Heisenberg’s uncertainty relation may be violated in a single measurement

Jacob J. Collings, Jean-François S. Van Huele

Jens Scheer, Klaus G�tsch, Thomas Koch +3 more

Jan Hilgevoord, Jos Uffink

Robert Prevedel, Bose-Einstein Condensate

Fumihiro Kaneda, So-Young Baek, Masanao Ozawa +1 more

We experimentally test the error-disturbance uncertainty relation (EDR) in generalized, strength-variable measurement of a single photon polarization qubit, making use of weak measurement that keeps the initial signal state practically unchanged. We demonstrate that the Heisenberg EDR is violated, yet the Ozawa and Branciard EDRs are valid throughout the range of our measurement strength.

Koji Nagata, Tadao Nakamura

Recently, violation of Heisenberg's uncertainty relation in spin measurements is discussed [J.Erhart et al., Nature Physics 8, 185 (2012)] and [G.Sulyok et al., Phys.Rev. A 88, 022110 (2013)].We derive the optimal limitation of Heisenberg's uncertainty principle in a specific two-level system (e.g., electron spin, photon polarizations, and so on).Some physical situation is that we would measure x σ and y σ , simultaneously.The optimality is certified by the Bloch sphere.We show that a violation of Heisenberg's uncertainty principle means a violation of the Bloch sphere in the specific case.Thus, the above experiments show a violation of the Bloch sphere when we use ±1 as measurement outcome.This conclusion agrees with recent researches [K.