Quantum Sensing, Spectroscopy & Information Diagnostics

The state of a quantum material contains more information than a single conductance or magnetization curve can reveal. A useful diagnostic must select the correlations relevant to a question while avoiding the cost of reconstructing everything. Agarwal's sensing and information work explores two versions of this problem: using local quantum sensors to interrogate matter, and using structured measurements or representations to estimate properties of many-body states. In both cases, the measurement model is part of the physics.

Figure to read

Opposite sensor spin initializations couple to magnetic fluctuations of opposite handedness. Figure 1 in the source paper. De, Suman Jyoti; Pereg-Barnea, Tami; Agarwal, Kartiek. Nanoscale Defects as Probes of Time-Reversal Symmetry Breaking, Physical Review X 16, 011001 (2026). Paper. CC BY 4.0. Original manuscript graphic; no alterations.

The two drawn sensors represent alternative initializations of the same sensor, not a required pair of defects. The important signal is the difference between relaxation channels; its relation to Hall response depends on the sample and geometry.

Noise as a source of information

A quantum sensor can accumulate a phase in a field or relax because of fluctuating fields. These are different measurement channels with different frequency sensitivities. The broader quantum-sensing framework emphasizes the preparation, evolution, and readout sequence needed to turn a microscopic interaction into an estimator. Greater sensitivity is valuable only if the relation between the signal and the target quantity is understood and calibrated. 1

For a spin sensor above a conducting sheet, the magnetic field arises from spatially distributed currents. Short-wavelength components decay rapidly with height. Changing the sensor's distance therefore changes which wavelengths contribute most strongly, providing a form of momentum selectivity without a conventional momentum-resolved scattering instrument. Agarwal and collaborators developed the connection between this noise and nonlocal transverse conductivity in two-dimensional materials. The result is an integral response with a known geometric kernel, not a perfect measurement at one wavevector. 2

The wider NV-magnetometry literature supplies the experimental context: shallow defects, scanning probes, sensor-sample distance, surface noise, and optical readout all shape achievable measurements. Those constraints should be read alongside a material-response calculation. A theoretically distinctive power law may be hard to recognize if the relevant distance window is narrow or the background overwhelms the sample contribution. 3

From generic fluctuations to discriminating probes

The graphene collaboration involving Andersen, Agarwal, and others illustrates how global and local noise measurements can test a nonequilibrium mechanism. The reported observations were interpreted through an electron-phonon Cherenkov instability when carrier drift becomes supersonic. The scientific value lies in connecting several measured dependences to a physical mechanism, rather than treating excess noise as an unexplained nuisance or a thermometer by default. 4

More recent work by De, Pereg-Barnea, and Agarwal uses the handedness of magnetic fluctuations to diagnose time-reversal symmetry breaking. Different spin initializations can couple differently to circularly polarized noise. This creates access to response information hidden from a scalar noise measurement, including Hall-related quantities under the assumptions developed in the paper. The comparison is especially useful for materials where conventional static signatures are difficult to interpret. 5

Estimating observables without full tomography

Classical shadows address a different bottleneck. Repeated randomized measurements can estimate many selected observables with a sample cost that depends on their structure, rather than requiring a complete exponentially large density matrix. The original protocol established the statistical framework; shallow entangling circuits provide a further design choice. The relevant resource is the number of state copies required at a specified accuracy and confidence. 6

Rozon, Bao, and Agarwal analyze how experimental noise changes the optimal depth of those circuits. Scrambling can improve the measurement ensemble, but noisy gates can undo the gain and amplify the cost of inversion. The appropriate depth is therefore a property of the observable, noise model, and measurement scheme together. Deeper circuits are not automatically better measurements. 7

Connections and unresolved inference problems

Follow local magnetometry for spatial and polarization filtering, fluctuation probes for materials examples, and information diagnostics for randomized measurements. The learning page then asks whether measurement-space descriptions can become variational models of quantum states.

Across these approaches, the central unresolved issue is identifiability: can two different physical situations yield similar observations? Good diagnostics combine control over several experimental parameters, comparisons with competing models, and uncertainty estimates. A measured spectrum or an optimized energy is a starting point for inference, not a complete state description. This makes sensing a natural bridge between the map's transport, topology, and control branches.

References

1. Degen, C. L.; Reinhard, F.; Cappellaro, P.. Quantum sensing. Reviews of Modern Physics 89, 035002 (2017). Open manuscript.
2. Agarwal, Kartiek; Schmidt, Richard; Halperin, Bertrand; Oganesyan, Vadim; Zaránd, Gergely; Lukin, Mikhail D.; Demler, Eugene. Magnetic noise spectroscopy as a probe of local electronic correlations in two-dimensional systems. Phys. Rev. B 95, 155107 (2017). Open manuscript.
3. Casola, Francesco; van der Sar, Toeno; Yacoby, Amir. Probing condensed matter physics with magnetometry based on nitrogen-vacancy centres in diamond. Nature Reviews Materials 3, 17088 (2018). Open manuscript.
4. Trond I. Andersen; Bo L. Dwyer; Javier D. Sanchez-Yamagishi; Joaquin F. Rodriguez-Nieva; Kartiek Agarwal; Kenji Watanabe; Takashi Taniguchi; Eugene A. Demler; Philip Kim; Hongkun Park; Mikhail D. Lukin. Electron-phonon instability in graphene revealed by global and local noise probes. Science 364, 154–157 (2019).
5. De, Suman Jyoti; Pereg-Barnea, Tami; Agarwal, Kartiek. Nanoscale Defects as Probes of Time-Reversal Symmetry Breaking. Physical Review X 16, 011001 (2026). Open manuscript.
6. Huang, Hsin-Yuan; Kueng, Richard; Preskill, John. Predicting many properties of a quantum system from very few measurements. Nature Physics 16, 1050-1057 (2020). Open manuscript.
7. Rozon, Pierre-Gabriel; Bao, Ning; Agarwal, Kartiek. Optimal Twirling Depth for Classical Shadows in the Presence of Noise. Physical Review Letters 133, 130803 (2024). Open manuscript.

Independent research synthesis. Literature checked 5 September 2026; preprints are identified in the references.