[Paper Review] Fulfilling entanglement's optimal advantage via converting correlation to coherence

Haowei Shi, Bingzhi Zhang+1 more|arXiv (Cornell University)|Jul 14, 2022

Quantum Information and Cryptography4 citations

TL;DR

This paper proposes a correlation-to-displacement (C2D) conversion module that transforms residual quantum correlations in noisy, entanglement-destroyed systems into coherent quadrature displacements, enabling optimal measurement design for a broad class of entanglement-enhanced protocols. By mapping multi-mode quantum detection to single-mode coherent state detection via heterodyne and passive linear optics, the method achieves optimal performance in quantum illumination, phase estimation, communication, and channel pattern classification, surpassing classical limits even in non-asymptotic regimes.

ABSTRACT

Entanglement boosts performance limits in sensing and communication, and surprisingly the advantage over classical protocols can be even larger in presence of entanglement-breaking noise. However, to maximally fulfill such advantages requires an optimal measurement design, a challenging task as information is encoded in the feeble quantum correlation after entanglement is destroyed by loss and noise. For this reason, the optimal measurement design is still elusive for various entanglement-enhanced protocols long after their debut. We propose a conversion module to capture and transform the quantum correlation to coherent quadrature displacement, which enables the optimal receiver design for a wide range of entanglement-enhanced protocols, including quantum illumination, phase estimation, classical communication, and arbitrary thermal-loss channel pattern classification. Via heterodyne and passive linear optics, the conversion module maps the multi-mode quantum detection problem to the semi-classical detection problem of a single-mode noisy coherent state, so that explicit measurements can be constructed to achieve the optimal performance. Our module provides a paradigm of processing noisy quantum correlations for near-term implementation.

Motivation & Objective

• To resolve the long-standing challenge of optimal measurement design in entanglement-enhanced protocols under entanglement-breaking noise.
• To enable near-term experimental realization of optimal quantum advantages in sensing and communication by converting fragile quantum correlations into measurable coherent states.
• To unify and extend optimal performance across diverse protocols—quantum illumination, phase estimation, classical communication, and channel pattern classification—using a single modular framework.
• To prove the existence of a six-decibel error exponent advantage in thermal-loss channel pattern classification, a long-standing folklore in quantum information.

Proposed method

• The C2D conversion module maps multi-mode quantum states with residual correlations into a single-mode noisy coherent state via passive linear optics and heterodyne detection.
• The transformation preserves all relevant quantum information, enabling optimal measurement via standard coherent-state detection techniques.
• The method relies on a mathematical mapping derived from Gaussian state theory and general-dyne measurement statistics, ensuring information preservation under loss and noise.
• It leverages known optimal receivers for coherent state discrimination, such as the Dolinar receiver, to achieve the Helstrom limit and Quantum Chernoff bound.
• The framework reduces complex multi-mode quantum detection to semi-classical detection, enabling explicit, implementable measurement designs.
• Theoretical analysis proves that the C2D conversion achieves the Helstrom limit for state discrimination and saturates the Quantum Fisher Information for phase estimation.

Experimental results

Research questions

• RQ1 Can quantum correlations surviving entanglement-breaking noise be harnessed to achieve optimal performance in sensing and communication protocols?
• RQ2 Is there a general-purpose method to convert residual quantum correlations into measurable coherent states without information loss?
• RQ3 Can the C2D module achieve optimal performance across diverse protocols such as quantum illumination, phase estimation, and classical communication?
• RQ4 Does the C2D framework enable the proof of a six-decibel error exponent advantage in thermal-loss channel pattern classification?
• RQ5 Can the optimal measurement design be realized using only linear optics and photon detection, enabling near-term experimental implementation?

Key findings

• The C2D conversion module achieves the Helstrom limit for quantum state discrimination in quantum illumination, enabling optimal target detection under loss and noise.
• The method enables optimal phase estimation by saturating the Quantum Fisher Information for Gaussian states, even in the presence of thermal noise and loss.
• The framework achieves the optimal error exponent in thermal-loss channel pattern classification, proving a six-decibel advantage over classical methods.
• The conversion reduces multi-mode quantum detection to single-mode coherent state detection, enabling explicit, implementable measurement designs using only heterodyne detection and passive linear optics.
• The approach enables non-asymptotic performance analysis, extending quantum advantages beyond the reach of traditional asymptotic tools.
• The C2D module provides a universal framework that unifies optimal performance across quantum illumination, phase sensing, classical communication, and pattern classification.