Verifying Heisenberg's error-disturbance relation using a single trapped ion

Journal article

Heisenberg's uncertainty relations have played an essential role in quantum physics since its very beginning. The uncertainty relations in the modern quantum formalism have become a fundamental limitation on the joint measurements of general quantum mechanical observables, going much beyond the original discussion of the trade-off between knowing a particle's position and momentum. Recently, the uncertainty relations have generated a considerable amount of lively debate as a result of the new inequalities proposed as extensions of the original uncertainty relations. We report an experimental test of one of the new Heisenberg's uncertainty relations using a single 40Ca+ ion trapped in a harmonic potential. By performing unitary operations under carrier transitions, we verify the uncertainty relation proposed by Busch, Lahti, and Werner (BLW) based on a general error-trade-off relation for joint measurements on two compatible observables. The positive operator-valued measure, required by the compatible observables, is constructed by single-qubit operations, and the lower bound of the uncertainty, as observed, is satisfied in a state-independent manner. Our results provide the first evidence confirming the BLW-formulated uncertainty at a single-spin level and will stimulate broad interests in various fields associated with quantum mechanics.

Authors: Zhou, F; Yan, L; Gong, S; Ma, Z; He, J

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Association for the Advancement of Science
• Journal: Science Advances
• Volume: 2
• Issue: 10
• Article number: e1600578
• Publication date: 2016-10-05
• Acceptance date: 2016-09-20
• DOI: 10.1126/sciadv.1600578
• EISSN: 2375-2548
• Pmid: 28861461
• Language: English
• Keywords: FFR