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Enhancing Phase Sensitivity in SU(1,1) Interferometers with Multiphoton Subtraction at the Output Port: A Theoretical Study Under Photon Loss Conditions


Core Concepts
Multiphoton subtraction at the output port of an SU(1,1) interferometer can significantly enhance phase sensitivity, even under photon loss conditions, surpassing the standard quantum limit and approaching the Heisenberg limit and quantum Cramér-Rao bound.
Abstract

Bibliographic Information:

Jiang, T., Zhao, Z., Kang, Q., Zhao, T., Zhou, N., Liu, C., & Hu, L. (2024). Phase sensitivity for an SU(1,1) interferometer via multiphoton subtraction at the output port. arXiv preprint arXiv:2410.17612.

Research Objective:

This research paper investigates the potential of multiphoton subtraction at the output port of an SU(1,1) interferometer to enhance phase sensitivity, particularly under realistic conditions involving photon loss.

Methodology:

The authors employ a theoretical framework based on quantum optics and quantum metrology. They model an SU(1,1) interferometer with vacuum and coherent state inputs, incorporating photon loss mechanisms. The phase sensitivity is calculated using the error propagation formula and compared to theoretical limits like the standard quantum limit (SQL), Heisenberg limit (HL), and quantum Cramér-Rao bound (QCRB). The impact of multiphoton subtraction on the quantum Fisher information (QFI) is also analyzed.

Key Findings:

  • Multiphoton subtraction operations at the output port significantly enhance the phase sensitivity of the SU(1,1) interferometer, even in the presence of photon loss.
  • Internal photon losses within the interferometer have a more detrimental effect on phase sensitivity compared to external losses.
  • Increasing the number of subtracted photons (m) leads to a greater improvement in both phase sensitivity and QFI.
  • The proposed scheme allows the phase sensitivity to surpass the SQL and approach the HL and QCRB, even under considerable photon loss (up to 40%).

Main Conclusions:

The study demonstrates that multiphoton subtraction is a powerful technique for enhancing the phase sensitivity of SU(1,1) interferometers, particularly in practical scenarios involving photon loss. This finding has significant implications for advancing quantum precision measurement applications.

Significance:

This research contributes to the field of quantum metrology by providing a theoretical basis for improving the accuracy and sensitivity of phase estimation using SU(1,1) interferometers. The proposed scheme offers a practical approach to overcome the limitations imposed by photon loss, paving the way for more precise quantum sensing and metrology applications.

Limitations and Future Research:

The study primarily focuses on a theoretical analysis. Experimental validation of the proposed scheme is crucial for confirming its practical feasibility and effectiveness. Further research could explore the impact of different input states, noise models, and experimental imperfections on the performance of the multiphoton subtraction scheme.

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Stats
The phase sensitivity can surpass the SQL even when photon losses reach 40%. A 30% photon loss (T = 0.7) can result in a reduction of over 50% in the QFI.
Quotes

Deeper Inquiries

How can the proposed multiphoton subtraction scheme be integrated with other quantum error correction techniques to further mitigate the impact of noise and losses in practical implementations?

Integrating the multiphoton subtraction scheme with quantum error correction (QEC) techniques presents a promising avenue for building robust, noise-resistant quantum sensors. Here's how this integration can be approached: 1. Encoding in Decoherence-Free Subspaces: Concept: Encode the quantum information (in this case, the phase information) into a subspace of the Hilbert space that is immune to certain types of noise. Implementation: Instead of using simple vacuum and coherent states, prepare the input states of the SU(1,1) interferometer in a decoherence-free subspace. This could involve using entangled photon states specifically designed to be insensitive to the dominant noise channels in the system (e.g., collective dephasing). Benefit: By encoding the phase information redundantly, the impact of photon loss and other errors can be significantly reduced. 2. Quantum Error Correction Codes: Concept: Employ quantum error correction codes to detect and correct errors that occur during the operation of the interferometer. Implementation: Logical Qubits: Encode the phase information onto logical qubits, which are protected by the QEC code. Stabilizer Measurements: Periodically perform stabilizer measurements on the system to detect errors without destroying the encoded information. Error Correction: Based on the measurement outcomes, apply correction operations to restore the system to the correct state. Benefit: QEC codes can provide active protection against a wider range of errors, including photon loss, dephasing, and even some types of gate errors that might occur within the OPAs. 3. Hybrid Approaches: Concept: Combine the strengths of decoherence-free subspaces and QEC codes. Implementation: Use a combination of specially prepared input states and error correction protocols tailored to the specific noise characteristics of the SU(1,1) interferometer. Benefit: This approach can offer a high degree of flexibility and robustness, adapting to different noise environments. Challenges and Considerations: Experimental Complexity: Implementing QEC in conjunction with multiphoton subtraction will significantly increase the experimental complexity. Resource Overhead: QEC codes typically require additional qubits and operations, which can be resource-intensive. Code Selection: Choosing the right QEC code will depend on the specific noise model of the experimental setup.

Could the use of non-classical states, such as squeezed states or entangled states, as inputs to the SU(1,1) interferometer further enhance the phase sensitivity achievable with multiphoton subtraction?

Yes, using non-classical states like squeezed states or entangled states as inputs to the SU(1,1) interferometer holds significant potential for further enhancing phase sensitivity, especially when combined with multiphoton subtraction. Here's why: 1. Squeezed States: Reduced Quantum Noise: Squeezed states exhibit reduced quantum noise in one quadrature (phase or amplitude) at the expense of increased noise in the other. Enhanced Phase Sensitivity: By injecting a squeezed state into the interferometer, the noise in the phase quadrature can be "squeezed" below the standard quantum limit, leading to improved phase sensitivity. Synergy with Multiphoton Subtraction: Multiphoton subtraction can further modify the statistical properties of the squeezed state, potentially amplifying the squeezing and leading to even greater sensitivity enhancements. 2. Entangled States: Quantum Correlations: Entangled states possess stronger correlations than classical states, allowing for more precise measurements. NOON States: NOON states, a specific type of entangled state, have been shown to offer Heisenberg-limited phase sensitivity in ideal conditions. Challenges with Entanglement: Generating and maintaining high-fidelity entangled states, especially in the presence of noise, remains a significant experimental challenge. Potential Benefits: Surpassing the Heisenberg Limit: While challenging, the combination of non-classical input states and multiphoton subtraction could potentially push phase sensitivity beyond the Heisenberg limit for certain parameter regimes. Enhanced Robustness: Some non-classical states, particularly those prepared in decoherence-free subspaces, can exhibit increased robustness to certain types of noise. Considerations: Experimental Feasibility: Generating and manipulating non-classical states adds complexity to the experimental setup. Noise Resilience: The choice of non-classical state should be carefully considered based on the dominant noise sources in the system.

What are the potential applications of this enhanced phase sensitivity in fields beyond quantum metrology, such as quantum communication or quantum information processing?

The enhanced phase sensitivity achieved through multiphoton subtraction in SU(1,1) interferometers, particularly when combined with non-classical states, has far-reaching implications beyond quantum metrology. Here are some potential applications in quantum communication and information processing: Quantum Communication: Quantum Key Distribution (QKD): Increased Secure Key Rate: Enhanced phase sensitivity can lead to more precise measurements of phase shifts in QKD protocols, potentially increasing the rate at which secure keys can be generated and shared between distant parties. Improved Eavesdropping Detection: The sensitivity to small phase disturbances could enable more sensitive detection of eavesdropping attempts, further enhancing the security of quantum communication channels. Quantum Imaging: High-Resolution Imaging: The ability to measure phase differences with extreme precision could be exploited to develop quantum imaging techniques capable of resolving objects with sub-wavelength resolution. Low-Light Imaging: The enhanced sensitivity of the interferometer might enable imaging applications in extremely low-light conditions, where conventional techniques struggle. Quantum Information Processing: Quantum Computing: Improved Gate Fidelity: Precise phase control is crucial for realizing high-fidelity quantum gates, which are the building blocks of quantum computers. Enhanced phase sensitivity could lead to more accurate gate operations, reducing errors in quantum computations. Quantum Error Correction: The ability to detect small phase errors could be beneficial for implementing certain quantum error correction codes, improving the stability and reliability of quantum computers. Quantum Simulation: Precise Parameter Estimation: Many quantum simulation protocols rely on precise measurements of phase shifts to extract information about the simulated system. Enhanced phase sensitivity would enable more accurate simulations of complex quantum phenomena. Quantum Sensing Networks: Distributed Sensing: By connecting multiple SU(1,1) interferometers with enhanced phase sensitivity, it might be possible to create distributed quantum sensor networks capable of performing highly sensitive measurements over large distances. Synchronization and Timing: The precise phase measurements could also be used for applications requiring ultra-precise synchronization and timing, such as in advanced communication networks and scientific instrumentation.
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