Local realism is the worldview in which physical properties of objects exist independently of measurement and where physical influences cannot travel faster than the speed of light. Bell's theorem states that this worldview is incompatible with the predictions of quantum mechanics, as is expressed in Bell's inequalities. Previous experiments convincingly supported the quantum predictions. Yet, every experiment requires assumptions that provide loopholes for a local realist explanation. Here, we report a Bell test that closes the most significant of these loopholes simultaneously. Using a well-optimized source of entangled photons, rapid setting generation, and highly efficient superconducting detectors, we observe a violation of a Bell inequality with high statistical significance. The purely statistical probability of our results to occur under local realism does not exceed 3.74 × 10 −31 , corresponding to an 11.5 standard deviation effect.

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. Introduction:In 1935, Einstein, Podolsky, and Rosen (EPR) (1) argued that quantum mechanics is incomplete when assuming that no physical influence can be faster than the speed of light and that properties of physical systems are elements of reality. They considered measurements on spatially separated pairs of entangled particles. Measurement on one particle of an entangled pair projects the other instantly on a well-defined state, independent of their spatial separation. In 1964, Bell (2) showed that no local realistic theory can reproduce all quantum mechanical predictions for entangled states. His renowned Bell inequality proved that there is an upper limit to the strength of the observed correlations predicted by local realistic theories. Quantum theory's predictions violate this limit.

The quantum internet is predicted to be the next-generation information processing platform, promising secure communication and an exponential speed-up in distributed computation. The distribution of single qubits over large distances via quantum teleportation is a key ingredient for realizing such a global platform. By using quantum teleportation, unknown quantum states can be transferred over arbitrary distances to a party whose location is unknown. Since the first experimental demonstrations of quantum teleportation of independent external qubits, an internal qubit and squeezed states, researchers have progressively extended the communication distance. Usually this occurs without active feed-forward of the classical Bell-state measurement result, which is an essential ingredient in future applications such as communication between quantum computers. The benchmark for a global quantum internet is quantum teleportation of independent qubits over a free-space link whose attenuation corresponds to the path between a satellite and a ground station. Here we report such an experiment, using active feed-forward in real time. The experiment uses two free-space optical links, quantum and classical, over 143 kilometres between the two Canary Islands of La Palma and Tenerife. To achieve this, we combine advanced techniques involving a frequency-uncorrelated polarization-entangled photon pair source, ultra-low-noise single-photon detectors and entanglement-assisted clock synchronization. The average teleported state fidelity is well beyond the classical limit of two-thirds. Furthermore, we confirm the quality of the quantum teleportation procedure without feed-forward by complete quantum process tomography. Our experiment verifies the maturity and applicability of such technologies in real-world scenarios, in particular for future satellite-based quantum teleportation.

In 1985, Leggett and Garg put forward the concept of macroscopic realism (macrorealism) and, in analogy to Bell's theorem, derived a necessary condition in terms of inequalities, which are now known as the Leggett-Garg inequalities. In this paper, we discuss another necessary condition called no-signaling in time. It solely bases on comparing the probability distribution for a macrovariable at some time for the cases where previously a measurement has or has not been performed. Although the concept is analogous to the no-signaling condition in the case of Bell tests, it can be violated according to quantum mechanical predictions even in situations where no violation of Leggett-Garg inequalities is possible.

Conceptually different from the decoherence program, we present a novel theoretical approach to macroscopic realism and classical physics within quantum theory. It focuses on the limits of observability of quantum effects of macroscopic objects, i.e., on the required precision of our measurement apparatuses such that quantum phenomena can still be observed. First, we demonstrate that for unrestricted measurement accuracy, no classical description is possible for arbitrarily large systems. Then we show for a certain time evolution that under coarse-grained measurements, not only macrorealism but even classical Newtonian laws emerge out of the Schrödinger equation and the projection postulate.

Bell's theorem shows that local realistic theories place strong restrictions on observable correlations between different systems, giving rise to Bell's inequality which can be violated in experiments using entangled quantum states. Bell's theorem is based on the assumptions of realism, locality, and the freedom to choose between measurement settings. In experimental tests, "loopholes" arise which allow observed violations to still be explained by local realistic theories. Violating Bell's inequality while simultaneously closing all such loopholes is one of the most significant still open challenges in fundamental physics today. In this paper, we present an experiment that violates Bell's inequality while simultaneously closing the locality loophole and addressing the freedom-of-choice loophole, also closing the latter within a reasonable set of assumptions. We also explain that the locality and freedom-of-choice loopholes can be closed only within non-determinism, i.e. in the context of stochastic local realism.Comment: 12 pages, 3 figures, 2 tables, published online before print: http://www.pnas.org/content/early/2010/10/29/1002780107.abstrac

Motivated by the question, which kind of physical interactions and processes are needed for the production of quantum entanglement, Peres has put forward the radical idea of delayed-choice entanglement swapping.There, entanglement can be "produced a posteriori, after the entangled particles have been measured and may no longer exist." In this work we report the first realization of Peres' gedanken experiment. Using four photons, we can actively delay the choice of measurement -implemented via a high-speed tunable bipartite state analyzer and a quantum random number generator -on two of the photons into the time-like future of the registration of the other two photons. This effectively projects the two already registered photons onto one definite of two mutually exclusive quantum states in which either the photons are entangled (quantum correlations) or separable (classical correlations). This can also be viewed as "quantum steering into the past".In the entanglement swapping 1-3 procedure, two pairs of entangled photons are produced, and one photon from each pair is sent to Victor. The two other photons from each pair are sent to Alice and Bob, respectively. If Victor projects his two photons onto an entangled state, Alice's and Bob's photons are entangled although they have never interacted or shared any common past. What might be considered as even more puzzling is Peres' idea of "delayed-choice for entanglement swapping" 4,5 . In this gedanken experiment, Victor is free to choose either to project his two photons onto an entangled state and thus project Alice's and Bob's photons onto an entangled state, or to measure them individually and then project Alice's and Bob's photons onto a separable state. If Alice and Bob measure their photons' polarization states before Victor makes his choice and projects his two photons either onto an entangled state or onto a separable state, it implies that whether their two photons are entangled (showing quantum correlations) or separable (showing classical correlations) can be defined after they have been measured.In order to experimentally realize Peres' gedanken experiment, we place Victor's choice and measurement in the time-like future of Alice's and Bob's measurements, providing a "delayed-choice" configuration in any and all reference frames. This is accomplished by (1) proper optical delays for Victor's photons and (2) a high-speed tunable bipartite state analyzer, which (3) is controlled in real time by a quantum random number generator (QRNG) 6 . Both delay and randomness are needed to avoid the possibility that the photon pairs can "know" in advance which setting will be implemented after they are registered and can behave accordingly by producing , illustrated by a Mach-Zehnder interferometer. In Bohr's gedanken experiment, he illustrated the complementarity principle, one of the most basic principles of quantum mechanics, with a double-slit apparatus. If both slits are open, the input quantum system exhibits "wave-like" behavior and shows interference on the...

Bell's theorem states that some predictions of quantum mechanics cannot be reproduced by a localrealist theory. That conflict is expressed by Bell's inequality, which is usually derived under the assumption that there are no statistical correlations between the choices of measurement settings and anything else that can causally affect the measurement outcomes. In previous experiments, this "freedom of choice" was addressed by ensuring that selection of measurement settings via conventional "quantum random number generators" was spacelike separated from the entangled particle creation. This, however, left open the possibility that an unknown cause affected both the setting choices and measurement outcomes as recently as mere microseconds before each experimental trial. Here we report on a new experimental test of Bell's inequality that, for the first time, uses distant astronomical sources as "cosmic setting generators." In our tests with polarization-entangled photons, measurement settings were chosen using real-time observations of Milky Way stars while simultaneously ensuring locality. Assuming fair sampling for all detected photons, and that each stellar photon's color was set at emission, we observe statistically significant ≳7.31σ and ≳11.93σ violations of Bell's inequality with estimated p values of ≲1.8 × 10 −13 and ≲4.0 × 10 −33 , respectively, thereby pushing back by ∼600 years the most recent time by which any local-realist influences could have engineered the observed Bell violation.