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arXiv:1212.2019 · Physical Review A

Testing nonlocality of a single photon without a shared reference frame

Jonatan Bohr Brask, Rafael Chaves, Nicolas Brunner

Published Jul 15, 2013• 32 citations
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Abstract

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.

DOI
10.1103/physreva.88.012111

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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.
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.
Entanglement does not always require one particle per party. It was predicted some thirty years ago that a single photon traversing a beam splitter could violate a Bell inequality. Although initially debated, single-photon nonlocality was eventually demonstrated via homodyne measurements. Here, we present an alternate realisation that avoids the complexity of homodyne measurements and potential loopholes in their implementation. We violate a Bell inequality by performing joint measurements on two copies of the same single-photon entangled state, where one photon acts as a phase reference for the other, making it self-referential. We observe CHSH parameters of 2.71±0.092.71\pm 0.092.71±0.09 and 2.23±0.072.23\pm 0.072.23±0.07, depending on the joint measurements implemented. This offers a new perspective on single-photon nonlocality and a more accessible experimental route, potentially applicable to general mode-entangled states in diverse platforms.
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.
Recently, much interest has been directed toward designing setups that achieve realistic loss thresholds for decisive tests of local realism---in particular in the optical regime. We analyze the feasibility of such Bell tests based on a WWW state shared between multiple parties, which can be realized, for example, by a single photon shared between spatial modes. We develop a general error model to obtain thresholds for the efficiencies required to violate local realism and also consider two concrete optical-measurement schemes.
Simply and reliably detecting and quantifying entanglement outside laboratory conditions will be essential for future quantum information technologies. Here we address this issue by proposing a method for generating expressions which can perform this task between two parties who do not share a common reference frame. These reference-frame-independent expressions require only simple local measurements, which allows us to experimentally test them using an off-the-shelf entangled photon source. We show that the values of these expressions provide bounds on the concurrence of the state and demonstrate experimentally that these bounds are more reliable than values obtained from state tomography since characterizing experimental errors is easier in our setting. Furthermore, we apply this idea to other quantities, such as the Renyi and von Neumann entropies, which are also more reliably calculated directly from the raw data than from a tomographically reconstructed state. This highlights the relevance of our approach for practical quantum information applications that require entanglement.
Nonclassical correlations arising in complex quantum networks are attracting growing interest, both from a fundamental perspective and for potential applications in information processing. In particular, in an entanglement swapping scenario a new kind of correlations arise, the so-called nonbilocal correlations that are incompatible with local realism augmented with the assumption that the sources of states used in the experiment are independent. In practice, however, bilocality tests impose strict constraints on the experimental setup and in particular to the presence of shared reference frames between the parties. Here, we experimentally address this point showing that false positive nonbilocal quantum correlations can be observed even though the sources of states are independent. To overcome this problem, we propose and demonstrate a scheme for the violation of bilocality that does not require shared reference frames and thus constitutes an important building block for future investigations of quantum correlations in complex networks.