Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-ph/0610408 · Brazilian Journal of Physics

Numerical symmetrization of state of identical particles

O. V. Utyuzh, Grzegorz Andrzej Wilk, Z. Włodarczyk

Published Jun 1, 2007• 5 citations
arXivHTMLPDF

Abstract

The method of numerical symmetrization of state of identical particles proposed by us before is clarified and discussed.
DOI
10.1590/s0103-97332007000500007

Related papers

Non-symmetrized Basis Function for Identical Particles

M. Gattobigio, Alejandro Kievsky, M. Viviani +1 more

Few-Body Systems•Feb 23, 2009•14 citations

Identical Particle Effect and Symmetrization in Mueller Amplitude

M. Biyajima, O. Miyamura

Progress of Theoretical Physics•Nov 1, 1978•0 citations

Colloquium: Quantum information processing with ensembles of identical particles

Matteo Piccolini, Marcin Karczewski, Jin-Shi Xu +5 more

Identical particles underpin most quantum technologies, but the role of indistinguishability in these processes extends far beyond the symmetrization of many-particle states. This Colloquium presents a unified operational perspective on how particle identity, indistinguishability, exchange statistics, and many-particle interference can instead be harnessed as resources for quantum information processing. We first clarify the notions of entanglement and indistinguishability for identical particles, emphasizing their dependence on the accessible measurements and information. We then review how spatial overlap, multiparticle interference, and path identity enable the generation, extraction, protection, and distillation of coherence and entanglement. Their applications to quantum metrology and imaging, state discrimination, teleportation, entanglement swapping, and quantum cloning are examined. Finally, we discuss the thermodynamic role of indistinguishability, from the Gibbs paradox to quantum thermal machines and statistics-driven engines. Across these settings, indistinguishability emerges as a controllable, task-dependent resource whose benefits are determined by state preparation, exchange statistics, interference, and measurement constraints.

quant-pharXiv:2610.40852•Nov 2, 2026

Permutation symmetry of wave functions of a system of identical particles

M. F. Sarry

Journal of Experimental and Theoretical Physics•Oct 1, 1979•3 citations

ON THE PROBLEM OF DISCRETE QUANTUM NUMBERS FOR THREE PARTICLE STATES

Andrzej Szymacha, J. Werle

A procedure for finding the discrete quantum numbers that, as previously noted, can replace continuous quantum numbers in a representation for systems of three particles of arbitrary mass and spin values is outlined. (D.C.W.)

•Jan 1, 1963•0 citations

Reduced Density Matrix of Identical Particles from Three Aspects: the First Quantization, Exterior Products, and GNS representation

Seungbeom Chin, Joonsuk Huh

We probe the theoretical connection among three different approaches to analyze the entanglement of identical particles, i.e., the first quantization language (1QL), exterior and elementary-symmetric products (which has the mathematical equivalence to no-labeling approaches), and the algebraic approach based on the GNS construction. Among several methods to quantify entanglement of identical particles, we focus on the computation of reduced density matrix, which can be achieved by the concept of \emph{symmetrized partial trace} defined in 1QL. We show that the symmetrized partial trace corresponds to the interior product between exterior (or elementary symmetric) state vectors, which also corresponds to the subalgebra restriction in the algebraic approach based on GNS representation. By expressing the state of identical particles as exterior and elementary symmetric state vectors, we can also prove that GHJW theorem holds for identical particles.

•Jun 3, 2019•0 citations
Identical particles underpin most quantum technologies, but the role of indistinguishability in these processes extends far beyond the symmetrization of many-particle states. This Colloquium presents a unified operational perspective on how particle identity, indistinguishability, exchange statistics, and many-particle interference can instead be harnessed as resources for quantum information processing. We first clarify the notions of entanglement and indistinguishability for identical particles, emphasizing their dependence on the accessible measurements and information. We then review how spatial overlap, multiparticle interference, and path identity enable the generation, extraction, protection, and distillation of coherence and entanglement. Their applications to quantum metrology and imaging, state discrimination, teleportation, entanglement swapping, and quantum cloning are examined. Finally, we discuss the thermodynamic role of indistinguishability, from the Gibbs paradox to quantum thermal machines and statistics-driven engines. Across these settings, indistinguishability emerges as a controllable, task-dependent resource whose benefits are determined by state preparation, exchange statistics, interference, and measurement constraints.
We probe the theoretical connection among three different approaches to analyze the entanglement of identical particles, i.e., the first quantization language (1QL), exterior and elementary-symmetric products (which has the mathematical equivalence to no-labeling approaches), and the algebraic approach based on the GNS construction. Among several methods to quantify entanglement of identical particles, we focus on the computation of reduced density matrix, which can be achieved by the concept of \emph{symmetrized partial trace} defined in 1QL. We show that the symmetrized partial trace corresponds to the interior product between exterior (or elementary symmetric) state vectors, which also corresponds to the subalgebra restriction in the algebraic approach based on GNS representation. By expressing the state of identical particles as exterior and elementary symmetric state vectors, we can also prove that GHJW theorem holds for identical particles.