#### Alladi Ramakrishnan Hall

#### Topological Quantum Sensors

#### Thomas B. Bahder

##### US Army Research Office, Asia Pacific Region, Tokyo - Japan

*From year 2005 to 2007, ARL (Army Research Laboratory) had a research program in quantum sensors. During that time, Bahder (ARL) and Lopata (NRC postdoc) worked out a detailed theory of a quantum sensor as a quantum channel of information, with Shannon mutual information as a metric for the quality of the sensor [1]. Part of this work was supported by the Army Research Office (ARO).*

In this talk, I will review the basic theory of "conventional" quantum sensors, as was worked out at ARL during 2005. Later, at AMRDEC, Bahder continued theoretical work on non-ideal quantum sensors, which are more relevant to experiments: where the initially prepared state may have errors, there is scattering (decoherence and dispersion) in the sensor, and output state detectors are not ideal [2,3]. Next, I will introduce simple 1-qubit and 2-qubit models of a quantum sensor that have an analogy with topological energy band theory [4]. In preparation, I review some topological concepts such as Berry curvature and the Quantum Geometric Tensor. I argue that there is possible a new class of quantum sensors called "topological quantum sensors". Finally, I will give a detailed example of a single-qubit topological quantum sensor of magnetic fields based on the dynamical quantum Hall effect [5].

1. T. B. Bahder and P. A. "Fidelity of quantum interferometers", Rev. A 74, 051801(R) (2006).

2. D. S. Simon, A. V. Sergienko, and T. B. Bahder, “Dispersion and fidelity in quantum

interferometry”, Phys. Rev. A 78, 053829 (2008).

3. T. B. Bahder, “Phase estimation with nonunitary interferometers: Information as a metric’’, Phys. Rev. A 83, 053601 (2011).

4. A. Bansil, H. Lin, and T. Das, "Colloquium: Topological Band Theory", Rev. Mod. Phys. 88, 021004 (2016).

5. V. Gritsev and A. Polkovnikov, PNAS (Proceedings of the National Academy of Sciences U. S.) 109, 6457 (2012).

Done