Experimental study of quantum uncertainty from lack of information

TL;DR

This paper experimentally investigates whether quantum uncertainty is intrinsic or largely due to lack of information, using guessing games in different dimensions, and introduces a compact method for high-dimensional Fourier gates.

Contribution

It provides experimental evidence that quantum uncertainty in guessing games largely stems from inaccessible quantum information, and presents a new compact method for constructing high-dimensional Fourier gates.

Findings

Quantum uncertainty is significantly influenced by inaccessible quantum information.

Experimental implementation of 2D and 3D guessing games confirms the role of inaccessible degrees of freedom.

A compact method for high-dimensional Fourier gate construction is proposed.

Abstract

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 similarly 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 the previous literature 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. Moreover, we offer an experimentally compact method to construct the high-dimensional Fourier gate which is a major building block for various tasks in quantum computation, quantum communication, and quantum metrology.