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arXiv:1111.1853 · Scientific Reports

Guaranteed violation of a Bell inequality without aligned reference frames or calibrated devices

Peter Shadbolt, Tamás Vértesi, Yeong-Cherng Liang, Cyril Branciard, Nicolas Brunner, Jeremy L. O’Brien

Published Jun 25, 2012• 80 citations
arXivHTMLPDF

Abstract

Bell tests - the experimental demonstration of a Bell inequality violation - are central to understanding the foundations of quantum mechanics, and are a powerful diagnostic tool for the development of quantum technologies. To date, Bell tests have relied on careful calibration of measurement devices and alignment of a shared reference frame between two parties - both technically demanding tasks. We show that neither of these operations are necessary, violating Bell inequalities (i) with certainty using unaligned, but calibrated, measurement devices, and (ii) with near-certainty using uncalibrated and unaligned devices. We demonstrate generic quantum nonlocality with randomly chosen measurements on a singlet state of two photons, implemented using a reconfigurable integrated optical waveguide circuit. The observed results demonstrate the robustness of our schemes to imperfections and statistical noise. This approach is likely to have important applications both in fundamental science and quantum technologies, including device-independent quantum key distribution.

DOI
10.1038/srep00470

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Bell tests - the experimental demonstration of a Bell inequality violation - are central to understanding the foundations of quantum mechanics, and are a powerful diagnostic tool for the development of quantum technologies. To date, Bell tests have relied on careful calibration of measurement devices and alignment of a shared reference frame between two parties - both technically demanding tasks. We show that neither of these operations are necessary, violating Bell inequalities (i) with certainty using unaligned, but calibrated, measurement devices, and (ii) with near-certainty using uncalibrated and unaligned devices. We demonstrate generic quantum nonlocality with randomly chosen measurements on a singlet state of two photons, implemented using a reconfigurable integrated optical waveguide circuit. The observed results demonstrate the robustness of our schemes to imperfections and statistical noise. This approach is likely to have important applications both in fundamental science and quantum technologies, including device-independent quantum key distribution.
The question of testing the nonlocality of a single photon has raised much debate over the last years. The controversy is intimately related to the issue of providing a common reference frame for the observers to perform their local measurements. Here we address this point by presenting a simple scheme for demonstrating the nonlocality of a single photon which does not require a shared reference frame. Specifically, Bell inequality violation can be obtained with certainty with unaligned devices, even if the relative frame fluctuates between each experimental run of the Bell test. Our scheme appears feasible with current technology and may simplify the realization of quantum communication protocols based on single-photon entanglement.
We experimentally demonstrate, using qubits encoded in photon polarization, that two parties who share a single reference direction and use locally orthogonal measurements will always violate a Bell inequality, up to experimental deficiencies. This contrasts with the standard view of Bell inequalities, in which the parties need to completely align their measurements. Furthermore, we experimentally demonstrate that as the reference direction degrades the probability of the observers randomly choosing measurements that violate a Bell inequality decreases gradually and smoothly to 39.739.7%\ifmmode\pm\else\textpm\fi{}0.1%39.7 in the limiting case that the observers do not share a reference direction. This result promises simplified distribution of entanglement between separated parties, with applications in fundamental investigations of quantum physics and tasks such as quantum communication.
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The observation that violating Bell inequalities with high probability is possible even when the local measurements are randomly chosen, as occurs when local measurements cannot be suitably calibrated or the parties do not share a common reference frame, has recently attracted much theoretical and experimental effort. Here we show that this observation is only valid when the overall detection efficiency is very high ($\ensuremath{\eta}\ensuremath{\ge}0.90$), otherwise, even when using the highest detection efficiency of recent photonic Bell tests, the probability of demonstrating nonlocality is negligible (e.g., it is smaller than 0.020.02%0.02 for $\ensuremath{\eta}=0.785$). Our results show that detection efficiency is a much more critical resource for real-world applications than it was previously thought.
Over the past few decades, experimental tests of Bell-type inequalities have been at the forefront of understanding quantum mechanics and its implications. These strong bounds on specific measurements on a physical system originate from some of the most fundamental concepts of classical physics-in particular that properties of an object are well-defined independent of measurements (realism) and only affected by local interactions (locality). The violation of these bounds unambiguously shows that the measured system does not behave classically, void of any assumption on the validity of quantum theory. It has also found applications in quantum technologies for certifying the suitability of devices for generating quantum randomness, distributing secret keys and for quantum computing. Here we report on the violation of a Bell inequality involving a massive, macroscopic mechanical system. We create light-matter entanglement between the vibrational motion of two silicon optomechanical oscillators, each comprising approx. 10^{10} atoms, and two optical modes. This state allows us to violate a Bell inequality by more than 4 standard deviations, directly confirming the nonclassical behavior of our optomechanical system under the fair sampling assumption.
We examine the problem of exhibiting Bell nonlocality for a two-qudit entangled pure state using a randomly chosen set of mutually unbiased bases (MUBs). Interestingly, even if we employ only two-setting Bell inequalities, we find a significant chance of obtaining a Bell violation if the two parties are individually allowed to measure a sufficient number of MUBs. In particular, for the case of maximally entangled qutrits and ququarts, our numerical estimates indicate that we can obtain near-guaranteed Bell violation by considering only such Bell inequalities. The case of maximally entangled ququints is similar, albeit the chance of ending up with a successful trial decreases somewhat to approximately 99.8499.84%99.84. Upon a closer inspection, we find that even all these no-violation instances violate some more-setting Bell inequalities. These results suggest that the experimental tests of Bell nonlocality for these higher-dimensional entangled states remain viable even if the two parties do not share a common reference frame.