Experimental non-classicality of an indivisible quantum system (1106.4481v1)

Abstract: Quantum theory demands that, in contrast to classical physics, not all properties can be simultaneously well defined. The Heisenberg Uncertainty Principle is a manifestation of this fact. Another important corollary arises that there can be no joint probability distribution describing the outcomes of all possible measurements, allowing a quantum system to be classically understood. We provide the first experimental evidence that even for a single three-state system, a qutrit, no such classical model can exist that correctly describes the results of a simple set of pairwise compatible measurements. Not only is a single qutrit the simplest system in which such a contradiction is possible, but, even more importantly, the contradiction cannot result from entanglement, because such a system is indivisible, and it does not even allow the concept of entanglement between subsystems.

• The paper demonstrates that an indivisible qutrit violates non-contextual hidden variable theories by surpassing the KCBS bound by over 120 standard deviations.
• The experiment employed a pentagram configuration with five measurement settings and photon detection across three modes to test quantum contextuality without entanglement.
• The findings confirm the inherent non-classicality of single quantum systems and open new avenues for research in quantum computation and cryptography.

Experimental Non-Classicality of an Indivisible Quantum System

The paper examines the violation of non-contextual hidden variable models by single, indivisible quantum systems, specifically using a qutrit. This research represents an experimental test to ascertain whether classical or classical-like descriptions can adequately model the fundamental properties of quantum systems. The experiment reported in this document demonstrates the non-classicality of a qutrit—a system of three quantum states—by focusing on the violation of the KCBS (Klyachko-Can-Binioğlu-Shumovsky) inequality in a single quantum system, specifically targeting contextuality without the involvement of entanglement.

Contextuality and Quantum Mechanics

A salient point of the work is the exploration of contextuality, a quintessential quantum property related to the failure of non-contextual hidden variable theories to reproduce the statistical predictions of quantum mechanics. Classical mechanics, under non-contextual realism, allows for the construction of joint probability distributions to describe systems; this is not the case in quantum mechanics as argued in the works of Specker, Bell, and Kochen-Specker, which the paper directly draws upon.

The paper crafts an experimental framework that uses a qutrit to demonstrate that even a single three-state system lacks a descriptive joint probability distribution that accounts for its observable results. This is critical because it rules out the possibility of describing such a system with a classical-like framework where properties are predefined. The indivisibility and simplicity of the qutrit negate any reliance on entanglement, providing a clean demonstration of fundamental quantum non-classicality.

The KCBS Inequality and Experiment

The KCBS inequality, derived for spin-1 systems, applies to any arrangements of five two-outcome measurements. In the paper, the measurement of interest forms a pentagram configuration, providing a pathway to explicitly test the KCBS inequality. The experimental procedure involved measuring single photons distributed across three modes and observing violations of the inequality. The result evidences statistically significant violations beyond 120 standard deviations from classical predictions, showing strong agreement with quantum mechanical expectations and, importantly, refuting any non-contextual hidden variable model.

Methodology and Results

The experimental setup relied on photon detection across three modes, with a total of seven configurations tested experimentally (five main terms, two additional for calibration and error measurement). The violations measured were not only ample but were derived under conditions minimizing the detection loophole. The paper reports achieving a bounding violation of the inequality by more than 120 standard deviations with an experimentally derived value of -3.893(6), as opposed to the classical limit of -3.

Implications and Future Research

This work highlights the non-classical characteristics of indivisible quantum systems with no entanglement, offering new insights into the ontological nature of quantum systems. Fundamentally, it challenges the adequacy of non-contextual hidden variable models, advancing the understanding of how intrinsic randomness and contextuality are average features of quantum reality.

Future research could explore deeper into combining these ideas with systems of higher complex configurations and looking at different quantum interpretations to find alternative non-classical signatures. Researchers might also investigate error reduction methods for even higher fidelity experimental results, bordering on practical applications in quantum technologies, such as quantum computation and cryptography, where contextuality may prove to be a resource rather than an obstacle.