2018/09/30 by Guillaume Thekkadath, G. S. Thekkadath, Felix Hufnagel +3
Computer Science · Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Economics #Limit (mathematics) #Mathematical analysis #Mathematics #Measurement uncertainty #Momentum (technical analysis) #Observable #Observational error #Physics #Position (finance) #Position and momentum space #Predictability #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum limit #Quantum mechanics #Statistical physics #Statistics #Uncertainty principle #Weak measurement #quant-ph
paper · pdf · doi:10.1088/1367-2630/aaecdf
published as New J. Phys. 20, 113034 (2018) · 10 pages, 2 figures
openalex created_date 2018/09/27 · openalex publication_date 2018/10/31 · arxiv created 2018/11/23 · arxiv updated 2018/11/26 · openalex updated_date 2026/08/06
It is often said that measuring a system's position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a 'weak-measurement', this disturbance can be reduced. One might expect this comes at the cost of also reducing the measurement's precision. However, it was recently demonstrated that a sequence consisting of a weak position measurement followed by a regular momentum measurement can probe a quantum system at a single point, with zero width, in position-momentum space. Here, we study this 'joint weak-measurement' and reconcile its compatibility with the uncertainty principle. While a single trial probes the system with a resolution that can saturate Heisenberg's limit, we show that averaging over many trials can be used to surpass this limit. The weak-measurement does not trade away precision, but rather another type of uncertainty called 'predictability' which quantifies the certainty of retrodicting the measurement's outcome.