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MON: Monday Contributed Sessions

MON 7: Foundational / Mathematical Aspects – Quantum Measurement

MON 7.1: Vortrag

Montag, 8. September 2025, 14:15–14:30, ZHG008

Weak values as stereographic projections — Lorena Ballesteros Ferraz^{1, 3}, Dominique L. Lambert², and •Yves Caudano³ — ¹Present address: Lab. de Physique Théorique et Modélisation, CNRS Unité 8089, CY Cergy Paris Université, France — ²SPS department, esphin and naXys, University of Namur, Belgium — ³Physics department, naXys and NISM, University of Namur, Belgium

Quantum weak measurements generate a lot of fundamental and practical interest, as weakly perturbing probes or means of amplifying small effects. In a pre- and post-selected weak measurement, the experimental deflection of the measuring device depends on the real part or on the imaginary part of the weak value, a complex number. However, weak values also possess a polar representation. We have connected the argument of weak values in N-level systems to a geometric phase [1] related to a geodesic triangle in the quantum state manifold. Building on results developed for open quantum systems [2], we now demonstrate that arbitrary weak values can be interpreted as a stereographic projection of the post-selected state. This offers a comprehensive geometric interpretation of the weak value's modulus and argument, enabling its visualisation jointly with the associated quantum states. Then, the geometric phase appears as both a complex-plane angle and a solid angle on the Bloch sphere, effectively mapping the weak value onto an effective two-level system.

[1] L. B. Ferraz, D. L. Lambert, and Y. Caudano, Quantum Sci. Technol. 7 (2022) 045028. [2] L. B. Ferraz, J. Martin, and Y. Caudano, Quantum Sci. Technol. 9 (2024) 035029.

Keywords: Weak measurement; Weak value; Post-selection; Geometric phase