Bounding the Minimum Time of a Quantum Measurement

Nathan Shettell1, Federico Centrone2, and Luis Pedro García-Pintos3,4

1Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
2ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
3Joint Center for Quantum Information and Computer Science and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
4Theoretical Division (T4), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

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Measurements take a singular role in quantum theory. While they are often idealized as an instantaneous process, this is in conflict with all other physical processes in nature. In this Letter, we adopt a standpoint where the interaction with an environment is a crucial ingredient for the occurrence of a measurement. Within this framework, we derive lower bounds on the time needed for a measurement to occur. Our bound scales proportionally to the change in entropy of the measured system, and decreases as the number of of possible measurement outcomes or the interaction strength driving the measurement increases. We evaluate our bound in two examples where the environment is modelled by bosonic modes and the measurement apparatus is modelled by spins or bosons.

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[1] Guillermo Perna and Esteban Calzetta, "Limits on quantum measurement engines", Physical Review E 109 4, 044102 (2024).

[2] Iman Sargolzahi, "Instantaneous measurement can isolate the information", arXiv:2306.09670, (2023).

[3] Federico Centrone and Manuel Gessner, "Breaking local quantum speed limits with steering", arXiv:2401.04599, (2024).

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