigate the effects of signalling will be crucial for advancing the practical implementation of these technologies and ensuring the validity of future quantum experiments.

Relaxed No-Signalling Models and Non-Classicality Witnessing

Researchers developed extensions to local hidden variable and local hidden state theories to accommodate bounded, operationally quantifiable signalling. The work addresses apparent violations of the no-signalling principle observed in Bell-inequality and quantum-steering experiments, moving beyond explanations based solely on finite-sample statistics.

These extensions introduce models where a measurable amount of signalling is permitted, allowing for analysis of data even when perfect no-signalling is not achieved. The methodology centres on developing non-classicality tests applicable to these relaxed models through two complementary approaches. Exact methods were implemented, utilising the complete set of observed statistical data to assess non-classical behaviour.

Additionally, corrections to standard Bell and steering inequalities were derived, providing alternative means of evaluating non-classicality in the presence of signalling. This dual approach enables robust analysis across diverse experimental scenarios. Demonstration of these methods involved two specific cases exhibiting apparent signalling: data obtained from an IBM quantum processor and post-selected data originating from inefficient detectors.

In the quantum processor scenario, researchers analysed correlations to quantify deviations from the no-signalling principle. For post-selected data, the study examined how detector inefficiencies introduce signalling effects and how these can be accounted for within the extended theoretical framework.

Operationally, a “signalling budget” was estimated from observed changes in local marginals across measurement settings in Bell tests. In EPR steering, signalling was quantified by assessing how accurately one party could predict the other’s measurement choice from their reduced states. Geometrically, these figures of merit define the distance of observed data from the no-signalling subspace, providing a visual representation of the degree of signalling present. This geometric interpretation connects the operational quantification of signalling to the underlying theoretical model.

Signalling probability and steering robustness variation with state preparation number and visibility

Researchers observed signalling probabilities ranging from 0.3458 to 0.5040, dependent on the number of initial state preparations and visibility settings. Specifically, with 10 state preparations and a visibility of 0.8, the guessing probability reached 0.5040, while at a visibility of 1.0, it was 0.4468.

Increasing the number of preparations to 600 yielded values of 0.3509 and 0.3721 for visibilities of 0.8 and 1.0 respectively. Further increasing preparations to 2500 resulted in guessing probabilities of 0.3599 and 0.3563, and at 10000 preparations, the values were 0.3748 and 0.3645. Steering signalling robustness values were also calculated, ranging from 0.0264 to 0.4226 across the same parameter space.

For 10 preparations and visibility 0.8, the steering signalling robustness was 0.0264, increasing to 0.0776 at visibility 1.0. At 600 preparations, these values became 0.0158 and 0.0603, and at 2500 preparations, 0.0292 and 0.0905. Finally, with 10000 preparations, the robustness values were 0.0499 and 0.1605 for visibilities 0.8 and 1.0 respectively.

Experiments utilising the ibm_brisbane backend, an Eagle r3 family processor with 127 superconducting transmon qubits, were central to these measurements. Analysis of post-selected Bell experiments revealed that the CHSH parameter could exceed the Tsirelson bound of 2√2 when detection efficiencies differed.

Specifically, the CHSH parameter, calculated as 2(η40 + 16√2η1η30 −2η21η20 + 16√2η31η0 + η41) / (η40 + 12η1η30 + 6η21η20 + 12η31η0 + η41), demonstrated values exceeding this bound under certain conditions. The study connected these signalling effects to potential systematic sources arising from hardware imperfections.

Bounded signalling and classical model enlargement for Bell and steering scenarios

Researchers have developed a framework for analysing Bell and EPR experiments where data exhibits small but measurable signalling. This approach extends local hidden variable and local hidden state models to accommodate bounded signalling, creating enlarged classical sets that can still be tested using established criteria.

Compatibility with these bounded-signalling models is determined through linear programming, allowing for the creation of tailored Bell inequalities and analytical corrections to standard inequalities. The methodology quantifies signalling through the guessing probability of a measurement choice and translates this into an inflation of the unsteerable set of quantum states.

Demonstrations included adjustments to linear steering inequalities, including those for high-dimensional steering, and the development of a semi-definite programming method for constructing optimal steering witnesses using data from a multi-qubit circuit on IBM quantum hardware. This work highlights the necessity of accounting for apparent signalling in experimental data, although it acknowledges that introducing assumptions to allow for signalling is distinct from rigorously enforcing the no-signalling principle fundamental to device-independent quantum information applications.

The authors note that accounting for signalling requires additional assumptions about the experiment’s ontology, which are not on par with the fundamental nature of a Bell test. Future research should focus on developing tests that rigorously satisfy the no-signalling requirement for truly device-independent applications. This research was supported by grants from the Swedish Research Council, the Wallenberg Initiative on Networks and Quantum Information, the Swiss National Science Foundation, and CAPES/PRINT and CAPES/PROEX in Brazil.