Based on the standard angular momentum theory, we create an experiment on preparing maximally path-entangled (|N,0 +|0,N )2 (NOON) states of triphotons. In order to explain the error between the theoretical and experimental data, we consider the background events during the experiment, and observe their effect on the uncertainty in S^1. Afterwards, we calculate the quantum Fisher information (QFI) of the states to evaluate their potential applications in quantum metrology. Our results show that by adding the appropriate background terms, the theoretical data of the produced states matches well with the experimental data. In this case, the QFI of the states is lower than maximally entangled NOON states, but still higher than a classical state.
Based on the standard angular momentum theory, we create an experiment on preparing maximally path-entangled (|N,0 +|0,N )2 (NOON) states of triphotons. In order to explain the error between the theoretical and experimental data, we consider the background events during the experiment, and observe their effect on the uncertainty in S^1. Afterwards, we calculate the quantum Fisher information (QFI) of the states to evaluate their potential applications in quantum metrology. Our results show that by adding the appropriate background terms, the theoretical data of the produced states matches well with the experimental data. In this case, the QFI of the states is lower than maximally entangled NOON states, but still higher than a classical state.
Based on the standard angular momentum theory, we create an experiment on preparing maximally pathentangled （︱N,0+︱0,N）2（NOON） states of triphotons. In order to explain the error between the theoretical and experimental data, we consider the background events during the experiment, and observe their effect on the uncertainty in 1. Afterwards, we calculate the quantum Fisher information（QFI） of the states to evaluate their potential applications in quantum metrology. Our results show that by adding the appropriate background terms, the theoretical data of the produced states matches well with the experimental data. In this case, the QFI of the states is lower than maximally entangled NOON states, but still higher than a classical state.
Based upon standard angular momentum theory, we develop a framework to investigate polarization squeezing and multipartite entanglement of a quantum light field. Both mean polarization and variances of the Stokes parameters are obtained analytically, with which we study recent observation of triphoton states [L. K. Shalm et al., Nature 457, 67 (2009)]. Our results show that the appearance of the maximally entangled NOON state accompanied by (|3,0⟩H,V−i|3,0⟩H,V)√2, is a flip of mean polarization and can be well understood in terms of quantum Fisher information.
Quantum metrology is superior to classical metrology in parameter estimation. This is because quantum states have coherence that, however, does not exist in classical states. Previous works were limited to the study of the relationship between quantum Fisher information (QFI) and coherence of the initial probe state only for a specific single-qubit parameter estimation process (e.g., a process described by a single-qubit spin angular momentum operator Jz). Here, we consider a more general case and study the relationship between QFI and coherence of the initial probe state for a single-qubit general parameter estimation process, which is described by a single-qubit spin angular momentum operator ${J}_{\stackrel{P\vec}{n}}$ with a general unit vector $\stackrel{P\vec}{n}$. We find that the QFI is proportional to the square of coherence of the initial probe state, when the single-qubit bases are eigenstates of the spin angular momentum operator ${J}_{\stackrel{P\vec}{n}}$ describing the parametrization process. We also design and conduct a linear optical experiment to support our theory. The experimental results are in good agreement with the theoretical ones. This work provides an important guideline for enhancing the precision of parameter estimation.
Entanglement measures such as concurrence, negativity and REE are well-known tools for quantifying non-classical correlations in quantum systems. However, these measures can lead to different state orderings for non-maximally entangled states. On the other hand, Quantum Fisher Information (QFI), while not an entanglement measure, provides a framework for analyzing a state's metrological potential. In this study, we numerically analyze the relationship between these entanglement measures and QFI for a large ensemble of random two-qubit states. We specifically focus on the maximized QFI (MQFI) obtained through local unitary rotations. Our findings demonstrate a strong correlation between entanglement and a state's metrological capacity, confirming that entanglement is a valuable resource. We show that while a state's QFI with a fixed generator can vary widely for a given entanglement value, local optimization to find the MQFI leads to a tighter, more predictable relationship. Our results also reinforce the principle that the metrological performance of all mixed states is fundamentally bounded by the theoretical limit of pure states. The polynomial fit equations for the upper and lower bounds of our data provide a quantitative description of these complex relationships.
Entanglement measures such as concurrence, negativity and REE are well-known tools for quantifying non-classical correlations in quantum systems. However, these measures can lead to different state orderings for non-maximally entangled states. On the other hand, Quantum Fisher Information (QFI), while not an entanglement measure, provides a framework for analyzing a state's metrological potential. In this study, we numerically analyze the relationship between these entanglement measures and QFI for a large ensemble of random two-qubit states. We specifically focus on the maximized QFI (MQFI) obtained through local unitary rotations. Our findings demonstrate a strong correlation between entanglement and a state's metrological capacity, confirming that entanglement is a valuable resource. We show that while a state's QFI with a fixed generator can vary widely for a given entanglement value, local optimization to find the MQFI leads to a tighter, more predictable relationship. Our results also reinforce the principle that the metrological performance of all mixed states is fundamentally bounded by the theoretical limit of pure states. The polynomial fit equations for the upper and lower bounds of our data provide a quantitative description of these complex relationships.
Quantum metrology promises phase sensitivity surpassing the shot-noise limit by exploiting entanglement and photon-number correlations. NOON states-maximally path-entangled N-photon superpositions (∣N,0⟩+∣0,N⟩)/2 -achieve the Heisenberg limit 1/N for single-parameter estimation, as demonstrated experimentally by Afek et al. (2010) using hybrid coherent-plus-squeezed light up to N=5. We present an end-to-end differentiable quantum-optical framework-implemented in Strawberry Fields (Killoran et al., 2019) with a TensorFlow backend -that learns optimal circuit parameters by maximising the classical Fisher information (CFI) across all coincidence channels for N=2,3,4,5. Starting from proper numerical reproductions of the Afek et al. coincidence fringes, verified by FFT analysis and parity measurements, we apply gradient descent (Adam) to the eight trainable circuit parameters. Raw CFI improvements grow dramatically with photon number: +153% (N=2), +834% to +956% (N=3), +829% to +1598% (N=4), and +1775% (N=5), alongside post-selection rate improvements of +153% to +3269%, and an 8× to 133× improvement in useful measurement events per pulse across N=2-5. A fundamental inter-channel trade-off is identified at N=2 but weakens at higher N where the Afek initialisation is further from optimal. These results provide numerically rigorous benchmarks for adaptive single-parameter quantum sensing and demonstrate that the Afek working point is significantly suboptimal at N≥3. QFI calculations confirm that the optimised probe reaches 82% of the Heisenberg limit at N=2 and improves from 36% to 58% at N=5, while useful measurement events per pulse improve by 8× to 133× across all N, making quantum-enhanced sensing at N≥3 experimentally practical.