[Paper Review] Quantifying the particle aspect of quantum systems

Sreetama Das, Indranil Chakrabarty+3 more|arXiv (Cornell University)|Dec 20, 2018

Quantum Mechanics and Applications1 references4 citations

TL;DR

This paper introduces a resource theory of 'particleness' to quantify the particle-like nature of quantum systems, analogous to how quantum coherence quantifies wave-like behavior. It proposes a distance-based measure of particleness using a photoelectric-effect-inspired model, demonstrating a complementarity relation between coherence and particleness in qutrit systems, with numerical evidence showing $ P_{\text{tr}} + 1.3C_{\text{tr}} \leq 1.8 $ for Haar-random states.

ABSTRACT

The possibility of a quantum system to exhibit properties that are akin to both the classically held notions of being a particle and a wave, is one of the most intriguing aspects of the quantum description of nature. These aspects have been instrumental in understanding paradigmatic natural phenomena as well as to provide nonclassical applications. A conceptual foundation for the wave nature of a quantum state has recently been presented, through the notion of quantum coherence. We introduce here a parallel notion for the particle nature of a quantum state of an arbitrary physical system. We provide elements of a resource theory of particleness, and give a quantification of the same. Finally, we provide evidence for a complementarity between the particleness thus introduced, and the coherence of an arbitrary quantum state.

Motivation & Objective

• To formalize the particle aspect of quantum systems independently of specific physical phenomena like the photoelectric effect.
• To develop a resource theory of 'particleness' analogous to the established resource theory of quantum coherence.
• To define free states and free operations within the particleness resource theory for arbitrary quantum systems.
• To quantify particleness using a distance-based measure from the set of free states.
• To investigate the complementarity between particleness and quantum coherence in arbitrary quantum states.

Proposed method

• A toy model is introduced where a d-level quantum system impinges on a two-level detector system, inspired by the photoelectric effect.
• The free states of the particleness resource theory are defined as those that cannot induce a photocurrent in the detector model.
• A distance-based measure of particleness is defined as the trace norm distance between a state and the nearest free state: $ P_{\text{tr}}(\rho) = \min_{\sigma \in \mathcal{F}_S} \| \rho - \sigma \|_1 $.
• The concept of entanglement witnesses is adapted to detect particleness in quantum states.
• Haar-uniformly generated pure and mixed states in $ \mathbb{C}^3 $ are numerically sampled to test the complementarity relation.
• The complementarity is quantified by plotting $ P_{\text{tr}} $ against $ C_{\text{tr}} $, revealing a bounding line $ P_{\text{tr}} + 1.3C_{\text{tr}} \leq 1.8 $.

Experimental results

Research questions

• RQ1 Can the particle nature of a quantum system be formalized as a resource theory independent of specific physical implementations?
• RQ2 What are the free states and free operations in a resource theory of particleness?
• RQ3 How can particleness be quantified in a way analogous to quantum coherence?
• RQ4 Is there a complementarity between particleness and coherence in arbitrary quantum states?
• RQ5 Can the complementarity between particleness and coherence be numerically validated across different ranks of quantum states?

Key findings

• The paper establishes a resource theory of particleness based on a photoelectric-effect-inspired model, defining free states as those that do not trigger a photocurrent in the detector system.
• A distance-based measure of particleness is introduced, defined as the trace norm distance to the nearest free state, enabling quantitative assessment of particle-like behavior.
• Numerical simulations of Haar-random states in $ \mathbb{C}^3 $ show that $ P_{\text{tr}} + 1.3C_{\text{tr}} \leq 1.8 $, with saturation observed for certain pure states.
• Rank-2 states lie below the bounding line, while rank-3 states are farther from saturation, indicating a dependence of complementarity on state rank.
• The complementarity between particleness and coherence is demonstrated as a new face of wave-particle duality, distinct from path-distinguishability-based relations.
• The framework allows for multiple wave and particle interpretations of a single quantum state, depending on the choice of Hamiltonians and basis, highlighting the contextuality of wave-particle duality.