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.
Entanglement and non-Gaussianity are physical resources essential for a large number of quantum-optics protocols. Non-Gaussian entanglement is indispensable for quantum-computing advantage and outperforms its Gaussian counterparts in a number of quantum-information protocols. The characterization of non-Gaussian entanglement is a critical matter as it is in general highly demanding in terms of resources. We propose a simple protocol based on the Fisher information for witnessing entanglement in an important class of non-Gaussian entangled states: photon-subtracted states. We demonstrate that our protocol is relevant for the detection of purely-non-Gaussian entanglement and that it is experimentally feasible through homodyne detection.
Entanglement and non-Gaussianity are physical resources that are essential for a large number of quantum-optics protocols. Non-Gaussian entanglement is indispensable for quantum-computing advantage and outperforms its Gaussian counterparts in a number of quantum-information protocols. The characterization of non-Gaussian entanglement is a critical matter as it is in general highly demanding in terms of resources. We propose a simple protocol based on the Fisher information for witnessing entanglement in an important class of non-Gaussian entangled states: photon-subtracted states. We demonstrate that our protocol is relevant for the detection of non-Gaussian entanglement generated by multiple photon-subtraction and that it is experimentally feasible through homodyne detection.
The entanglement of Gaussian continuous-variable (CV) states is fully determined by the state's second moments. In contrast, some entangled non-Gaussian states evade every second-moment criterion, and non-Gaussian entanglement detection remains an experimental challenge. The
p3-PPT criterion detects entanglement using moments of the partial transpose of the density matrix. This criterion was recently extended to CV systems using photon-number-resolving detectors and multi-copy interferometry; here we introduce a single-copy homodyne protocol that detects bipartite CV entanglement via the same criterion. Unbiased U-statistic estimators for the partial-transpose moments
p2 and
p3 are constructed directly from randomized homodyne data and used to evaluate the
p3-PPT entanglement witnesses: a linear one for detection, and a quadratic one whose violation yields a dimension-free lower bound on the entanglement negativity. The protocol estimates
p2 and
p3 up to additive error
ε at Fock cutoff
N from
O((N+1)14/3/ε2) measurements at fixed confidence. We demonstrate the protocol on six families of Gaussian and non-Gaussian states, reaching
95% empirical one-sided detection probability from
∼103 to
104 homodyne measurements for states with
nˉ≈2, placing non-Gaussian entanglement detection within reach of current homodyne experiments.
Abstract Entanglement and non-Gaussianity are physical resources that are essential for a large number of quantum-optics protocols. Non-Gaussian entanglement is indispensable for quantum-computing advantage and outperforms its Gaussian counterparts in a number of quantum-information protocols. The characterization of non-Gaussian entanglement is a critical matter as it is in general highly demanding in terms of resources. We propose a simple protocol based on the Fisher information for witnessing entanglement in an important class of non-Gaussian entangled states: photon-subtracted states. We demonstrate that our protocol is relevant for the detection of non-Gaussian entanglement generated by multiple photon-subtraction and that it is experimentally feasible through homodyne detection.
Abstract Non-Gaussian quantum states are a known necessary resource for reaching a quantum advantage and for violating Bell inequalities in continuous variable systems. As one kind of manifestation of quantum correlations, Einstein–Podolsky–Rosen steering enables verification of shared entanglement even when one of the subsystems is not characterized. However, how to detect and classify such an effect for non-Gaussian states is far from being well understood. Here, we present an efficient non-Gaussian steering criterion based on the high-order observables and conduct a systematic investigation into the hierarchy of non-Gaussian steering criteria. Moreover, we apply our criterion to three experimentally-relevant non-Gaussian states under realistic conditions and, in particular, propose a feasible scheme to create multi-component cat states with tunable size by performing a suitable high-order quadrature measurement on the steering party. Our work reveals the fundamental characteristics of non-Gaussianity and quantum correlations, and offers new insights to explore their applications in quantum information processing.