Quantum Mechanics of Single-Particle and Non-Identical Particle Systems

G. Compagno, Alessia Castellini, Rosario Lo Franco

Here, we discuss a particle-based approach to deal with systems of many identical quantum objects (particles) that never employs labels to mark them. We show that it avoids both methodological problems and drawbacks in the study of quantum correlations associated with the standard quantum mechanical treatment of identical particles. The core of this approach is represented by the multiparticle probability amplitude, whose structure in terms of single-particle amplitudes we derive here by first principles. To characterize entanglement among the identical particles, this new method uses the same notions, such as partial trace, adopted for non-identical ones. We highlight the connection between our approach and second quantization. We also define spin-exchanged multipartite states which contain a generalization of W states to identical particles. We prove that particle spatial overlap plays a role in the distributed entanglement within multipartite systems and is responsible for the appearance of non-local quantum correlations.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.

Emily Marshman, Christof Keebaugh, Chandralekha Singh

We discuss an investigation of upper-level undergraduate and graduate students' difficulties with fundamental concepts involving a system of identical particles.The investigation was carried out in advanced quantum mechanics courses by administering written questions and conducting individual interviews with students.We find that students share many common difficulties related to these quantum mechanical concepts, e.g., with regard to the many-particle Hamiltonian and stationary state wavefunctions for a system of non-interacting identical particles.

Takafumi Kita

Alex Kamenev

Fabio Benatti, Roberto Floreanini B, Ugo Marzolino

We study the role of entanglement and non-locality in quantum protocols that make use of systems of identical particles. Unlike in the case of distinguishable particles, the notions of entanglement and non-locality for systems whose constituents cannot be distinguished and singly addressed are still debated. We clarify why the only approach that avoids incongruities and paradoxes is the one based on the second quantization formalism, whereby it is the entanglement of the modes that can be populated by the particles that really matters and not the particles themselves. Indeed, by means of a metrological and of a teleportation protocol, we show that inconsistencies arise in formulations that force entanglement and non-locality to be properties of the identical particles rather than of the modes they can occupy. The reason resides in the fact that orthogonal modes can always be addressed while identical particles cannot.