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Recent developments, such as the experimental realization of large-scale cluster states, have built a valid case for continuous-variable quantum optics as a promising platform for quantum information processing. The capability of creating non-Gaussian states is key to building a universal quantum computer and achieving a quantum computational advantage. On the other hand, quantum correlations are also at the core of current developments in quantum technologies. Yet, quantum correlations in non-Gaussian states are still poorly understood for continuous-variable systems.
In this contribution we will focus on quantum steering, where Alice and Bob each share a part of bipartite quantum state and perform local measurements on their respective subsystem. Quantum steering from Alice to Bob occurs when Bob can exploit information from Alice’s measurements to infer the outcome of his observables’ measurement more precisely than allowed by classical correlations. The paradigmatic example for this phenomenon is found when Alice and Bob both measure field quadratures. In this case, Bob can construct conditional variances that violate Heisenberg’s inequality. This violation, known as Reid’s criterion, is a signature of quantum steering that relies purely on Gaussian features of the state.
More generally, we speak of Gaussian steering when we can violate steering inequality using only information from the state’s covariance matrix. For non-Gaussian states, the covariance matrix only offers limited information about the state, and many properties remain under the radar. Therefore, certification protocols of quantum steering for non-Gaussian states are scarce and generally highly demanding from an experimental point of view. In this contribution, we use a recently established connection between quantum steering and the (quantum) Fisher information to develop a new protocol for detection of quantum steering in non-Gaussian. This protocol relies exclusively on homodyne measurements.
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