We experimentally implement the separation estimation between to incoherent optical sources. Our method, relying on spatial-mode demultiplexing and intensity measurements, saturates the Cramèr-Rao bound, with a five orders of magnitude gain compared to the Rayleigh limit.
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.
Resolving light sources below the diffraction limit is a fundamental task both for astronomy and microscopy. Several recent works, analysed this problem through the lens of quantum parameter estimation theory and proved that the separation between two point sources can be estimated at the quantum limit using intensity measurements after spatial-mode demultiplexing. However, most previous works have either consider low-intensity, or thermal sources.
To broaden the applicability of this approach, it is important to extend these results to more general light sources.
To this goal, we will present an analytical expression for the Quantum Fisher Information, determining the ultimate resolution limit, for the separation between two sources in an arbitrary Gaussian state.
Applying this result to different quantum states, we can shine some light on some relevant questions. We can for example explore the role of partial coherence considering displaced and correlated thermal states, or investigate the importance of quantum correlations by considering squeezed light.
In addition to the ultimate quantum limit, we will discuss a simple estimation technique, requiring access only to the mean value of a linear combination of demultiplexed intensity measurements, which is often sufficient to saturate these limits, and can easily be adapted to incorporate the most common noise sources.
Finally, we will present our experimental setup that allows for the generation of the images of two sources with different photon statistics, as well as for spatial mode demultiplexing and we will discuss the first practical implementations if the above mentioned estimation techniques.
Recent works showed that the separation between two point sources can be estimated at the quantum limit using intensity measurements after spatial-mode demultiplexing. However, so far these results have been either limited to low-intensity, or thermal sources. In this talk, we will present an analytical expression for the Quantum Fisher Information for the separation between two sources in an arbitrary Gaussian states. This expression allows us to determine the ultimate resolution limit for a series of practically relevant states, e.g. correlated or displaced thermal states (corresponding to partially coherent sources) and squeezed states (exhibiting quantum correlations). Moreover, we will show how a simple estimation technique, requiring access only to the mean value of a linear combination of demultiplexed intensity measurements can be used to saturate these limits. Finally, we will discuss the applicability of the proposed methods in present experimental setups.
Recently, it has been demonstrated that demultiplexing Hermite-Gauss (HG) modes represents the quantum-optimal measurement to estimate the distance between two incoherent sources. However, it remains unclear how to practically combine the information contained into several demultiplexing measurements to reach the ultimate resolution limits. In this contribution, we show how estimators saturating the Cramér-Rao bound for the distance between two thermal point sources can be constructed from an optimised linear combination of intensity measurements in a given number of HG modes, in presence of practical imperfection such as misalignment, crosstalk and detector noise. Moreover, we demonstrate that our strategy saturates the quantum Cramér-Rao bound, in the noiseless case, if sufficiently many modes are measured.
Superresolution techniques based on intensity measurements after a spatial mode decomposition can overcome the precision of diffraction-limited direct imaging. We present both the experimental implementation of simultaneous spatial multimode demultiplexing as a distance measurement tool and the theoretical analysis of the actual sensitivity limits given the main experimental imperfection: cross-talks between channels. We demonstrate the distance estimation between two incoherent beams in both directions of the transverse plane, and find a perfect accordance with theoretical predictions, given a proper calibration of the demultiplexer. We show that, even though sensitivity is limited by the cross-talk between channels, we can perform measurements in two dimensions much beyond the Rayleigh limit over a large dynamic range. Combining statistical and analytical tools, we obtain the scaling of the precision limits for weak, generic crosstalk from a device-independent model as a function of the crosstalk probability and N.
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