Year: 2026
Type: review
Abstract: Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique physical properties: they exhibit genuine multipartite entanglement and notable robustness against noise and perturbations. These features make such states particularly well-suited for a wide range of quantum information tasks. Here, we provide a pedagogic analysis of the mathematical structure and relevant physical properties of this class of states. Beyond the theoretical framework, robust tools for certifying and verifying the properties of symmetric states in experimental settings are essential. In this regard, we explore how standard techniques-such as quantum state tomography, Bell tests, and entanglement witnesses-can be specifically adapted for symmetric systems. Next, we provide an up-to-date overview of the most relevant applications in which these states outperform other classes of states in specific tasks. Specifically, we address their central role in quantum metrology, highlight their use in quantum error correction codes, and examine their contribution in computation and communication tasks. Finally, we present the current state-of-the-art in their experimental generation, ranging from systems of cold atoms to implementations via quantum algorithms. We also review the most significant results obtained in the different experimental realizations. Despite the notable progress made in recent years with regard to the characterisation and application of symmetric quantum states, several intriguing questions remain unsolved. We conclude this review by discussing some of these open problems and outlining promising directions for future research.
Source: Reports on Progress in Physics
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: Centres de Recerca de Catalunya, Institut de Ciències Fotòniques, European Commission, Generalitat de Catalunya, Ministerio de Ciencia e Innovación, Barcelona Supercomputing Center, QuantERA, FUNDACIÓ Privada MIR-PUIG, HORIZON EUROPE Framework Programme, Agencia Estatal de Investigación, H2020 European Research Council, NextGenerationEU
Awards: G1167306976, G1171162939, G1188902550, G120905174, G121809054, G1272927172, G1526731822, NExt level Quantum information processing for Science and Technology, G1848969253, G1855990336, G1908469581, Programmable Atomic Large-scale Quantum Simulation 2 - SGA1, G2262748287, G2309174360, G231876985, G2339292572, G2425719011, G2460755258, G2489287867, G2660406951, G2719595533, G2763573136, G2871827553, G2877376689, G2988934680, G3003884371, G3005324705, G3022749744, G3203908756, G3241330029, G3269556148, G3480869486, G3514304032, G3518538256, G356394092, G357246561, G3606912791, G363809202, G3681454997, G3690828678, G3723121148, G3976037732, G4042783231, G42194784, G4239348134, G425668148, G4359800586, G4368799831, G4391008399, G4442677895, G4526231891, G4571205363, G4727238542, G4856404060, G490073602, G4920849106, G5080475149, G526456201, G5297285534, G531036588, G5421974903, G575169067, G5800121100, G5845768719, QuantERA II ERA-NET Cofund in Quantum Technologies, G5922099756, G5987792135, G6166689270, G631184005, G6482940084, G6552004136, G6656126374, G6743926034, G6835105602, G6934145699, G704744937, G7048927246, G7084143925, G7327758667, G7425137858, G7455520032, G7613962116, G773280237, G8180681537, G8188167876, G8210619067, G8546142835, Optical Topologic Logic, G8665153912, G8684520763, G8920660035, G8959349008, G897484643
OpenAlex ID: W4417348384