Quantum Uncertainty Dynamics

Abstract

Quantum uncertainty relations have deep-rooted significance on the formalism of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed interest for its applications in quantum information science. Robertson derived a general form of Heisenberg's uncertainty relations for a pair of arbitrary observables represented by Hermitian operators. In the present work, we discover a temporal version of the Heisenberg-Robertson uncertainty relations for the measurement of two observables at two different times, where the dynamical uncertainties crucially depend on the time evolution of the observables. The uncertainties not only depend on the choice of observables, but they also depend on the times at which the physical observables are measured. The time correlated two-time commutator dictates the trade-off between the dynamical uncertainties. We demonstrate the dynamics of these uncertainty relations for a spin-1/2 system and for a quantum harmonic oscillator. The temporal uncertainty relations discovered in this work can be experimentally verified with the present quantum technology.

5 pages

References in corpus (12)

• Sideband Cooling Micromechanical Motion to the Quantum Ground State
• Quantum computing with trapped ions
• Quantum speed limit for physical processes
• Heisenberg's Uncertainty Principle
• State-independent experimental test of quantum contextuality
• The uncertainty principle determines the non-locality of quantum mechanics
• Stronger uncertainty relations for the sum of variances
• Negative quasiprobabilities enhance phase estimation in quantum-optics experiment
• Optimized entropic uncertainty relations for multiple measurements
• Uncertainty limits for quantum metrology obtained from the statistics of weak measurements
• Uncertainty Relations for Quantum Coherence
• Experimental study of quantum uncertainty from lack of information