Multipartite Einstein-Podolsky-Rosen (EPR) steering and multimode quantum squeezing are essential resources for various quantum applications. The paper focuses on studying a coupled three-mode squeezed vacuum (C3MSV), which is a typical multimode squeezed Gaussian state and will exhibit peculiar steering property. Using the technique of integration within ordered products, we give the normal-ordering form for the coupled three-mode squeezing operator and derive the general analytical expressions of the statistical quantities for the C3MSV. Under Gaussian measurements, we analyze all bipartite Gaussian steerings (including no steering, one-way steering, and two-way steering) in detail and study the monogamy relations for the C3MSV. Then, we study the decoherence of all these steerings in noisy channels and find that sudden death will happen in a certain threshold time. Through the steerings shared in the C3MSV, we propose conceptual (and ideal) schemes of remotely generating Wigner negativity by performing appropriate photon subtraction(s) in the local position. Our obtained results may lay a solid theoretical foundation for a future practical study. We also believe that the C3MSV will be one of good candidate resources in future quantum protocols.
Multipartite Einstein-Podolsky-Rosen (EPR) steering and multimode quantum squeezing are essential resources for various quantum applications. The paper focuses on studying a coupled three-mode squeezed vacuum (C3MSV), which is a typical multimode squeezed Gaussian state and will exhibit peculiar steering property. Using the technique of integration within ordered products, we give the normal-ordering form for the coupled three-mode squeezing operator and derive the general analytical expressions of the statistical quantities for the C3MSV. Under Gaussian measurements, we analyze all bipartite Gaussian steerings (including no steering, one-way steering, and two-way steering) in detail and study the monogamy relations for the C3MSV. Then, we study the decoherence of all these steerings in noisy channels and find that sudden death will happen in a certain threshold time. Through the steerings shared in the C3MSV, we propose conceptual (and ideal) schemes of remotely generating Wigner negativity by performing appropriate photon subtraction(s) in the local position. Our obtained results may lay a solid theoretical foundation for a future practical study. We also believe that the C3MSV will be one of good candidate resources in future quantum protocols.
We investigate a fully-connected three-mode squeezed vacuum (FC-C3MSV) state, where all three modes are pairwise coupled through nonlinear interactions in a triangle (K3) topology. Using the integration-within-ordered-product technique, we derive the normal product form of the squeezing operator and obtain the covariance matrix directly from the Bogoliubov transformation. Under symmetric coupling, the physical state is genuinely tripartite entangled for any nonzero squeezing, while the three Armstrong-type witnesses provide a finite-window sufficient experimental test; in the chain-type C3MSV only one of these witnesses is violated. We find that, despite two-mode entanglement, the fully-connected topology admits \emph{no} two-mode Gaussian steering (Gi→j=0) between any pair of physical modes; the steering resource is instead collective one-mode-versus-two steering Gi→jk, which is θ-independent and grows with r. We analyze independent vacuum losses and obtain critical transmittances for steering survival: under full symmetric loss at r=0.5, one-to-two collective steering disappears at η≈0.58, whereas reverse two-to-one collective steering survives down to η≈0.502 and the underlying two-mode entanglement persists for all η>0. Finally, we revisit photon subtraction using a normalized phase-space derivation. A photon subtraction on a single physical mode does not generate Wigner negativity on another single mode, consistent with the absence of two-mode steering. Wigner negativity can instead be generated when Bob subtracts from the collective mode (b+c)/2, with a loss threshold ηc≈0.667 at r=0.5. These results distinguish pairwise and collective nonclassical resources in the FC-C3MSV and clarify the operational role of the complete-graph topology.
Wigner negativity, as a well-known indicator of nonclassicality, plays an essential role in quantum computing and simulation using continuous-variable systems. Recently, it has been proven that Einstein-Podolsky-Rosen steering is a prerequisite to generate Wigner negativity between two remote modes. Motivated by the demand of real-world quantum network, here we investigate the shareability of generated 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 operation -- we provide a general method to quantify the remotely generated Wigner negativity. With this method, we find that there is no direct quantitative relation between the Gaussian steerability and the amount of 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.
Abstract A class of non-Gaussian entangled states is introduced by applying the nonlocal single-photon addition to two-mode squeezed vacuum state and the properties of entanglement are numerically investigated according to linear entropy and Einstein–Podolsky–Rosen (EPR) steering. After the nonlocal single-photon addition operation, Wigner function of the generated state appears some negative region and loses its Gaussian property in phase space. In essence, non-Gaussian entangled states are generated after applying nonlocal single-photon addition. Additionally, by studying the linear entropy and EPR steering, we find that single-photon addition can enhance their entanglement degree and non-Gaussian steering can be witnessed in a large range of squeezing parameter for the second-order quadratures, which may provide a well application in the fields of quantum information processing.
We present a comprehensive phase diagram of quantum correlations in a three-mode Gaussian state generated by a tritter, driven by a two-mode squeezed vacuum and a coherent state. The coherent amplitude does not affect the correlation structure, which is solely governed by the initial squeezing. By systematically analyzing five physically relevant asymmetric loss configurations, we map out the exact resilience thresholds for entanglement and Einstein-Podolsky-Rosen (EPR) steering under all bipartite partitions. We reveal that EPR steering exhibits a pronounced directional asymmetry under loss, and its survival can be maintained over a much wider range of loss by strategically protecting a single channel. This tunable fragility provides practical guidance for one-sided device-independent quantum protocols in noisy asymmetric networks. We further confirm the limitations of Rényi-2 entropy in the quantification of entanglement and steering. Our results transform the abstract correlation hierarchy into a calculable, experimentally relevant guide for engineering robust quantum resources.
Negativity of the Wigner function is seen as a crucial resource for reaching a quantum computational advantage with continuous variable systems. However, these systems, while they allow for the deterministic generation of large entangled states, require an extra element such as photon subtraction to obtain such negativity. Photon subtraction is known to affect modes beyond the one where the photon is subtracted, an effect which is governed by the correlations of the state. In this Letter, we build upon this effect to remotely prepare states with Wigner negativity. More specifically, we show that photon subtraction can induce Wigner negativity in a correlated mode if and only if that correlated mode can perform Einstein-Podolsky-Rosen steering in the mode of subtraction.
The coupled three-mode squeezed vacuum is a representative multimode squeezed Gaussian state featuring unique steerability. This work investigates Gaussian quantum steering distributions of the coupled three-mode squeezed vacuum under an expanding universe. Due to causal separation between the interior and exterior spacetime regions, quantum information behind the event horizon is inaccessible to Alice, Bob and Charlie. We separately analyze steering behaviors for physically accessible and inaccessible modes. Our analysis shows that greater total mean photon number and momentum, combined with reduced expansion volume and expansion rate, enhance quantum steering strength. Notably, Gaussian quantum steering for physically inaccessible modes undergoes the "sudden death" phenomenon when a critical threshold parameter φ is exceeded. These results deliver novel insights into quantum correlations in curved spacetime.