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We experimentally demonstrate a method for enhancing and flattening multiplexed entanglement in the four-wave mixing (FWM) process, which is implemented by replacing Laguerre–Gaussian (LG) modes with perfect vortex (PV) modes. For the topological charge l ranging from −5 to 5, the entanglement degrees of orbital angular momentum (OAM) multiplexed entanglement with PV modes are all larger than those of OAM multiplexed entanglement with LG modes. More importantly, for OAM multiplexed entanglement with PV modes, the degree of entanglement almost does not change with the topology value. In other words, we experimentally flatten the OAM multiplexed entanglement, which cannot be achieved in OAM multiplexed entanglement with LG modes based on the FWM process. In addition, we experimentally measure the entanglement with coherent superposition OAM modes. Our scheme provides a new, to the best of our knowledge, platform to construct an OAM multiplexed system and may find potential applications in realizing the parallel quantum information protocols.

Multipartite entanglement is one of the most fundamental and important resources for quantum information processing in both discrete variable and continuous variable (CV) regimes. For its applications in the CV regime, such as the realization of quantum teleportation networks and quantum dense coding, the quadrature squeezing of multipartite entanglement plays a significant role. Here, we report the first, to the best of our knowledge, experimental measurement of the quadrature squeezing in the quadripartite entanglement generated by the two-beam pumped cascaded four-wave mixing process in a 85Rb vapor cell. Moreover, we find that the quadrature squeezing is nonexistent in each pair of beams, but exists in the whole quadripartite entanglement. Our results may find potential applications in building a multi-user quantum secret sharing network.

Entanglement swapping, which is a core component of quantum network and an important platform for testing the foundation of quantum mechanics, can enable the entangling of two independent particles without direct interaction both in discrete variable and continuous variable systems. Conventionally, the realization of entanglement swapping relies on the Bell-state measurement. In particular, for entanglement swapping in continuous variable regime, such Bell-state measurement involves the optic-electro and electro-optic conversion, which limits the applications of the entanglement swapping for constructing broadband quantum network. In this Letter, we propose and demonstrate a measurement-free all-optical entanglement swapping. In our scheme, a high-gain parametric amplifier based on the four-wave mixing process is exploited to realize the function of Bell-state measurement without detection, which avoids the introduction of the optic-electro and electro-optic conversion. Our results provide an all-optical paradigm for implementing entanglement swapping and pave the way to construct a measurement-free all-optical broadband quantum network.

The phase manipulation of the two-mode entangled state, which can flexibly control the combination of quadrature components on demand, is important for continuous variable (CV) quantum information and quantum metrology. Here, we experimentally demonstrate the phase manipulation of entangled state by using a phase-sensitive amplifier (PSA) based on four-wave mixing (FWM) process. The entanglement with different phase space squeezing orientations can be generated by directly changing the phase of the PSA. Our scheme is concise and can be expanded to generate multi-parties entangled states on demand. Our results here pave the way to realize a phase-coded quantum key distribution protocol and squeezing-enhanced Raman spectroscopy.

To beat the channel capacity limit of conventional quantum dense coding (QDC) with fixed quantum resources, we experimentally implement the orbital angular momentum (OAM) multiplexed QDC (MQDC) in a continuous variable system based on a four-wave mixing process. First, we experimentally demonstrate that the Einstein-Podolsky-Rosen entanglement source coded on OAM modes can be used in a single channel to realize the QDC scheme. Then, we implement the OAM MQDC scheme by using the Einstein-Podolsky-Rosen entanglement source coded on OAM superposition modes. In the end, we make an explicit comparison of channel capacities for four different schemes and find that the channel capacity of the OAM MQDC scheme is substantially enhanced compared to the conventional QDC scheme without multiplexing. The channel capacity of our OAM MQDC scheme can be further improved by increasing the squeezing parameter and the number of multiplexed OAM modes in the channel. Our results open an avenue to construct high-capacity quantum communication networks.

The laws of quantum mechanics forbid the perfect copying of an unknown quantum state, known as the no-cloning theorem. In spite of this, approximate cloning with imperfect fidelity is possible, which opens up the field of quantum cloning. In general, quantum cloning can be divided into discrete variable and continuous variable (CV) categories. In the CV regime, all-optical implementation of the optimal N→M quantum cloning has been proposed in two original parallel works, which involves a parametric amplifier and a set of beam splitters and thus avoids the optic-electro and electro-optic conversions in the current CV quantum cloning technologies. However, such original proposal of all-optical CV optimal N→M quantum cloning scheme has never been experimentally implemented. Here, we show that optimal N→M quantum cloning of coherent states can be realized by utilizing a parametric amplifier based on four-wave mixing process in a hot atomic vapor and a set of beam splitters. In particular, we realize 1→M, 2→M, and 4→M quantum cloning. We find that the fidelity of N→M quantum cloning increases with the decrease of clone number M and the increase of original replica number N. The best cloning fidelity achieved in our experiment is about 93.3% ±1.0% in the 4→5 case. Our results may find potential applications in realizing all-optical high-fidelity quantum state transfer and all-optical high-compatibility eavesdropping attack in quantum communication networks.

We give the general expressions of intensity-difference squeezing (IDS) generated from two types of optical parametric amplifiers [i.e. phase-sensitive amplifier (PSA) and phase-insensitive amplifier (PIA)] based on the four-wave mixing process, which clearly shows the IDS transition between the ultra-low average input photon number regime and the ultra-high average input photon number regime. We find that both the IDS of the PSA and the IDS of the PIA get enhanced with the decrease of the average input photon number especially in the ultra-low average input photon number regime. This result is substantially different from the result in the ultra-high average input photon number regime where the IDS does not vary with the average input photon number. Moreover, under the same intensity gain, we find that the optimal IDS of the PSA is better than the IDS of the PIA in the ultra-low average input photon number regime. Our theoretical work predicts the presence of strong quantum correlation in the ultra-low average input photon number regime, which may have potential applications for probing photon-sensitive biological samples.

Quantum information protocol with quantum resources shows a great advantage in substantially improving security, fidelity, and capacity of information processing. Various quantum information protocols with diverse functionalities have been proposed and implemented. However, in general, the present quantum information system can only carry out a single information protocol or deal with a single communication task, which limits its practical application in the future. Therefore, it is essential to develop a multifunctional platform compatible with multiple different quantum information protocols. In this Letter, by utilizing an all-optical platform consisting of a gain-tunable parametric amplifier, a beam splitter, and an entanglement source, we experimentally realize the partially disembodied quantum state transfer protocol, which links the all-optical quantum teleportation protocol and the optimal 1→N coherent state cloning protocol. As a result, these three protocols, which have different physical essences and functionalities, are implemented in a single all-optical machine. In particular, we demonstrate that the partially disembodied quantum state transfer protocol can enhance the state transfer fidelity compared with all-optical quantum teleportation under the same strength of entanglement. Our all-optical quantum state transfer machine paves a way to implement the multifunctional quantum information system.

The laws of quantum mechanics forbid the perfect copying of an unknown quantum state, known as the no-cloning theorem. In spite of this, approximate cloning with imperfect fidelity is possible, which opens up the field of quantum cloning. In general, quantum cloning can be divided into discrete variable and continuous variable (CV) categories. In the CV regime, all-optical implementation of the optimal N→M quantum cloning has been proposed in two original parallel works, which involves a parametric amplifier and a set of beam splitters and thus avoids the optic-electro and electro-optic conversions in the current CV quantum cloning technologies. However, such original proposal of all-optical CV optimal N→M quantum cloning scheme has never been experimentally implemented. Here, we show that optimal N→M quantum cloning of coherent states can be realized by utilizing a parametric amplifier based on four-wave mixing process in a hot atomic vapor and a set of beam splitters. In particular, we realize 1→M, 2→M, and 4→M quantum cloning. We find that the fidelity of N→M quantum cloning increases with the decrease of clone number M and the increase of original replica number N. The best cloning fidelity achieved in our experiment is about 93.3% ±1.0% in the 4→5 case. Our results may find potential applications in realizing all-optical high-fidelity quantum state transfer and all-optical high-compatibility eavesdropping attack in quantum communication networks.

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 nonclassical resources such as squeezed light. However, practical methods to achieve quantum enhancement in the stochastic phase estimation remain 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 fundamental quantum scaling, achieve stochastic Heisenberg scaling, and surpass the precision of the canonical measurement.

Quantum teleportation is one of the most essential protocol in quantum information. In addition to increasing the scale of teleportation distance, improving its information transmission capacity is also vital importance for its practical applications. Recently, the orbital angular momentum (OAM) of light has attracted wide attention as an important degree of freedom for realizing multiplexing to increase information transmission capacity. Here we show that by utilizing the OAM multiplexed continuous variable entanglement, 9 OAM multiplexed channels of parallel all-optical quantum teleportation can be deterministically established in experiment. More importantly, our parallel all-optical quantum teleportation scheme can teleport OAM-superposition-mode coded coherent state, which demonstrates the teleportation of more than one optical mode with fidelity beating the classical limit and thus ensures the increase of information transmission capacity. Our results open the avenue for deterministically implementing parallel quantum communication protocols and provide a promising paradigm for constructing high-capacity all-optical quantum communication networks., All-optical quantum teleportation is a variant of the standard teleportation protocol, typically based on linear amplification of the input state. Here, the authors use an OAM mode-matched parametric amplifier to demonstrate multiplexed all-optical quantum teleportation, also on OAM-mode superpositions.

We experimentally demonstrate a method for realizing quantum squeezing enhancement which is induced by the interference in a two-beam phase-sensitive amplifier (PSA) based on a four-wave mixing process. Compared to the normal phase-insensitive amplifier with an intensity-difference squeezing (IDS) of $8.97\ifmmode\pm\else\textpm\fi{}0.24\text{ }\text{ }\mathrm{dB}$ or $8.76\ifmmode\pm\else\textpm\fi{}0.26\text{ }\text{ }\mathrm{dB}$, the IDS of our two-beam PSA is enhanced to $10.13\ifmmode\pm\else\textpm\fi{}0.21\text{ }\text{ }\mathrm{dB}$ under the same experimental situation. Furthermore, we study how various parameters influence the quantum squeezing enhancement of the PSA. These results clearly show that the physical mechanism inducing the IDS enhancement of the two-beam PSA is its intrinsic interference nature. Our results may find potential applications in improving the fidelity of quantum information processing and the precision of quantum metrology.

Multipartite entanglement serves as a vital resource for quantum information processing. Generally, its generation requires complex beam splitting processes which limit scalability. A promising trend is to integrate multiple nonlinear processes into a single device via frequency or time multiplexing. The generated states in these schemes are useful for quantum computation. However, they are confined in one or two beams and hard to be spatially separated for applications in quantum communication. Here, we experimentally demonstrate a scheme to generate spatially separated hexapartite entangled states by means of spatially multiplexing seven concurrent four-wave mixing processes. In addition, we show that the entanglement structure characterized by subsystem entanglement distribution can be modified by appropriately shaping the pump characteristics. Such reconfigurability of the entanglement structure gives the possibility to target a desired multipartite entangled state for a specific quantum communication protocol. Our results here provide a new platform for generating large scale spatially separated reconfigurable multipartite entangled beams.

SU(1,1) interferometers, based on nonlinear optical processes, potentially offer better phase sensitivity than traditional instruments. Bright-seeded variants are important for applications with large numbers of photons, yet have remained uncharacterized experimentally, for lack of a real-time technique to measure phase sensitivity. This study uses a direct intensity-detection technique to demonstrate the quantum enhancement of phase sensitivity in real time for a bright-seeded SU(1,1) system, compared to the classical shot-noise limit. It is hoped that these results will promote applications of this class of interferometer in quantum metrology.

We experimentally explore the relationships between the number of multiple quantum correlated beams generated by two-beam pumped cascaded four-wave mixing (CFWM) process and the system parameters, such as the angle between the two pump beams, one-photon detuning and two-photon detuning. We find that all of three system parameters can influence the number of multiple quantum correlated beams. Under the optimal system parameters, we can observe the emission of up to 14 quantum correlated beams with the intensity-difference squeezing of -6.29 ± 0.20 dB (-7.93 ± 0.64 dB after accounting for losses) from such CFWM scheme. Our results may find potential applications in building multi-user quantum network and multi-parameter quantum metrology.

We propose a two-beam pumped cascaded four-wave-mixing (CFWM) scheme with a double-$\mathrm{\ensuremath{\Lambda}}$ energy-level configuration in $^{85}\mathrm{Rb}$ vapor cell and experimentally observe the emission of up to 10 quantum correlated beams from such CFWM scheme. During this process, the seed beam is amplified; four new signal beams and five idler beams are generated. The 10 beams show strong quantum correlation which is characterized by the intensity-difference squeezing of about $\ensuremath{-}6.7\ifmmode\pm\else\textpm\fi{}0.3$ dB. Then, by altering the angle between the two pump beams, we observe the notable transition of the number of the output beams from 10 to eight, and even to six. We find that both the number of the output quantum correlated beams and their degree of quantum correlation from such two-beam pumped CFWM scheme increase with the decrease of the angle between the two pump beams. Such system may find potential applications in quantum information and quantum metrology.

Optical interferometer has played an important role in optics. Up to now, many kinds of interferometers have been realized and found their applications. In this letter, we experimentally construct an interferometer by using parametric amplifier as a wave splitter and beam splitter as a wave combiner. We make measurements of interference fringes and explore the relationships between the interference visibility of the interferometer and various system parameters, such as the gain of the parametric amplifier, the one-photon detuning and the temperature of the Rb-85 vapor cell.