KEYWORDS: Quantum limits, Quantum imaging, Partial coherence, Quantum coherence, Point spread functions, Super resolution, Quantum sources, Quantum Fisher information, Image resolution, Signal to noise ratio
We discuss the quantum-limited resolution of two partially coherent point sources. By establishing the Cramér-Rao bound for measuring the transverse separation of the sources, we show that the precision limit for resolving two points can be greatly improved in the sub-Rayleigh region. Here, we use a Digital Micromirror Devices (DMD) to demonstrate a new measurement scheme called spatial-mode demultiplexing (SPADE), which projects the input light field into different spatial modes. By analyzing the noise model of EMCCD, we measure the intensity of different modes of HG and estimate the separation between two partially coherent sources. Compared with direct imaging, our implementation of SPADE can surpass the Rayleigh limit and approach the quantum limit given by Quantum Fisher Information (QFI) over a range. Our result provides a new vision for super-resolution imaging. It is of great potential in imaging fields such as optical astronomy and fluorescence microscopy.
Weak measurement enables the direct measurement of the wavefunction by associating the weak values with the probability amplitudes, which is known as Direct Tomography (DT). Compared to standard quantum state tomography, DT requires far fewer measurement bases and avoids reconstruction algorithm, showing distinct advantages in the characterization of high-dimensional quantum states. Here, we propose a general parallel extension of the DT protocol for entangled systems involving multiple particles with the probability amplitudes corresponding to the joint weak values. By coupling each particle of the quantum system with the independent meter state, we obtain joint weak values of nonlocal observables through collective measurements on the post-selected meter states. Our rigorous derivation allows for large coupling strengths, which significantly reduces statistical errors. We experimentally demonstrate the feasibility of our protocol by performing DT of path-entangled photonic states in three dimensions, achieving fidelities between the results of DT and those of standard quantum state tomography of over 95%. Our results provide a powerful tool for tomography of entangled states and investigation of their nonlocal properties.
The large-photon-number quantum state is a fundamental but nonresolved request for practical quantum information applications. We propose an N-photon state generation scheme that is feasible and scalable, using lithium niobate on insulator circuits. Such a scheme is based on the integration of a common building block called photon-number doubling unit (PDU) for deterministic single-photon parametric downconversion and upconversion. The PDU relies on a 107-optical-quality-factor resonator and mW-level on-chip power, which is within the current fabrication and experimental limits. N-photon state generation schemes, with cluster and Greenberger–Horne–Zeilinger state as examples, are shown for different quantum tasks.
The quantum properties of quantum measurements are indispensable resources in quantum information processing and have drawn extensive research interest. The conventional approach to revealing quantum properties relies on the reconstruction of entire measurement operators by quantum detector tomography. However, many specific properties can be determined by a part of the matrix components of the measurement operators, which makes it possible to simplify the characterization process. We propose a general framework to directly obtain individual matrix elements of the measurement operators by sequentially measuring two noncompatible observables. This method allows us to circumvent the complete tomography of the quantum measurement and extract the required information. We experimentally implement this scheme to monitor the coherent evolution of a general quantum measurement by determining the off-diagonal matrix elements. The investigation of the measurement precision indicates the good feasibility of our protocol for arbitrary quantum measurements. Our results pave the way for revealing the quantum properties of quantum measurements by selectively determining the matrix components of the measurement operators.
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