Quantum computers are unnecessary for exponentially-efficient computation or simulation if the Extended Church-Turing thesis---a foundational tenet of computer science---is correct. The thesis would be directly contradicted by a physical device that efficiently performs a task believed to be intractable for classical computers. Such a task is BosonSampling: obtaining a distribution of n bosons scattered by some linear-optical unitary process. Here we test the central premise of BosonSampling, experimentally verifying that the amplitudes of 3-photon scattering processes are given by the permanents of submatrices generated from a unitary describing a 6-mode integrated optical circuit. We find the protocol to be robust, working even with the unavoidable effects of photon loss, non-ideal sources, and imperfect detection. Strong evidence against the Extended Church-Turing thesis will come from scaling to large numbers of photons, which is a much simpler task than building a universal quantum computer.Comment: See also Crespi et al., arXiv:1212.2783; Spring et al., arXiv:1212.2622; and Tillmann et al., arXiv:1212.224

Topological phases exhibit some of the most striking phenomena in modern physics. much of the rich behaviour of quantum Hall systems, topological insulators, and topological superconductors can be traced to the existence of robust bound states at interfaces between different topological phases. This robustness has applications in metrology and holds promise for future uses in quantum computing. Engineered quantum systems-notably in photonics, where wavefunctions can be observed directly-provide versatile platforms for creating and probing a variety of topological phases. Here we use photonic quantum walks to observe bound states between systems with different bulk topological properties and demonstrate their robustness to perturbations-a signature of topological protection. Although such bound states are usually discussed for static (time-independent) systems, here we demonstrate their existence in an explicitly time-dependent situation. moreover, we discover a new phenomenon: a topologically protected pair of bound states unique to periodically driven systems.

Quantum walks have a host of applications, ranging from quantum computing to the simulation of biological systems. We present an intrinsically stable, deterministic implementation of discrete quantum walks with single photons in space. The number of optical elements required scales linearly with the number of steps. We measure walks with up to 6 steps and explore the quantum-to-classical transition by introducing tunable decoherence. Finally, we also investigate the effect of absorbing boundaries and show that decoherence significantly affects the probability of absorption.

We demonstrate a wavelength-tunable, fiber-coupled source of polarization- entangled photons with extremely high spectral brightness and quality of entanglement. Using a 25 mm PPKTP crystal inside a polarization Sagnac interferometer we detect a spectral brightness of 273000 pairs (s mW nm)(-1), a factor of 28 better than comparable previous sources while state tomography showed the two-photon state to have a tangle of T = 0.987. This improvement was achieved by use of a long crystal, careful selection of focusing parameters and single-mode fiber coupling. We demonstrate that, due to the particular geometry of the setup, the signal and idler wavelengths can be tuned over a wide range without loss of entanglement.

The resources required to characterize the dynamics of engineered quantum systems-such as quantum computers and quantum sensors-grow exponentially with system size. Here we adapt techniques from compressive sensing to exponentially reduce the experimental configurations required for quantum process tomography. Our method is applicable to processes that are nearly sparse in a certain basis and can be implemented using only single-body preparations and measurements. We perform efficient, highfidelity estimation of process matrices of a photonic two-qubit logic gate. The database is obtained under various decoherence strengths. Our technique is both accurate and noise robust, thus removing a key roadblock to the development and scaling of quantum technologies. Understanding and controlling the world at the nanoscale-be it in biological, chemical or physical phenomena-requires quantum mechanics. It is therefore essential to characterize and monitor realistic complex quantum systems that inevitably interact with typically uncontrollable environments. One of the most general descriptions of the dynamics of an open quantum system is a quantum map-typically represented by a process matrix [1]. Methods to identify this matrix are collectively known as quantum process tomography (QPT) [1,2]. For a d-dimensional quantum system, they require Oðd 4 Þ experimental configurations: combinations of input states, on which the process acts, and a set of output observables. For a system of n qubits-two level quantum systemsd ¼ 2 n . The required physical resources hence scale exponentially with system size. Recently, a number of alternative methods have been developed for efficient and selective estimation of quantum processes [3]. However, full characterization of quantum dynamics of comparably small systems, such as an 8-qubit ion trap [4], would still require over a billion experimental configurations, clearly impractical. So far, process tomography has therefore been limited by experimental and off-line computational resources, to systems of 2 and 3 qubits [5][6][7].Here we adapt techniques from compressive sensing to develop an experimentally efficient method for QPT. It requires only Oðs logdÞ configurations if the process matrix is s compressible in some known basis, i.e., it is nearly sparse in that it can be well approximated by an s-sparse process matrix. This is usually the case, because engineered quantum systems aim to implement a unitary process which is maximally sparse in its eigenbasis. In practice, as observed in liquid-state NMR [8], photonics [5,9,10], ion traps [11], and superconducting circuits [6], a near-unitary process will still be nearly sparse in this basis, and still compressible. The near sparsity is due to few dominant system environment interactions. This is more apparent for weakly decohering systems [12].We experimentally demonstrate our algorithm by estimating the 240 real parameters of the process matrix of a canonical photonic two-qubit gate, Fig. 1, from a reduced number of configurations. From...

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

Quantum steering allows two parties to verify shared entanglement even if one measurement device is untrusted. A conclusive demonstration of steering through the violation of a steering inequality is of considerable fundamental interest and opens up applications in quantum communication. To date, all experimental tests with single-photon states have relied on post selection, allowing untrusted devices to cheat by hiding unfavourable events in losses. Here we close this 'detection loophole' by combining a highly efficient source of entangled photon pairs with superconducting transition-edge sensors. We achieve an unprecedented ∼62% conditional detection efficiency of entangled photons and violate a steering inequality with the minimal number of measurement settings by 48 s.d.s. Our results provide a clear path to practical applications of steering and to a photonic loophole-free Bell test.

Quantum entanglement enables tasks not possible in classical physics. Many quantum communication protocols [1] require the distribution of entangled states between distant parties. Here we experimentally demonstrate the successful transmission of an entangled photon pair over a 144 km free-space link. The received entangled states have excellent, noise-limited fidelity, even though they are exposed to extreme attenuation dominated by turbulent atmospheric effects. The total channel loss of 64 dB corresponds to the estimated attenuation regime for a two-photon satellite quantum communication scenario. We confirm that the received two-photon states are still highly entangled by violating the CHSH inequality by more than 5 standard deviations. From a fundamental point of view, our results show that the photons are subject to virtually no decoherence during their 0.5 ms long flight through air, which is encouraging for future world-wide quantum communication scenarios.Entanglement is at the heart of many peculiarities encountered in quantum mechanics and has allowed many ground-breaking tests on the fundamentals of nature. Entangled photons are ideal tools to investigate the laws of quantum mechanics over long distances and timescales since they are not subject to decoherence. Furthermore photons can be easily generated, manipulated and transmitted over large distances via optical fibres or free-space links. Since the maximal distance for the distribution of quantum entanglement in optical fibres is limited to the order [2, 3, 4, 5] of ∼ 100 km, the most promising option for testing quantum entanglement on a global scale is currently free-space transmission, ultimately using satellites and ground stations [6].In recent years, various free-space quantum communication experiments with weak coherent laser pulses [7,8,9,10,11] and entangled photons [12,13,14,15] have been performed on ever larger distance scales and with increasing bit rates. The to-date most advanced test bed for free-space distribution of entanglement is a 144 km free-space link between two Canary Islands, where the successful transmission of one photon of an entangled pair was recently achieved [16]. In the present experiment we demonstrate a fundamentally more interesting scenario by sending both photons of an entangled pair over this free-space channel. By violating a Clauser-HorneShimony-Holt (CHSH) Bell inequality [17] we find that entanglement is highly stable over these long time spans -the photon-pair flight time of ∼ 0.5 ms is the longest lifetime of photonic Bell states reported so far, almost twice as long as the previous high [4,5] of ∼ 250 µs.The achieved noise-limited fidelity paves the way for free-space implementations of quantum communication protocols that require the transmission of two photons, e.g. quantum dense coding [18], entanglement purification [19], quantum teleportation [20] and quantum key distribution without a shared reference frame [21]. From a technological perspective, the overall two-photon loss bridged in our exper...