This Colloquium examines the field of the Einstein, Podolsky, and Rosen ͑EPR͒ gedanken experiment, from the original paper of Einstein, Podolsky, and Rosen, through to modern theoretical proposals of how to realize both the continuous-variable and discrete versions of the EPR paradox. The relationship with entanglement and Bell's theorem are analyzed, and the progress to date towards experimental confirmation of the EPR paradox is summarized, with a detailed treatment of the continuous-variable paradox in laser-based experiments. Practical techniques covered include continuous-wave parametric amplifier and optical fiber quantum soliton experiments. Current proposals for extending EPR experiments to massive-particle systems are discussed, including spin squeezing, atomic position entanglement, and quadrature entanglement in ultracold atoms. Finally, applications of this technology to quantum key distribution, quantum teleportation, and entanglement swapping are examined.

Quantum information science attempts to exploit capabilities from the quantum realm to accomplish tasks that are otherwise impossible in the classical domain. Although sufficient conditions have been formulated for the physical resources required to achieve quantum computation and communication, there is a growing understanding of the power of quantum measurement combined with the conditional evolution of quantum states for accomplishing diverse tasks in quantum information science. For example, a protocol has recently been developed for the realization of scalable long-distance quantum communication and the distribution of entanglement over quantum networks. Here we report the first enabling step in the realization of this protocol, namely the observation of quantum correlations for photon pairs generated in the collective emission from an atomic ensemble. The nonclassical character of the fields is demonstrated by the violation of an inequality involving their normalized correlation functions. Compared to previous investigations of non-classical correlations for photon pairs produced in atomic cascades and in parametric down-conversion, our experiment is distinct in that the correlated photons are separated by a programmable time interval (of about 400 nanoseconds in our initial experiments).

Over the past decade, strong interactions of light and matter at the single-photon level have enabled a wide set of scientific advances in quantum optics and quantum information science. This work has been performed principally within the setting of cavity quantum electrodynamics with diverse physical systems, including single atoms in Fabry-Perot resonators, quantum dots coupled to micropillars and photonic bandgap cavities and Cooper pairs interacting with superconducting resonators. Experiments with single, localized atoms have been at the forefront of these advances with the use of optical resonators in high-finesse Fabry-Perot configurations. As a result of the extreme technical challenges involved in further improving the multilayer dielectric mirror coatings of these resonators and in scaling to large numbers of devices, there has been increased interest in the development of alternative microcavity systems. Here we show strong coupling between individual caesium atoms and the fields of a high-quality toroidal microresonator. From observations of transit events for single atoms falling through the resonator's evanescent field, we determine the coherent coupling rate for interactions near the surface of the resonator. We develop a theoretical model to quantify our observations, demonstrating that strong coupling is achieved, with the rate of coherent coupling exceeding the dissipative rates of the atom and the cavity. Our work opens the way for investigations of optical processes with single atoms and photons in lithographically fabricated microresonators. Applications include the implementation of quantum networks, scalable quantum logic with photons, and quantum information processing on atom chips.

We propose a new coherent state quantum key distribution protocol that eliminates the need to randomly switch between measurement bases. This protocol provides significantly higher secret key rates with increased bandwidths than previous schemes that only make single quadrature measurements. It also offers the further advantage of simplicity compared to all previous protocols which, to date, have relied on switching.

Quantum metrology provides a route to overcome practical limits in sensing devices. It holds particular relevance to biology, where sensitivity and resolution constraints restrict applications both in fundamental biophysics and in medicine. Here, we review quantum metrology from this biological context, focussing on optical techniques due to their particular relevance for biological imaging, sensing, and stimulation. Our understanding of quantum mechanics has already enabled important applications in biology, including positron emission tomography (PET) with entangled photons, magnetic resonance imaging (MRI) using nuclear magnetic resonance, and bio-magnetic imaging with superconducting quantum interference devices (SQUIDs). In quantum metrology an even greater range of applications arise from the ability to not just understand, but to engineer, coherence and correlations at the quantum level. In the past few years, quite dramatic progress has been seen in applying these ideas into biological systems. Capabilities that have been demonstrated include enhanced sensitivity and resolution, immunity to imaging artifacts and technical noise, and characterisation of the biological response to light at the single-photon level. New quantum measurement techniques offer even greater promise, raising the prospect for improved multi-photon microscopy and magnetic imaging, among many other possible applications. Realization of this potential will require cross-disciplinary input from researchers in both biology and quantum physics. In this review we seek to communicate the developments of quantum metrology in a way that is accessible to biologists and biophysicists, while providing sufficient detail to allow the interested reader to obtain a solid understanding of the field. We further seek to introduce quantum physicists to some of the central challenges of optical measurements in biological science. We hope that this will aid in bridging the communication gap that exists between the fields, and thereby guide the future development of this multidisciplinary research area.

Quantum noise places a fundamental limit on the per photon sensitivity attainable in optical measurements. This limit is of particular importance in biological measurements, where the optical power must be constrained to avoid damage to the specimen. By using non-classically correlated light, we demonstrated that the quantum limit can be surpassed in biological measurements. Quantum enhanced microrheology was performed within yeast cells by tracking naturally occurring lipid granules with sensitivity 2.4 dB beyond the quantum noise limit. The viscoelastic properties of the cytoplasm could thereby be determined with a 64% improved measurement rate. This demonstration paves the way to apply quantum resources broadly in a biological context

We demonstrate a multipartite protocol to securely distribute and reconstruct a quantum state. A secret quantum state is encoded into a tripartite entangled state and distributed to three players. By collaborating, any two of the three players can reconstruct the state, while individual players obtain nothing. We characterize this (2,3) threshold quantum state sharing scheme in terms of fidelity, signal transfer, and reconstruction noise. We demonstrate a fidelity averaged over all reconstruction permutations of 0.73+/-0.04, a level achievable only using quantum resources.

We report the experimental demonstration of quantum teleportation of the quadrature amplitudes of a light field. Our experiment was stably locked for long periods, and was analyzed in terms of fidelity, F; and with signal transfer, Tq = T + + T − , and noise correlation, Vq = V + in|out V − in|out . We observed an optimum fidelity of 0.64 ± 0.02, Tq = 1.06 ± 0.02 and Vq = 0.96 ± 0.10. We discuss the significance of both Tq > 1 and Vq < 1 and their relation to the teleportation no-cloning limit. PACS numbers: 42.50Dv, 42.65Yj, 03.67Hk, 03.65Ud Quantum teleportation [1] is a key quantum information technology both in terms of communicating [2] and processing [3] quantum information. Experimental demonstrations of teleportation have so far fallen into three main categories: teleportation of photon states [4]; of ensemble properties in liquid NMR [5]; and of optical field states [6]. An important feature of the technique used in the optical field state experiment of Furusawa et al. [6] is its high efficiency. This results in the ability to faithfully teleport arbitrary input states continuously. This is due to the in principle ability to perform the required joint measurements exactly and the technical maturity of optical field detection. In contrast, the efficiency of single photon experiments is presently restricted in principle due to the inability to identify all four Bell states, and also in practice by the low efficiency of single photon production and detection.Since the Furusawa et al. experiment there have been many proposals for how quantum teleportation may be repeated using different systems [7,8,9]; applied to different input states [10,11]; generalized to multi-party situations [12]; and more comprehensively characterized [13,14]. In spite of the considerable interest, to date no new experiment has been performed [15]. This paper reports the quantum teleportation of the quadrature amplitudes of a light beam. Our scheme has a number of notable differences to the previously published experiment. The input and output states are both analyzed by the same homodyne detector, allowing a more consistent evaluation of their properties. Our experiment is based on a Nd:YAG laser that produces two squeezed beams in two independently pumped optical parametric amplifiers (OPAs). We use a more compact configuration for Alice's measurements. Finally, the encoding and decoding of the input and output signals using a total of 4 independent modulators. This allows us to completely span the phase space of the input state.We analyze our results using the fidelity, F , between the input and output states, and also with signal transfer (T q ) and noise correlation (V q ) in a manner analogous to QND analysis [7] (which we refer to as the T-V measure henceforth). This enables us to give a more detailed characterization of the performance of our teleporter.Teleportation is usually described as the disembodied transportation of an unknown quantum state from one place (Alice) to another (Bob). In our experiment, as in ref.[6],...