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Register a new userQuantum uncertainty from lack of information: experimental verification
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Quantum uncertainty is a well-known property of quantum mechanics that states the impossibility of predicting measurement outcomes of multiple incompatible observables simultaneously. In contrast, the uncertainty in the classical domain comes from the lack of information about the exact state of the system. One may naturally ask, whether the quantum uncertainty is indeed a fully intrinsic property of the quantum theory, or whether similar to the classical domain lack of knowledge about specific parts of the physical system might be the source of this uncertainty. This question has been addressed in [New J. Phys.19 023038 (2017)] where the authors argue that in the entropic formulation of the uncertainty principle that can be illustrated using the so-called, guessing games, indeed such lack of information has a significant contribution to the arising quantum uncertainty. Here we investigate this issue experimentally by implementing the corresponding two-dimensional and three-dimensional guessing games. Our results confirm that within the guessing-game framework, the quantum uncertainty to a large extent relies on the fact that quantum information determining the key properties of the game is stored in the degrees of freedom that remain inaccessible to the guessing party.
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As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state. Here we present a method for geometrically characterizing uncertainty relations as an entire area of variances of the observables, ranging over all possible input states. We find that for the pair of position $x$ and momentum $p$ operators, Heisenbergs uncertainty principle points exactly to the area of the variances of $x$ and $p$. Moreover, for finite-dimensional systems, we prove that the corresponding area is necessarily semialgebraic; in other words, this set can be represented via finite polynomial equations and inequalities, or any finite union of such sets. In particular, we give the analytical characterization of the areas of variances of (a) a pair of one-qubit observables, (b) a pair of projective observables for arbitrary dimension, and give the first experimental observation of such areas in a photonic system.
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A quantum money scheme enables a trusted bank to provide untrusted users with verifiable quantum banknotes that cannot be forged. In this work, we report an experimental demonstration of the preparation and verification of unforgeable quantum banknotes. We employ a security analysis that takes experimental imperfections fully into account. We measure a total of $3.6times 10^6$ states in one verification round, limiting the forging probability to $10^{-7}$ based on the security analysis. Our results demonstrate the feasibility of preparing and verifying quantum banknotes using currently available experimental techniques.
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