Precision channel loss estimation for quantum networks

Optica 12, 2001 (2025) · DOI: 10.1364/OPTICA.562203

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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.

Figures

11 panels with data across 5 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.

Fig. 1

• panel (b-1): Theoretically predicted Fisher information $\mathcal{F}$ against idler transmissivity $\eta_i$ at signal transmissivity $\eta_s = 1$, on a log axis, three curves: TMSV, TMSV with noise and Coherent state ideal. The top plot of panel (b). data.csv
• panel (b-2): Theoretically predicted Fisher information $\mathcal{F}$ against idler transmissivity $\eta_i$ at signal transmissivity $\eta_s = 0.5$, on a log axis, three curves: TMSV, TMSV with noise and Coherent state ideal. The bottom plot of panel (b). data.csv

Fig. 2

• panel (1): Top surface of the inset of Fig. 2: TES histogram of the joint photon-number distribution at $\eta_i = 0.86$, as a 3D surface of TES counts on a log scale against signal photon number (m) and idler photon number (n). Each photon number, 0 to 5, labels a pulse-height region; the regions have unequal widths. data.csv
• panel (2): Middle surface of the inset of Fig. 2: TES histogram of the joint photon-number distribution at $\eta_i = 0.40$, as a 3D surface of TES counts on a log scale against signal photon number (m) and idler photon number (n). Each photon number, 0 to 5, labels a pulse-height region; the regions have unequal widths. data.csv
• panel (3): Bottom surface of the inset of Fig. 2: TES histogram of the joint photon-number distribution at $\eta_i = 0.27$, as a 3D surface of TES counts on a log scale against signal photon number (m) and idler photon number (n). Each photon number, 0 to 5, labels a pulse-height region; the regions have unequal widths. data.csv

Fig. 3

• panel (a): Heatmap of the measured joint photon-number distribution at $\eta_s = 0.89$ and $\eta_i = 0.86$: signal photon number ($m$) against idler photon number ($n$), each 0 to 2, with the joint probability on a natural-log scale. data.csv
• panel (b): Individual probabilities, $P_{mn}$, against $\eta_i$ on a log axis, nine series for up to two photons, $P_{00}$ to $P_{22}$. Solid lines are the theoretical calculations, with shaded 95% fitting-uncertainty bands, and open circles are the experimental data. The 68% error bars of the data are not drawn, as in the print. data.csv

Fig. 4

• panel (1): Fisher information $\mathcal{F}$ against $\eta_i$ at $\eta_s = 0.89$, the upper plot: $\mathcal{F}_{\mathrm{TMSV}}$ (theory, with its 68% band), $\mathcal{F}_{\mathrm{TMSV\_Poly}}$ (direct estimation from the data, markers) and $\mathcal{F}_{\mathrm{CO}}$ (coherent state). The printed 68% error bars of the markers are drawn as a band, the dB labels are left out, and the inset is its own panel. data.csv
• panel (1-inset): Inset of the upper plot of Fig. 4: Fisher information $\mathcal{F}$ against $\eta_i$ for the post-selection measurement, on a log axis, three curves: Coherent state, 1 photon (11.9 dB) and 2 photon (14.4 dB). data.csv
• panel (2): Fisher information $\mathcal{F}$ against $\eta_i$, the lower plot of Fig. 4, two series of markers: TMSV, with its 68% uncertainty, and Coherent state. The printed per-point error bars of the TMSV series are drawn as a shaded band, and the 3.9 dB label is not drawn. data.csv

Fig. 5

• panel (1): Fisher information $\mathcal{F}$ of the transmissivity against $\eta_i$ for a TMSV state with three photon-resolving detection capabilities, TMSV (Click/no-click), TMSV (0, 1 and 2+) and TMSV (0, 1, 2, and 3+), and the maximum attainable with a coherent state (Coherent state, black line). data.csv

Fig. 6

Illustrative figure, no extractable data. Shown in the paper PDF.

Cite

M. V. Jabir, Riley B. Dawkins, J. Sabines-Chesterking, Dileep V. Reddy, A. E. Lita, A. Battou, Thomas Gerrits. Precision channel loss estimation for quantum networks. Optica 12, 2001 (2025). https://doi.org/10.1364/OPTICA.562203

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