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Random numbers are a basic ingredient of simulation algorithms and cryptography, and play a significant part in computer simulation and information processing. One prominent feature of a squeezed light is its lower fluctuation and more randomness in a pair

Quantum dense coding (QDC) means to transmit two classical bits by only transferring one quantum bit, which has enabled high-capacity information transmission and strengthened system security. Continuousvariable QDC offers a promising solution to increase communication rates while achieving seamless integration with classical communication systems. Here, we propose and experimentally demonstrate a high-speed quantum radio-frequency-over-light (RFoL) communication scheme based on QDC with entangled state, and achieve a practical rate of 20 Mbps through digital modulation and RFoL communication. This scheme bridges the gap between quantum technology and real-world communication systems, which bring QDC closer to practical applications and offer prospects for further enhancement of metropolitan communication networks.

High-performance quantum memory for quantized states of light is a prerequisite building block of quantum information technology. Despite great progresses of optical quantum memories based on interactions of light and atoms, physical features of these memories still cannot satisfy requirements for applications in practical quantum information systems, since all of them suffer from trade-off between memory efficiency and excess noise. Here, we report a high-performance cavity-enhanced electromagnetically-induced-transparency memory with warm atomic cell in which a scheme of optimizing the spatial and temporal modes based on the time-reversal approach is applied. The memory efficiency up to 67% is directly measured and a noise level close to quantum noise limit is simultaneously reached. It has been experimentally demonstrated that the average fidelities for a set of input coherent states with different phases and amplitudes within a Gaussian distribution have exceeded the classical benchmark fidelities. Thus the realized quantum memory platform has been capable of preserving quantized optical states, and is ready to be applied in quantum information systems, such as distributed quantum logic gates and quantum-enhanced atomic magnetometry., Comment: 15 pages,2 figures

High precision interferometers are the building blocks of precision metrology and the ultimate interferometric sensitivity is limited by the quantum noise. Here we propose and experimentally demonstrate a compact quantum interferometer involving two optical parametric amplifiers and the squeezed states generated within the interferometer are directly used for the phase-sensing quantum state. By both squeezing shot noise and amplifying phase-sensing intensity the sensitivity improvement of $4.86\pm 0.24$ dB beyond the standard quantum limit is deterministically realized and a minimum detectable phase smaller than that of all present interferometers under the same phase-sensing intensity is achieved. This interferometric system has significantly potential applications in a variety of measurements for tiny variances of physical quantities., Comment: 6 pages,3 figures

Quantum phase estimation protocols can provide a measuring method of phase shift with precision superior to standard quantum limit (SQL) due to the application of a nonclassical state of light. A squeezed vacuum state, whose variance in one quadrature is lower than the corresponding SQL, has been pointed out a sensitive resource for quantum phase estimation and the estimation accuracy is directly influenced by the properties of the squeezed state. Here we detailedly analyze the influence of the purity and squeezing level of the squeezed state on the accuracy of quantum phase estimation. The maximum precision that can be achieved for a squeezed thermal state is evaluated, and the experimental results are in agreement with the theoretical analyses. It is also found that the width of the phase estimation interval $\Delta \theta $ beyond SQL is correlated with the purity of the squeezed state., Comment: 7 pages, 5 figures

The positivity of the partial transpose is in general only a necessary condition for separability. There exist quantum states that are not separable, but nevertheless are positive under partial transpose. States of this type are known as bound entangled states meaning that these states are entangled but they do not allow distillation of pure entanglement by means of local operations and classical communication (LOCC). We present a parametrization of a class of $2\times 2$ bound entangled Gaussian states for bipartite continuous-variable quantum systems with two modes on each side. We propose an experimental protocol for preparing a particular bound entangled state in quantum optics. We then discuss the robustness properties of this protocol with respect to the occupation number of thermal inputs and the degrees of squeezing., Comment: 10 pages, 2 figures

Using a nondegenerate four-wave mixing (FWM) process based on a double-{\Lambda} scheme in hot cesium vapor, we demonstrate a compact diode-laser-pumped quantum light source for the generation of quantum correlated twin beams with a maximum squeezing of 6.5 dB. The squeezing is observed at a Fourier frequency in the audio band down to 0.7 kHz which, to the best of our knowledge, is the first observation of sub-kilohertz intensity-difference squeezing in an atomic system so far. A phase-matching condition is also investigated in our system, which confirms the spatial-multi-mode characteristics of the FWM process. Our compact low-frequency squeezed light source may find applications in quantum imaging, quantum metrology, and the transfer of optical squeezing onto a matter wave., Comment: 5 pages, 4 figures

The multipartite polarization entangled states of bright optical beams directly associating with the spin states of atomic ensembles are one of the essential resources in the future quantum information networks, which can be conveniently utilized to transfer and convert quantum states across a network composed of many atomic nodes. In this letter, we present the experimental demonstration of tripartite polarization entanglement described by Stokes operators of optical field. The tripartite entangled states of light at the frequency resonant with D1 line of Rubidium atoms are transformed into the continuous variable polarization entanglement among three bright optical beams via an optical beam splitter network. The obtained entanglement is confirmed by the extended criterion for polarization entanglement of multipartite quantized optical modes.

It is crucial for physical realization of quantum information networks to first establish entanglement among multiple space-separated quantum memories and then at a user-controlled moment to transfer the stored entanglement to quantum channels for distribution and conveyance of information. Here we present an experimental demonstration on generation, storage and transfer of deterministic quantum entanglement among three spatially separated atomic ensembles. The off-line prepared multipartite entanglement of optical modes is mapped into three distant atomic ensembles to establish entanglement of atomic spin waves via electromagnetically-induced-transparency light-matter interaction. Then the stored atomic entanglement is transferred into a tripartite quadrature entangled state of light, which is space-separated and can be dynamically allocated to three quantum channels for conveying quantum information. The existence of entanglement among released three optical modes verifies that the system has capacity of preserving multipartite entanglement. The presented protocol can be directly extended to larger quantum networks with more nodes.

Using a nondegenerate four-wave mixing process based on a double-$\Lambda$ scheme in hot cesium vapor, we generate quantum correlated twin beams with a maximum intensity-difference squeezing of 6.5 dB. The substantially improved squeezing can be mainly attributed to very good frequency and phase-difference stability between the pump and probe beams in our experiment. Intensity-difference squeezing can be observed within a wide experimental parameter range, which guarantees its robust generation. Since this scheme produces multi-spatial-mode twin beams at the Cs $D_{1}$ line, it is of interest for experiments involving quantum imaging and coherent interfaces between atomic and solid-state systems., Comment: 6 pages, 5 figures, comments are welcome

Entangled state of light is one of the essential quantum resources in quantum information science and technology. Especially, when the fundamental principle experiments have been achieved in labs and the applications of continuous variable quantum information in the real world are considered, it is crucial to design and construct the generation devices of entangled states with high entanglement and compact configuration. We have designed and built an efficient and compact light source of entangled state, which is a non-degenerate optical parametric amplifier (NOPA) with the triple resonance of the pump and two subharmonic modes. A wedged type-II KTP crystal inside the NOPA is used for implementing frequency-down-conversion of the pump field to generate the optical entangled state and achieving the dispersion compensation between the pump and the subharmonic waves. The EPR entangled state of light with quantum correlations of 8.4 dB for both amplitude and phase quadratures are experimentally produced by a single NOPA under the pump power of 75 mW.

Single-mode squeezing and Fourier transformation operations are two essential logical gates in continuous-variable quantum computation, which have been experimentally implemented by means of an optical four-mode cluster state. In this paper, we present a simpler and more efficient protocol based on the use of Einstein-Podolsky-Rosen two-mode entangled states to realize the same operations. The theoretical calculations and the experimental results demonstrate that the presented scheme not only decreases the requirement to the resource quantum states at the largest extent but also enhances significantly the squeezing degree and the fidelity of the resultant modes under an identical resource condition. That is because in our system the influence of the excess noises deriving from the imperfect squeezing of the resource states is degraded. The gate operations applying two-mode entanglement can be utilized as a basic element in a future quantum computer involving a large-scale cluster state.

Measurement-based one-way quantum computation (QC) using cluster states as resources provides an efficient model to perform computation and information processing of quantum codes. Arbitrary Gaussian QC can be implemented by sufficiently long single-mode and two-mode gate sequences. However, continuous variable (CV) gate sequences have not been realized so far due to an absence of cluster states larger than four submodes. Here we present the first CV gate sequence consisting of a single-mode squeezing gate and a two-mode controlled-phase gate based on a six-mode cluster state. The quantum property of this gate sequence is confirmed by the fidelities and the quantum entanglement of two output modes, which depend on both the squeezing and controlled-phase gates. The experiment demonstrates the feasibility of implementing Gaussian QC by means of accessible gate sequences.

Multi-color entangled states of light including low-loss optical fiber transmission and atomic resonance frequencies are essential resources for future quantum information network. We present the experimental achievement on the three-color entanglement generation at 852 nm, 1550 nm and 1440 nm wavelengths for optical continuous variables. The entanglement generation system consists of two cascaded non-degenerated optical parametric oscillators (NOPOs). The flexible selectivity of nonlinear crystals in the two NOPOs and the tunable property of NOPO provide large freedom for the frequency selection of three entangled optical beams, so the present system is possible to be developed as practical devices used for quantum information networks with atomic storage units and long fiber transmission lines., Comment: 4pages, 4 figures

The preparation of multipartite entangled states is the prerequisite for exploring quantum information networks and quantum computation. In this letter, we present the first experimental demonstration of eight-partite spatially separated CV entangled states. The initial resource quantum states are eight squeezed states of light, through the linearly optical transformation of which two types of the eight-partite cluster entangled states are prepared, respectively. The generated eight entangled photonic qumodes are spatially separated, which provide valuable quantum resources to implement more complicated quantum information task., Comment: 14 pages, 7 figures

Coherent feedback control (CFC) of multipartite optical entangled states produced by a non-degenerate optical parametric amplifier is theoretically studied. The features of the quantum correlations of amplitude and phase quadratures among more than two entangled optical modes can be controlled by tuning the transmissivity of the optical beam splitter in CFC loop. The physical conditions to enhance continuous variable multipartite entanglement of optical fields utilizing CFC loop are obtained. The numeric calculations based on feasible physical parameters of realistic systems provide direct references for the design of experimental devices., Comment: 6 pages, 4 figures

We present a cascaded system consisting of three non-degenerate optical parametric amplifiers (NOPAs) for the generation and the enhancement of quantum entanglement of continuous variables. The entanglement of optical fields produced by the first NOPA is successively enhanced by the second and the third NOPAs from -5.3 $dB$ to -8.1 $dB$ below the quantum noise limit. The dependence of the enhanced entanglement on the physical parameters of the NOPAs and the reachable entanglement limitation for a given cascaded NOPA system are calculated. The calculation results are in good agreement with the experimental measurements., Comment: 5 pages, 4 figures

In this paper, we present the first experimental demonstration on continuous variable quantum key distribution using determinant Einstein-Podolsky-Rosen entangled states of optical field. By means of the instantaneous measurements of the quantum fluctuations of optical modes respectively distributed at sender and receiver, the random bits of secret key are obtained without the need for signal modulation. The post-selection boundaries for the presented entanglement-based scheme against both Gaussian collective and individual attacks are theoretically concluded. The final secret key rates of 84 kbits/s and 3 kbits/s are completed under the collective attack for the transmission efficiency of 80% and 40%, respectively.

We experimentally demonstrate that the quantum entanglement between amplitude and phase quadratures of optical modes produced from a non-degenerate optical parametric amplifier (NOPA) can be enhanced and manipulated phase-sensitively by means of another NOPA. When both NOPAs operate at de-amplification, the entanglement degree is increased at the cavity resonance of the second NOPA. When the first NOPA operates at de-amplification and the second one at amplification, the spectral features of the correlation variances are significantly changed. The experimental results are in good agreement with the theoretical expectation.

We propose two types of quantum dense coding communication networks with optical continuous variables, in which a quadripartite entangled state of the optical field with totally three-party correlations of quadrature amplitudes is utilized. In the networks, the exchange of information between any two participants can be manipulated by one or two of the remaining participants. The channel capacities for a variety of communication protocols are numerically calculated. Due to the fact that the quadripartite entangled states applied in the communication systems have been successfully prepared already in the laboratory, the proposed schemes are experimentally accessible at present.

We report the experimental generation of squeezed light at 852 nm, locked on the Cesium D2 line. 50% of noise reduction down to 50 kHz has been obtained with a doubly resonant optical parametric oscillator operating below threshold, using a periodically-polled KTP crystal. This light is directly utilizable with Cesium atomic ensembles for quantum networking applications

The pure quantum correlations totally independent of the classical coherence of light have been experimentally demonstrated. By measuring the visibility of the interference fringes and the correlation variances of amplitude and phase quadratures between a pair of bright twin optical beams with different frequencies produced from a non-degenerate optical parametric oscillator, we found that when classical interference became worse even vanished, the quadrature quantum correlations were not influenced, completely. The presented experiment obviously shows the quantum correlations of light do not necessarily imply the classical coherence.

We experimentally prepare a new type of continuous variable genuine four-partite entangled states, the quantum correlation property of which is different from that of the four-mode GHZ and cluster states, and which has not any qubit counterpart to be proposed at present. In the criterion inequalities for the full inseparability of the genuine four-partite entangled states, the amplitude and phase quadrature correlation variances totally consisting of three-party combination from the four entangled modes are involved. The measured correlation variances among the quadratures of the prepared entangled states satisfy the sufficient requirements for the full inseparability. The type of entangled states has especially potential application in quantum information with continuous quantum variables.

The dependence of quantum correlation of twin beams on the pump finesse of an optical parametric oscillator is studied with a semi-classical analysis. It is found that the phase-sum correlation of the output signal and idler beams from an optical parametric oscillator operating above threshold depends on the finesse of the pump field when the spurious pump phase noise generated inside the optical cavity and the excess noise of the input pump field are involved in the Langevin equations. The theoretical calculations can explain the previously experimental results, quantitatively., Comment: 27 pages, 8 figures

The influence of the phase fluctuation of the pump laser on the phase-correlation between the signal and idler modes of the output fields from as non-degenerate optical parametric oscillator operating above oscillation threshold was experimentally investigated. The noise spectra of the intensity-difference and the phase-sum of the entangled optical beams were measured with a pair of unbalanced fiber Match-Zehnder interferometers specifically designed. The experimental results proved the previously theoretical prediction and are in reasonable agreement with the calculation based on semiclassical theory involving the phase fluctuation of pump laser., Comment: 15 pages

The cluster states and Greenberger-Horne-Zeilinger (GHZ) states are two different types of multipartite quantum entangled states. We present the first experimental results generating continuous variable quadripartite cluster and GHZ entangled states of electromagnetic fields. Utilizing four two-mode squeezed states of light and linearly optical transformations, the two types of entangled states for amplitude and phase quadratures of light are experimentally produced. The combinations of the measured quadrature variances prove the full inseparability of the generated four subsystems. The presented experimental schemes show that the multipartite entanglement of continuous variables can be deterministically generated with the relatively simple implementation.

The quantum characteristics of sum-frequency process in an optical cavity with an input signal optical beam, which is a half of entangled optical beams, are analyzed. The calculated results show that the quantum properties of the signal beam can be maintained after its frequency is conversed during the intracavity nonlinear optical interaction. The frequency-conversed output signal beam is still in an entangled state with the retained other half of initial entangled beams. The resultant quantum correlation spectra and the parametric dependences of the correlations on the initial squeezing factor, the optical losses and the pump power of the sum-frequency cavity are calculated. The proposed system for the frequency conversion of entangled state can be used in quantum communication network and the calculated results can provide direct references for the design of experimental systems., Comment: Accepted by Phys. Rev. A

The quantum entanglement of amplitude and phase quadratures between two intense optical beams with the total intensity of 22mW and the frequency difference of 1nm, which are produced from an optical parametric oscillator operating above threshold, is experimentally demonstrated with two sets of unbalanced Mach-Zehnder interferometers. The measured quantum correlations of intensity and phase are in reasonable agreement with the results calculated based on a semi-classical analysis of the noise characteristics given by C. Fabre et al., Comment: Accepted in Opt. Lett

A new and simple quantum key distribution scheme based on the quantum intensity correlation of optical twin beams and the directly local measurements of intensity noise of single optical beam is presented and experimentally demonstrated. Using the twin beams with the quantum intensity correlation of 5dB the effective bit rate of $2\times 10^7bits/s$ is completed. The noncloning of quantum systems and the sensitivity of the existing correlations to losses provide the physical mechamism for the security against eavesdropping. In the presented scheme the signal modulation and homodyne detection are not needed., Comment: submitted to journal on March 22,2005

The unconditional entanglement swapping for continuous variables is experimentally demonstrated. Two initial entangled states are produced from two nondegenerate optical parametric amplifiers operating at deamplification. Through implementing the direct measurement of Bell-state between two optical beams from each amplifier the remaining two optical beams, which have never directly interacted with each other, are entangled. The quantum correlation degrees of 1.23dB and 1.12dB below the shot noise limit for the amplitude and phase quadratures resulting from the entanglement swapping are straightly measured., Comment: new version