Pointer-based simultaneous measurements of conjugate observables in a thermal environment

Abstract

We combine traditional pointer-based simultaneous measurements of conjugate observables with the concept of quantum Brownian motion of multipartite systems to phenomenologically model simultaneous measurements of conjugate observables in a thermal environment. This approach provides us with a formal solution of the complete measurement dynamics for quadratic Hamiltonians and we can therefore discuss the measurement uncertainty and optimal measurement times. As a main result, we obtain a lower bound for the uncertainty of a noisy measurement, which is an extension of a previously known uncertainty relation and in which the squeezing of the system state to be measured plays an important role. This also allows us to classify minimal uncertainty states in more detail.

References in corpus (6)

• Heisenberg's Uncertainty Principle
• Fundamental Aspects of Quantum Brownian Motion
• Exact Master Equation and Quantum Decoherence of Two Coupled Harmonic Oscillators in a General Environment
• Exact analytical solutions to the master equation of quantum Brownian motion for a general environment
• Initial state preparation with dynamically generated system-environment correlations
• Entropic uncertainty relation for pointer-based simultaneous measurements of conjugate observables

Cited by in corpus (2)

• Effects of the free evolution in the Arthurs-Kelly model of simultaneous measurement and in the retrodictive predictions of the Heisenberg uncertainty relations
• Entropic uncertainty bound for open pointer-based simultaneous measurements of conjugate observables