Demonstration of monogamy laws for Gaussian steering in optomechanics

Abstract

Secrecy and security are crucial in communication. So, quantum secret sharing protocol has recently been proposed to distribute a secret message to a set of parties, where the decoding procedure is forbidden individually, and a cooperative operation is needed. For this, quantum steering as an intriguing kind of nonlocality, is proven to be a useful resource for efficient implementations of the QSS protocol. Here, we study the distribution of Gaussian steering over an asymmetric three-mode optomechanical state. We show that a single-mode cannot be jointly steered by the two others, and further verify the monogamy inequalities of Gaussian steering. The state at hand displays genuine tripartite steering. Also, we observe one-way steering in the configuration (1vs1) mode as well as (1vs2) mode, hence, we reveal that the asymmetry introduced into the state we consider, is a necessary condition but not sufficient for reaching one way steering. As well, we detect one-way steering between two modes never directly interact. Strikingly, our model exhibits an extreme level of steering, where two single-mode cannot steer individually the third mode, while, they can collectively, which is decisive for practical execution of the QSS protocol.

References in corpus (20)

• Sideband Cooling Micromechanical Motion to the Quantum Ground State
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Optomechanical entanglement between a movable mirror and a cavity field
• Theory of ground state cooling of a mechanical oscillator using dynamical back-action
• Observation of strong coupling between a micromechanical resonator and an optical cavity field
• Entanglement, EPR-correlations, Bell-nonlocality, and Steering
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• State Transfer Between a Mechanical Oscillator and Microwave Fields in the Quantum Regime
• Quantification of Gaussian quantum steering
• Observation of one-way Einstein-Podolsky-Rosen steering
• Multipartite Einstein-Podolsky-Rosen steering and genuine tripartite entanglement with optical networks
• Creating and probing macroscoping entanglement with light
• Classifying directional Gaussian quantum entanglement, EPR steering and discord
• Steering bound entangled states: A counterexample to the stronger Peres conjecture
• Entanglement detection in hybrid optomechanical systems
• Schur complement inequalities for covariance matrices and monogamy of quantum correlations
• EPR paradox and quantum steering in a three-mode optomechanical system
• Quantum steering of multimode Gaussian states by Gaussian measurements: monogamy relations and the Peres conjecture
• Role of thermal noise in tripartite quantum steering
• Einstein-Podolsky-Rosen steering and Bell nonlocality of two macroscopic mechanical oscillators in optomechanical systems