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Optica

Precision channel loss estimation for quantum networks

M. V. Jabir, Riley B. Dawkins, Javier Sabines-Chesterking, Dileep V. Reddy, Adriana E. Lita, A. Battou, Thomas Gerrits

Published Oct 27, 2025• 1 citation

Abstract

Quantum metrology plays a crucial role in characterizing and stabilizing optical channels in a quantum network, where precise estimation of loss is critical for loss-sensitive quantum protocols. Optical fiber channels are the primary medium for linking quantum nodes, where loss estimation with optical quantum states may enhance the precision compared to classical probes. In this study, we investigate the use of two-mode squeezed vacuum (TMSV) states, an optical quantum state generated via parametric down-conversion, and their detection with photon-number-resolving detectors for characterization of transmission loss. Theoretical analysis indicates that TMSV states exhibit higher Fisher information for transmission parameter estimation than coherent states, suggesting they are superior probes that can significantly enhance measurement precision. Our experimental results confirm that these TMSV states outperform coherent states in the context of loss estimation in an optical channel, achieving up to 3.9 dB higher Fisher information for transmissivity estimation without relying on post-selection measurements. This source can effectively probe transmission losses in optical fibers up to 35 km, maintaining a measurement precision advantage over coherent probe states. These findings underscore the potential of TMSV states to advance quantum metrology and improve the robustness of quantum network applications.

DOI: 10.1364/optica.562203

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Enhancing the precision of a measurement requires maximizing the information that can be gained about the quantity of interest from probing a system. For optical-based measurements, such an enhancement can be achieved through two approaches, increasing the number of photons used to interrogate the system and using quantum states of light to increase the amount of quantum Fisher information gained per photon. Here we consider the use of quantum states of light with a large number of photons, namely the bright single-mode squeezed state and the bright two-mode squeezed state, which take advantage of both of these approaches for the problem of transmission estimation. We show that, in the limit of large squeezing, these states approach the maximum possible quantum Fisher information per photon for transmission estimation that is achieved with the Fock state and the vacuum two-mode squeezed state. Since the bright states we consider can be generated at powers much higher than those of the quantum states that achieve the maximum quantum Fisher information per photon, they can achieve a much higher absolute precision as quantified by the quantum Cram\'er-Rao bound. We discuss the effects of losses external to the system on the precision of transmission estimation and identify simple measurement techniques that can saturate the quantum Cram\'er-Rao bound for the bright squeezed states even in the presence of such external losses.

Abstract Gaussian quantum channels constitute a cornerstone of continuous-variable quantum information science, underpinning a wide array of protocols in quantum optics and quantum metrology. While the action of such channels on arbitrary states is well-characterized under full channel knowledge, we address the inverse problem, namely, the precise estimation of fundamental channel parameters, including the beam splitter transmissivity and the two-mode squeezing amplitude. Employing the quantum Fisher information (QFI) as a benchmark for metrological sensitivity, we demonstrate that the symmetry inherent in mode mixing critically governs the amplification of QFI, thereby enabling high-precision parameter estimation. In addition, we investigate quantum thermometry by estimating the average photon number of thermal states, revealing that the transmissivity parameter significantly modulates estimation precision. Our results underscore the metrological utility of two-mode Gaussian states and establish a robust framework for parameter inference in noisy and dynamically evolving quantum systems.

Network tomography refers to the use of inference techniques for inferring internal network states from end-to-end probes. Quantum probes, implemented by sending blocks of

n

coherent-state pulses augmented with continuous-variable (CV) squeezing (

n=1

) or weak temporal-mode entanglement (

n>1

) over a lossy channel to a receiver with homodyne detection capabilities, are known to carry information about the channel transmissivity. Assuming a subset of nodes in an optical network is capable of sending and receiving such probes through intermediate nodes with all-optical switching capabilities, we leverage these quantum probes to estimate link transmissivities. To determine how to route the probes in a network, we propose a probe construction algorithm that guarantees link identifiability, while maximizing the number of information orthogonal sets of transmissivities. A set of probes induces a Fisher information matrix (FIM). We then derive two metrics, the determinant of the FIM and the trace of its inverse, to evaluate the performance of the probes. In particular, our results can be used to characterize the quantum improvement in estimating link transmissivities in a general optical network.