Highly entangled quantum networks cluster states lie at the heart of recent approaches to quantum computing [1,2]. Yet, the current approach for constructing optical quantum networks does so one node at a time [3][4][5], which lacks scalability. Here we demonstrate the singlestep fabrication of a multimode quantum network from the parametric downconversion of femtosecond frequency combs. Ultrafast pulse shaping [6] is employed to characterize the comb's spectral entanglement [7]. Each of the 511 possible bipartitions among ten spectral regions is shown to be entangled; furthermore, an eigenmode decomposition reveals that eight independent quantum channels [8] (qumodes) are subsumed within the comb. This multicolor entanglement imports the classical concept of wavelength-division multiplexing (WDM) to the quantum domain by playing upon frequency entanglement as a means to elevate quantum channel capacity. The quantum frequency comb is easily addressable, robust with respect to decoherence, and scalable, which renders it a unique tool for quantum information.Theoretical Description The use of photonic architectures to realize quantum networks is appealing since photons are immune from environmental disturbances, readily manipulated with classical tools, and subject to high efficiency detection [10,11]. We consider here the creation of nonclassical, continuous variable states with an optical parametric oscillator (OPO), in which a pump photon of frequency 2ω 0 splits into a pair of lower energy photons subject to energy conservation and the cavity resonance condition. The generation of a photon pair initiates a nonclassical correlation between the cavity modes ω −p and ω p , where ω p = ω 0 + p · ω FSR and ω FSR is the cavity free spectral range. Given a sufficiently large phase-matching bandwidth, a frequency comb emerges from the cavity with all of the resonant photon pairs independently entangled [12]. The inclusion of additional pump photons of frequencies 2ω 0 + p · ω FSR opens the possibility for richer frequency correlations beyond purely symmetric pair creation. Femtosecond pulse trains contain upwards of ∼ 10 5 individual frequency modes, and the simultaneous injection of all these modes into a nonlinear optical element induces an intricate network of both symmetric and asymmetric frequency correlations [13]. To access such states, a synchronously pumped optical parametric oscillator (SPOPO), which consists of an OPO driven by a femtosecond pulse train with a repetition rate matching the cavity free spectral range, is exploited and creates correlations governed by the Hamil-where g regulates the overall interaction strength and a † m is the photon creation operator associated with a mode of frequency ω m . The coupling strength between modes at frequencies ω m and ω n is dictated by the matrix L m,n = f m,n · p m+n , where f m,n is the phase-matching function [14,15] and p m,n is the pump spectral amplitude at frequency ω m + ω n [16]. Frequency Entanglement We experimentally demonstrate that the photonic s...

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],...

The measurement sensitivity of the pointing direction of a laser beam is ultimately limited by the quantum nature of light. To reduce this limit, we have experimentally produced a quantum laser pointer, a beam of light whose direction is measured with a precision greater than that possible for a usual laser beam. The laser pointer is generated by combining three different beams in three orthogonal transverse modes, two of them in a squeezed-vacuum state and one in an intense coherent field. The result provides a demonstration of multichannel spatial squeezing, along with its application to the improvement of beam positioning sensitivity and, more generally, to imaging.

We calculate the quantum Cram\'er--Rao bound for the sensitivity with which one or several parameters, encoded in a general single-mode Gaussian state, can be estimated. This includes in particular the interesting case of mixed Gaussian states. We apply the formula to the problems of estimating phase, purity, loss, amplitude, and squeezing. In the case of the simultaneous measurement of several parameters, we provide the full quantum Fisher information matrix. Our results unify previously known partial results, and constitute a complete solution to the problem of knowing the best possible sensitivity of measurements based on a single-mode Gaussian state

Multimode entanglement is an essential resource for quantum information processing and quantum metrology. However, multimode entangled states are generally constructed by targeting a specific graph configuration. This yields to a fixed experimental setup that therefore exhibits reduced versatility and scalability. Here we demonstrate an optical on-demand, reconfigurable multimode entangled state, using an intrinsically multimode quantum resource and a homodyne detection apparatus. Without altering either the initial squeezing source or experimental architecture, we realize the construction of thirteen cluster states of various sizes and connectivities as well as the implementation of a secret sharing protocol. In particular, this system enables the interrogation of quantum correlations and fluctuations for any multimode Gaussian state. This initiates an avenue for implementing on-demand quantum information processing by only adapting the measurement process and not the experimental layout.

Quantum models for synchronously pumped type I optical parametric oscillators (SPOPO) are presented. The study of the dynamics of SPOPOs, which typically involves millions of coupled signal longitudinal modes, is significantly simplified when one considers the "supermodes", which are independent linear superpositions of all the signal modes diagonalizing the parametric interaction. In terms of these supermodes the SPOPO dynamics becomes that of about a hundred of independent, single mode degenerate OPOs, each of them being a squeezer. One derives a general expression for the squeezing spectrum measured in a balanced homodyne detection experiment, valid for any temporal shape of the local oscillator. Realistic cases are then studied using both analytical and numerical methods: the oscillation threshold is derived, and the spectral and temporal shapes of the squeezed supermodes are characterized.

We report the experimental transformation of quadrature entanglement between two optical beams into continuous variable polarization entanglement. We extend the inseparability criterion proposed by Duan et al. [9] to polarization states and use it to quantify the entanglement between the three Stokes operators of the beams. We propose an extension to this scheme utilizing two quadrature entangled pairs for which all three Stokes operators between a pair of beams are entangled. PACS numbers: 42.50.Dv, 42.65.Yj, 03.67.Hk The polarization state of light has been extensively studied in the quantum mechanical regime of single (or few) photons. The demonstration of entanglement of the polarization states of pairs of photons has been of particular interest. This entanglement has facilitated the study of many interesting quantum phenomena such as Bell's inequality [1]. Comparatively, research on continuous variable quantum polarization states has been cursory. Recently, however, interest in the field has increased due to the demonstration of transfer of continuous variable quantum information from optical polarization states to the spin state of atomic ensembles [2]; and to its potential for local oscillator-free continuous variable quantum communication networks. A number of theoretical papers have now been published [3,4], of particular interest is the work of Korolkova et al. [5] which introduces the new concept of continuous variable polarization entanglement, and proposes methods for its generation and characterization. Previous to the work presented here however, only the squeezing of polarization states had been experimentally demonstrated [2,6,7].In this paper we report the experimental transformation of the commonly studied and well understood entanglement between the phase and amplitude quadratures of two beams (quadrature entanglement) [8] onto a polarization basis. Quadrature entanglement can be characterized using the inseparability criterion proposed by Duan et al. [9]. We generalize this criterion to an arbitrary pair of observables and apply it to the Stokes operators that define quantum polarization states. We experimentally generate entanglement of Stokes operators between a pair of beams, satisfying both the inseparability criterion, and the product of conditional variances which is a signature of the EPR paradox [10]. Interacting this entanglement with a pair of distant atomic ensembles could entangle the atomic spin states. We also analyze the polarization state generated by combining two quadrature entangled pairs. We show that if the quadrature entanglement is strong enough to beat a bound √ 3 times lower than that for the inseparability criterion, then all three Stokes operators can be simultaneously entangled.The polarization state of a light beam can be described as a Stokes vector on a Poincaré sphere and is determined by the four Stokes operators [11]:Ŝ 0 represents the beam intensity whereasŜ 1 ,Ŝ 2 , andŜ 3 characterize its polarization and form a cartesian axis system. If the Stokes ve...

Entanglement between large numbers of quantum modes is the quintessential resource for future technologies such as the quantum internet. Conventionally, the generation of multimode entanglement in optics requires complex layouts of beamsplitters and phase shifters in order to transform the input modes into entangled modes. Here we report the highly versatile and efficient generation of various multimode entangled states with the ability to switch between different linear optics networks in real time. By defining our modes to be combinations of different spatial regions of one beam, we may use just one pair of multi-pixel detectors in order to measure multiple entangled modes. We programme virtual networks that are fully equivalent to the physical linear optics networks they are emulating. We present results for N=2 up to N=8 entangled modes here, including N=2, 3, 4 cluster states. Our approach introduces the highly sought after attributes of flexibility and scalability to multimode entanglement.