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.

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Cited by in corpus (4)

• Quantum Darwinism and non-Markovian dissipative dynamics from quantum phases of the spin-1/2 XX model
• On the effects of biased quantum random numbers on the initialization of artificial neural networks
• 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