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Science & philosophy

Can the entanglement be considered a basic concept of quantum mechanics?

Canio Noce, Lidia Truda, Alberto Trotta

Published Jun 30, 2022• 1 citation
Publisher

Abstract

Recently, several experimental tests devoted to quantitatively establish complementarity relations in quantum systems have been reported. Starting from the results of fully quantum single-particle self-interference experiments, we critically review the concept of entanglement, arguing that this quantity is a peculiar trait of composite quantum systems, and thus it can be looked as a basic concept of quantum mechanics.

DOI
10.23756/sp.v10i1.739

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Recently, several experimental tests devoted to quantitatively establish complementarity relations in quantum systems have been reported. Starting from the results of fully quantum single-particle self-interference experiments, we critically review the concept of entanglement, arguing that this quantity is a peculiar trait of composite quantum systems, and thus it can be looked as a basic concept of quantum mechanics.
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Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a quantitative relation between classically incompatible properties, such as the visibility of interference fringes and ``which-way'' information, but also between purely quantum mechanical properties, such as measures of entanglement. We discuss different complementarity relations for systems of two-, three-, or nnn qubits. Using nuclear magnetic resonance techniques, we have experimentally verified some of these complementarity relations in a two-qubit system.
Bohr's complementarity principle is of fundamental historic and conceptual importance for quantum mechanics (QM), and states that, with a given experimental apparatus configuration, one can observe either the wave-like or the particle-like character of a quantum system, but not both. However, it was eventually realized that these dual behaviors can both manifest partially in the same experimental setup, and, using ad hoc proposed measures for the wave and particle aspects of the quanton, complementarity relations were proposed limiting how strong these manifestations can be. Recently, a formalism was developed and quantifiers for the particleness and waveness of a quantum system were derived from the mathematical structure of QM entailed in the density matrix's basic properties ($\ensuremath{\rho}\ensuremath{\ge}0, \mathrm{Tr}\ensuremath{\rho}=1$). In this article, using IBM Quantum Experience quantum computers, we perform experimental tests of these complementarity relations applied to a particular class of one-qubit quantum states and also for random quantum states of one, two, and three qubits.
An experimental test of the quantum complementarity principle based on single neutral atoms trapped in a blue detuned bottle trap was here performed. A Ramsey interferometer was used to assess the wavelike behavior or particlelike behavior with second $\ensuremath{\pi}/2$ rotation on or off. The wavelike behavior or particlelike behavior is characterized by the visibility VVV of the interference or the predictability PPP of which-path information, respectively. The measured results fulfill the complementarity relation ${P}^{2}+{V}^{2}\ensuremath{\le}1$. Imbalance losses were deliberately introduced to the system and we find the complementarity relation is then formally ``violated.'' All the experimental results can be completely explained theoretically by quantum mechanics without considering the interference between wave and particle behaviors. This observation complements existing information concerning Bohr's complementarity principle based on wave-particle duality of a massive quantum system.