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The optical cat state, known as the superposition of coherent states, has broad applications in quantum computation and quantum metrology. Increasing the number of optical cat states is crucial to implement complex quantum information tasks based on them. Here, we prepare two optical cat states simultaneously based on a nondegenerate optical parametric amplifier. By subtracting one photon from each of two squeezed vacuum states, two odd cat states with orthogonal superposition direction in phase space are prepared simultaneously, which have similar fidelity of 60% and amplitude of 1.2. Compared with the traditional method to generate two odd optical cat states based on two degenerate optical parametric amplifiers, only one nondegenerate optical parametric amplifier is applied in our experiment, which saves half of the quantum resource of nonlinear cavities. The presented results make a step toward preparing the four-component cat state, which has potential applications in fault-tolerant quantum computation.

Remote state preparation enables one to prepare and manipulate quantum state non-locally. As an essential quantum resource, optical cat state is usually prepared locally by subtracting photons from a squeezed vacuum state. For remote quantum information processing, it is essential to prepare and manipulate optical cat states remotely based on Gaussian entanglement, which remains a challenge. Here, we present experimental preparation of optical cat states based on a remotely distributed two-mode Gaussian entangled state in a lossy channel. By performing photon subtraction and homodyne projective measurement at Alice's station, an optical cat state is prepared remotely at Bob's station. Furthermore, the prepared cat state is rotated by changing Alice's measurement basis of homodyne detection, which demonstrates the remote manipulation of it. By distributing two modes of the two-mode Gaussian entangled state in lossy channels, we demonstrate that the remotely prepared cat state can tolerate much more loss in Alice's channel than that in Bob's channel. We also show that cat states with amplitudes larger than 2 can be prepared by increasing the squeezing level and subtracting photon numbers. Our results make a crucial step toward remote hybrid quantum information processing involving discrete- and continuous-variable techniques.

Remote state preparation enables one to create and manipulate a quantum state based on the shared entanglement between distant nodes. Here, we experimentally demonstrate remote preparation and manipulation of squeezed light. By performing homodyne projective measurement on one mode of the continuous variable entangled state at Alice's station, a squeezed state is created at Bob's station. Moreover, rotation and displacement operations are applied on the prepared squeezed state by changing the projective parameters on Alice's state. We also show that the remotely prepared squeezed state is robust against loss and N-1 squeezed states can be remotely prepared based on a N-mode continuous variable Greenberger-Horne-Zeilinger-like state. Our results verify the entanglement-based model used in security analysis of quantum key distribution with continuous variables and have potential application in remote quantum information processing.

Non-Gaussian states with Wigner negativity are of particular interest in quantum technology due to their potential applications in quantum computing and quantum metrology. However, how to create such states at a remote location remains a challenge, which is important for efficiently distributing quantum resource between distant nodes in a network. Here, we experimentally prepare optical non-Gaussian state with negative Wigner function at a remote node via local non-Gaussian operation and shared Gaussian entangled state existing quantum steering. By performing photon subtraction on one mode, Wigner negativity is created in the remote target mode. We show that the Wigner negativity is sensitive to loss on the target mode, but robust to loss on the mode performing photon subtraction. This experiment confirms the connection between the remotely created Wigner negativity and quantum steering. As an application, we present that the generated non-Gaussian state exhibits metrological power in quantum phase estimation., Comment: Phys. Rev. Lett. (Accepted)

Besides quantum entanglement and steering, quantum coherence has also been identified as a useful quantum resource in quantum information. It is important to investigate the evolution of quantum coherence in practical quantum channels. In this paper, we experimentally quantify the quantum coherence of a squeezed state and a Gaussian Einstein-Podolsky-Rosen (EPR) entangled state transmitted in Gaussian thermal noise channel, respectively. By reconstructing the covariance matrix of the transmitted states, quantum coherence of these Gaussian states is quantified by calculating the relative entropy. We show that quantum coherence of the squeezed state and the Gaussian EPR entangled state is robust against loss and noise in a quantum channel, which is different from the properties of squeezing and Gaussian entanglement. Our experimental results pave the way for application of Gaussian quantum coherence in lossy and noisy environments.

As two valuable quantum resources, Einstein-Podolsky-Rosen entanglement and steering play important roles in quantum-enhanced communication protocols. Distributing such quantum resources among multiple remote users in a network is a crucial precondition underlying various quantum tasks. We experimentally demonstrate the deterministic distribution of two- and three-mode Gaussian entanglement and steering by transmitting separable states in a network consisting of a quantum server and multiple users. In our experiment, entangled states are not prepared solely by the quantum server, but are created among independent users during the distribution process. More specifically, the quantum server prepares separable squeezed states and applies classical displacements on them before spreading out, and users simply perform local beam-splitter operations and homodyne measurements after they receive separable states. We show that the distributed Gaussian entanglement and steerability are robust against channel loss. Furthermore, one-way Gaussian steering is achieved among users that is useful for further directional or highly asymmetric quantum information processing.

Einstein-Podolsky-Rosen (EPR) steering is one of the most intriguing features of quantum mechanics and an important resource for quantum communication. For practical applications, it remains a challenge to protect EPR steering from decoherence due to its intrinsic difference from entanglement. Here, we experimentally demonstrate the distillation of Gaussian EPR steering and entanglement in lossy and noisy environments using measurement-based noiseless linear amplification. Different from entanglement distillation, the extension of steerable region happens in the distillation of EPR steering besides the enhancement of steerabilities. We demonstrate that the two-way or one-way steerable region is extended after the distillation of EPR steering when the NLA is implemented based on Bob's or Alice's measurement results. We also show that the NLA helps to extract secret key from insecure region in one-sided device-independent quantum key distribution with EPR steering. Our work paves the way for quantum communication exploiting EPR steering in practical quantum channels., Comment: Figure 9 is replaced

Uncertainty relation is one of the fundamental principle in quantum mechanics and plays an important role in quantum information science. We experimentally test the error-disturbance uncertainty relation (EDR) with continuous variables for Gaussian states. Two conjugate continuous-variable observables, amplitude and phase quadratures of an optical mode, are measured simultaneously by using a heterodyne measurement system. The EDR with continuous variables for a coherent state, a squeezed state and a thermal state are verified experimentally. Our experimental results demonstrate that Heisenberg's EDR with continuous variables is violated, yet Ozawa's and Branciard's EDR with continuous variables are validated.

Heisenberg's original uncertainty relation is related to measurement effect, which is different from the preparation uncertainty relation. However, it has been shown that Heisenberg's error-disturbance uncertainty relation can be violated in some cases. We experimentally test the error-tradeoff uncertainty relation by using a continuous-variable Einstein-Podolsky-Rosen (EPR) entangled state. Based on the quantum correlation between the two entangled optical beams, the errors on amplitude and phase quadratures of one EPR optical beam coming from joint measurement are estimated respectively, which are used to verify the error-tradeoff relation. Especially, the error-tradeoff relation for error-free measurement of one observable is verified in our experiment. We also verify the error-tradeoff relations for nonzero errors and mixed state by introducing loss on one EPR beam. Our experimental results demonstrate that Heisenberg's error-tradeoff uncertainty relation is violated in some cases for a continuous-variable system, while the Ozawa's and Brainciard's relations are valid.