Abstract
Wigner negativity, as a well-known indicator of nonclassicality, plays an essential role in quantum computing and simulation using continuous-variable systems. The conditional preparation of Wigner-negative states through appropriate non-Gaussian operations on an auxiliary mode is common procedure in quantum optics experiments. Motivated by the demand of real-world quantum network, here we investigate the remote creation and distribution of Wigner negativity in the multipartite scenario from a quantitative perspective. By establishing a monogamy relation akin to the generalized Coffman-Kundu-Wootters inequality, we show that the amount of Wigner negativity cannot be freely distributed among different modes. Moreover, for photon subtraction—one of the main experimentally realized non-Gaussian operations—we provide an intuitive method to quantify remotely generated Wigner negativity. Our results pave the way for exploiting Wigner negativity as a valuable resource for numerous quantum information protocols based on non-Gaussian scenario.
Highlights
Continuous-variable (CV) systems have attained impressive success in quantum information processing[1]
If the system is prepared in a Gaussian state, the properties can be completely determined by its covariance matrix (CM)
We develop the scheme for remote generation of Wigner negativity through EPR steering to multimode scenario, and show the presence of constraints for distributing Wigner negativity over different modes
Summary
Continuous-variable (CV) systems have attained impressive success in quantum information processing[1]. It was proven that a necessary requirement for such scheme is the existence of Einstein-Podolsky-Rosen (EPR) steering18,19—a particular type of quantum correlation where local measurements performed on one party can adjust (steer), instantaneously, the state of the other remote party[20–22] Based on this kind of nonlocal effect, one can remotely produce negativity in the steering mode by applying a set of appropriate operations on the steered mode. As an intermediate type of quantum correlation between entanglement and Bell nonlocality, multipartite quantum steering[23] has received extensive attention in recent developments of quantum information theory[24,25]. It has been successfully implemented in CV optical network[26–29], photonic network[30–32], and atomic ensembles[33]. Inspired by the shareability of EPR steering, known as monogamy[34–40], it is interesting to explore how can the remotely generated Wigner negativity be distributed over different modes? Is there any monogamy relations imposing quantitative constraints on that negativity? Does stronger steerability generate more negativity?
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