Fundamental limits to the accuracy of quantum detectors and quantum processors

At its most fundamental level, the world is described by quantum mechanics. Since the beginning of the 20th century, the fast development of quantum theory has shaped modern society, for example, giving rise to the semiconductor industry on which our information technology is built. However, the connection between quantum mechanics and information theory is far from being limited to the fabrication of semiconductor hardware. ``Information is physical",  proclaims a famous quote by Rolf Landauer. This statement stands as a reminder that information acquisition and information processing are implemented by actual physical systems that obey the laws of physics, and, in particular, the laws of quantum mechanics.

What are the fundamental limits to the accuracy of information acquisition and processing imposed by the quantum laws? How can we achieve higher accuracy? These are the two major questions addressed in this thesis. We will focus on quantum detectors and quantum processors, find the fundamental limits to their accuracy, and show how to increase their accuracy using quantum resources and better control.

To begin with, we investigate how quantum entanglement as a resource affects the detection accuracy of quantum illumination. We find that the optimal probe state for one-shot quantum illumination has an entanglement spectrum that is inversely proportional to the environmental noise spectrum. With the optimal probe state at hand, we derive the ultimate accuracy of the detection protocol, and find that the dependence of accuracy on the environmental noise and the amount of entanglement.
Secondly, we investigate how the uncertainty principle of quantum mechanics affects the detection accuracy. We find the analytic expression for the minimal value of the variance-based uncertainty relation for a set of spin-1/2 observables. Using this value, we quantify the degree of incompatibility of these observables and derive entanglement and steering criteria using local uncertainty relations. Thirdly, we quantify the interplay between thermodynamic resources and the accuracy of quantum processors. Using a resource-theoretic approach, we obtain a fundamental tradeoff between the accuracy of information processing and the amount of non-equilibrium resources used. Within the tradeoff, we also identify an entropic quantity that measures the non-equilibrium cost of a given information task, which we call it min-entropy of the task. Finally, we analyze a concrete scenario in atomic physics, in which we try to increase the information processing accuracy by designing an optimal control of quantum interactions that is noise-resilient. The above findings contribute to an improved understanding of the fundamental limits to the accuracy of quantum detectors and quantum processors, and may find applications in the optimized design of future quantum technologies.

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