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Algorithms for intelligent systems

Uncertainty Principle in the Light of Quantum Information Science

Saptarshi Sahoo, Amit Kumar Mandal, Nirmalya Misra, Vishal Mandal

Published Jan 1, 2022• 0 citations
Publisher
DOI
10.1007/978-981-19-1657-1_16

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As the fundamental tool in quantum information science, the uncertainty principle is essential for manifesting nonclassical properties of quantum systems. Plenty of efforts on the uncertainty principle with two observables have been achieved, making it an appealing challenge to extend the scenario to multiple observables. Here, based on an optical setup, we demonstrate the uncertainty relations in two-qubit systems involving three physical components with the tight constant 2/32/\sqrt{3}2/3​, which signifies a more precise limit in the measurement of multiple quantum components and offers deeper insights into the trade-offs between observables. Furthermore, we reveal the correspondence of the maximal values of the uncertainty functions and the degree of entanglement, where the more uncertainty is proportional to the higher degree of entanglement. Our results provide a new insight into understanding the uncertainty relations with multiple observables and may motivate more innovative applications in quantum information science.
Uncertainty principle, one of the most iconic features of quantum mechanics, was originally viewed as a fundamental limitation. Since the inception of quantum information science, researchers began to use it to achieve quantum advantages. To better understand the origin of these advantages, an essential question is: To what extent can the uncertainty principle's signatures be simulated by a single measurement? As a single measurement clearly cannot demonstrate the uncertainty principle, such a simulation, if exists, implies the claimed advantages may either stem from other quantum features, or just be reproducible in a less resourceful way. In this work, we report a series of noise-robust no-go theorems, showing that strong enough signatures of uncertainty principle cannot be simulated by a single measurement, even when assisted by quantum pre- or post-processing. This signature is modelled by complementary instruments. We completely characterise complementary instruments by a numerically feasible measure and show that they are necessary and sufficient resources for the advantage in an operational task that aims to unambiguously send classical information.