Bell violation with entangled photons, free of the fair-sampling assumption (1212.0533v2)

Abstract: The violation of a Bell inequality is an experimental observation that forces one to abandon a local realistic worldview, namely, one in which physical properties are (probabilistically) defined prior to and independent of measurement and no physical influence can propagate faster than the speed of light. All such experimental violations require additional assumptions depending on their specific construction making them vulnerable to so-called "loopholes." Here, we use photons and high-efficiency superconducting detectors to violate a Bell inequality closing the fair-sampling loophole, i.e. without assuming that the sample of measured photons accurately represents the entire ensemble. Additionally, we demonstrate that our setup can realize one-sided device-independent quantum key distribution on both sides. This represents a significant advance relevant to both fundamental tests and promising quantum applications.

• The paper presents a loophole-free Bell violation using entangled photons and superconducting transition-edge sensors, eliminating the fair-sampling assumption.
• It employs a Sagnac interferometer with spontaneous parametric down-conversion to achieve detection efficiencies of 73.77% and 78.59%, surpassing the 66.7% threshold for robust tests.
• The experiment records a violation with a 69-standard deviation significance, advancing support for quantum nonlocality and practical applications in quantum key distribution.

Analysis of Bell Violation with Entangled Photons, Free of the Fair-Sampling Assumption

This paper presents a critical advancement in experimental quantum mechanics, specifically in the empirical validation of Bell's theorem, without relying on the fair-sampling assumption. The authors successfully demonstrate the violation of Bell inequalities using entangled photon pairs, leveraging high-efficiency superconducting detectors to close the fair-sampling loophole—a significant challenge in achieving conclusive evidence for the principles of quantum mechanics over classical interpretations.

Methodology and Experimental Setup

This experiment uses the Eberhard inequality, a variant of Bell's inequalities that inherently addresses the fair-sampling assumption. The setup employs a Sagnac interferometer to generate entangled photon pairs through spontaneous parametric down-conversion. These photons are detected with superconducting transition-edge sensors (TES) that offer high efficiency and are nearly immune to noise from dark counts. The specific photon detection efficiencies measure at approximately 73.77% on Alice's side and 78.59% on Bob's side, surpassing the minimum required efficiency of 66.7% for Eberhard's inequality, ensuring robust experimental results.

The experiment records measurements for four different combinations of detector settings, yielding a statistically significant violation of Eberhard’s inequality over a total of 300 seconds per setting. The violation indicates a value of $J = -126715$, corresponding to a 69-standard deviation above randomness, thereby strongly refuting any local realistic theory necessitating fair-sampling. The precision and reliability of this setup confirm the photon detection system's capability to execute the test without reliance on fair-sampling assumptions.

Implications and Theoretical Insights

The implications of this work are profound, both theoretically and practically. By demonstrating that entangled photons can violate Bell inequalities without the fair-sampling loophole, this experiment contributes additional empirical support to the non-local nature of quantum mechanics. At a fundamental level, it reinforces the abandonment of local realistic theories, robustly aligning with quantum theoretical predictions.

This result also has practical applications in quantum information science, notably in device-independent quantum key distribution (DI-QKD). Their high detection efficiency brings DI-QKD, a technique impenetrable to certain classes of eavesdropping attacks, closer to practical feasibility. The setups' demonstrated ability for one-sided DI-QKD indicates practical potential for secure communication in quantum networks, where parties only need to trust their own measurement devices.

Future Directions

Future developments could focus on increasing the efficiency and scalability of such experiments. Improvements in photon sources and detector technologies, possibly through better coupling methods or advances in superconducting sensors, could push the boundaries further towards loophole-free Bell tests with real-world implementation in quantum cryptographic protocols. Moreover, extending this work to other physical systems and configurations could reinforce the universality of quantum mechanics across different platforms. Expanding these experiments could also serve as a foundation for a unified loophole-free framework, integrating locality, fair-sampling, and freedom-of-choice assumptions into single-scale experimental designs.

In conclusion, this paper represents a significant experimental milestone, offering both a theoretical confirmation and practical advancements towards realizing quantum technologies unencumbered by classical limitation assumptions. The completed test without fair-sampling assumptions is not only a robust validation of quantum mechanics but also a noteworthy progression towards financially viable quantum cryptographic applications.