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Entanglement is an indispensable quantum resource for quantum information technology. In continuous-variable quantum optics, photon subtraction can increase the entanglement between Gaussian states of light, but for mixed states the extent of this entanglement increase is poorly understood. In this work, we use an entanglement measure based the R\'enyi-2 entropy to prove that single-photon subtraction increases bipartite entanglement by no more than log 2. This value coincides with the maximal amount of bipartite entanglement that can be achieved with one photon. The upper bound is valid for all Gaussian input states, regardless of the number of modes and the purity.

The quantum stochastic phase estimation has many applications in the precise measurement of various physical parameters. Similar to the estimation of a constant phase, there is a standard quantum limit for stochastic phase estimation, which can be obtained with the Mach-Zehnder interferometer and coherent input state. Recently, it has been shown that the stochastic standard quantum limit can be surpassed with non-classical resources such as the squeezed light. However, practical methods to achieve the quantum enhancement in the stochastic phase estimation remains largely unexplored. Here we propose a method utilizing the SU(1,1) interferometer and coherent input states to estimate a stochastic optical phase. As an example, we investigate the Ornstein-Uhlenback stochastic phase. We analyze the performance of this method for three key estimation problems: prediction, tracking and smoothing. The results show significant reduction of the mean square error compared with the Mach-Zehnder interferometer under the same photon number flux inside the interferometers. In particular, we show that the method with the SU(1,1) interferometer can achieve the fundamental quantum scaling, the stochastic Heisenberg scaling, and surpass the precision of the canonical measurement.

Fundamentally, the dynamics of micro-macro transitions is instrumental to understanding the process of quantum-to-classical transitions; technologically, it can also facilitate the detection of the microscopic signals in quantum experiments via convenient detectors. Here, we demonstrate a scheme to characterize micro-macro transitions based on a four-wave mixing linear optical amplification process in a hot rubidium vapor. The linear optical amplifier provides a large optical gain of $10^7$ for injected single-photon-level pulses, enabling photon-number-resolving detection by average via non-single-photon counting detectors with a large dynamic range. The scheme exhibits strong dispersion which is sensitive to the input's change at the single-photon level, resulting in the group-velocity delay time scaling with $1/\sqrt{N}$, where $N$ is the average input photon number. The output probe and conjugate modes have different coefficients of this $1/\sqrt{N}$ scaling, indicating the coefficient can serve as an efficient parameter to characterize the specified micro-macro transitions. The demonstrated results are generally applicable for quantum detection and optical signal processing in light-atom interfaces. Furthermore, the present system is suitable for the study of relevant time-resolved dynamics of the quantum-to-classical transitions., Comment: 9 pages, 7 figures

We present a scheme to realize versatile quantum networks by cascading several four-wave mixing (FWM) processes in warm rubidium vapors. FWM is an efficient $\chi^{(3)}$ nonlinear process, already used as a resource for multimode quantum state generation and which has been proved to be a promising candidate for applications to quantum information processing. We analyze theoretically the multimode output of cascaded FWM systems, derive its independent squeezed modes and show how, with phase controlled homodyne detection and digital post-processing, they can be turned into a versatile source of continuous variable cluster states., Comment: 7 pages, 6 figures, Quantum optics

Quantum correlations and entanglement shared among multiple quantum modes are important for both fundamental science and the future development of quantum technologies. This development will also require an efficient quantum interface between multimode quantum light sources and atomic ensembles, which makes it necessary to implement multimode quantum light sources that match the atomic transitions. Here we report on such a source that provides a method for generating quantum correlated beams that can be extended to a large number of modes by using multiple four-wave mixing (FWM) processes in hot rubidium vapor. Experimentally we show that two cascaded FWM processes produce strong quantum correlations between three bright beams but not between any two of them. In addition, the intensity-difference squeezing is enhanced with the cascaded system to -7.0 $\pm$ 0.1 dB from the -5.5 $\pm$ 0.1/-4.5 $\pm$ 0.1 dB squeezing obtained with only one FWM process. One of the main advantages of our system is that as the number of quantum modes increases, so does the total degree of quantum correlations. The proposed method is also immune to phase instabilities due to its phase insensitive nature, can easily be extended to multiple modes, and has potential applications in the production of multiple quantum correlated images., Comment: 5 pages, 4 figures

One way quantum computing uses single qubit projective measurements performed on a cluster state (a highly entangled state of multiple qubits) in order to enact quantum gates. The model is promising due to its potential scalability; the cluster state may be produced at the beginning of the computation and operated on over time. Continuous variables (CV) offer another potential benefit in the form of deterministic entanglement generation. This determinism can lead to robust cluster states and scalable quantum computation. Recent demonstrations of CV cluster states have made great strides on the path to scalability utilizing either time or frequency multiplexing in optical parametric oscillators (OPO) both above and below threshold. The techniques relied on a combination of entangling operators and beam splitter transformations. Here we show that an analogous transformation exists for amplifiers with Gaussian inputs states operating on multiple spatial modes. By judicious selection of local oscillators (LOs), the spatial mode distribution is analogous to the optical frequency comb consisting of axial modes in an OPO cavity. We outline an experimental system that generates cluster states across the spatial frequency comb which can also scale the amount of quantum noise reduction to potentially larger than in other systems., Comment: fixed typos; synced with journal version

We propose a scheme via three-level cascade atoms to entangle two optomechanical oscillators as well as two-mode fields. We show that two movable mirrors and two-mode fields can be entangled even for bad cavity limit. We also study entanglement of the output two-mode fields in frequency domain. The results show that the frequency of the mirror oscillation and the injected atomic coherence affect the output entanglement of the two-mode fields., Comment: 6 pages, 4 figures

We present a scheme to obtain the coherently enhanced Raman scattering in atomic vapor which is induced by a spin wave initially written by a weak write laser. The enhancement of Raman scattering is dependent on the number and the spatial distribution of the flipped atoms generated by the weak write laser. Such an enhanced Raman scattering may have practical applications in quantum information, nonlinear optics and laser spectroscopy because of its simplicity., Comment: 7 pages, 4 figures, submitted to Phys. Rev. A

An intrinsically stable type-I optical parametric oscillator was built with a periodically poled KTiOPO4 (PPKTP) crystal to generate a stable bright, continuous-wave, broadband phase-squeezed beam. A 3.2 dB sensitivity enhancement of optical interferometry was demonstrated on weak electrooptic modulation signals within a 20 MHz squeezing bandwidth. This also realized a channel capacity increase beyond that of coherent optical communication., Comment: 9 pages, 4 figs, submitted for publication

We proposed a scheme of continuous-variable quantum key distribution, in which the bright Einstein-Podolsky-Rosen entangled optical beams are utilized. The source of the entangled beams is placed inside the receiving station, where half of the entangled beams are transmitted with round trip and the other half are retained by the receiver. The amplitude and phase signals modulated on the signal beam by the sender are simultaneously extracted by the authorized receiver with the scheme of the dense-coding correlation measurement for continuous quantum variables, thus the channel capacity is significantly improved. Two kinds of possible eavesdropping are discussed. The mutual information and the secret key rates are calculated and compared with those of unidirectional transmission schemes.

We observed continuous-variable entanglement between the bright beams emitted above threshold by an ultrastable optical parametric oscillator, classically phase-locked at a frequency difference of 161.8273240(5) MHz. The amplitude-difference squeezing is -3 dB and the phase-sum one is -1.35 dB. Besides proving entanglement in a new physical system, the phase-locked OPO, such unprecedented frequency-difference stability paves the way for transferring entanglement between different optical frequencies and densely implementing continuous-variable quantum information in the frequency domain., Comment: 4 pages, 4 figures, submitted for publication

A tripartite entangled state of bright optical field is experimentally produced using an Einstein-Podolsky-Rosen entangled state for continuous variables and linear optics. The controlled dense coding among a sender, a receiver and a controller is demonstrated by exploiting the tripartite entanglement. The obtained three-mode position correlation and relative momentum correlation between the sender and the receiver and thus the improvements of the measured signal to noise ratios of amplitude and phase signals with respect to the shot noise limit are 3.28dB and 3.18dB respectively. If the mean photon number $\bar{n}$ equals 11 the channel capacity can be controllably inverted between 2.91 and 3.14. When $\bar{n}$ is larger than 1.0 and 10.52 the channel capacities of the controlled dense coding exceed the ideal single channel capacities of coherent and squeezed state light communication., Comment: 8 pages, 4 figures

Quantum cryptography with the predetermined key was experimentally realized using Einstein-Podolsky-Rosen(EPR) correlations of continuously bright optical beams. Only one of two EPR correlated beams is transmitted with the signals modulated on quadrature phases and amplitudes, and the other one is retained by the authorized receiver. The modulated small signals are totally submerged in the large quantum noise of the signal beam, therefore nobody except the authorized receiver can decode the signals. Usability of imperfect quantum correlation, high transmission and detection efficiencies, and security provided by quantum mechanics are the favorable features of the presented scheme., Comment: 8 pages, 3 figures, 1 table

Highly efficient quantum dense coding for continuous variables has been experimentally accomplished by means of exploiting bright EPR beam with anticorrelation of amplitude quadratures and correlation of phase quadratures, which is generated from a nondegenerate optical parametric amplifier operating in the state of deamplification. Two bits of classical information are encoded on two quadratures of a half of bright EPR beam at the sender Alice and transmitted to the receiver Bob via one qubit of the shared quantum state after encoding. The amplitude and phase signals are simultaneously decoded with the other half of EPR beam by the direct measurement of the Bell-state at Bob. The signal to noise ratios of the simultaneously measured amplitude and phase signals are improved 5.4dB and 4.8dB with respect to that of the shot noise limit respectively. A high degree of immunity to unauthorized eavesdropping of the presented quantum communication scheme is experimentally demonstrated., Comment: 11 pages, 5 figures