Quantum entanglement in systems of identical particles is often obscured by the interplay between exchange-induced correlations and the operational framework used to define entanglement. To study the role of exchange statistics, we propose a scheme using two \textit{distinguishable} particles where an exchange symmetry is artificially engineered via a relative phase
θ in the initial state. This approach allows continuous tuning from bosonic (
θ=0) to fermionic (
θ=π) statistics. By monitoring the interplay between purity and coherence, we uncover distinct dynamical regimes dictated by the interaction strength
U and the phase
θ. For particles initially loaded in a bound state, strong
U suppresses coherence development by avoiding the scattering band, reducing the purity toward its minimum. For particles initially on neighboring sites, coherence grows linearly in time. While non-symmetric inputs feature a sharp purity reduction at intermediate
U, due to the competition between bound and unbound states, symmetric initial conditions produce transient coherence bursts that significantly enhance the purity. More generally, tuning the phase
θ reveals a high-purity region over a range of
θ at intermediate interactions, with the purity collapsing to
1/2 as
θ approaches the fermionic limit. Our results show that the imposed statistics, or lack thereof, reshapes the entanglement dynamics and its response to the interaction
U.
Anyons, particles displaying a fractional exchange statistics intermediate between bosons and fermions, play a central role in the fractional quantum Hall effect and various spin–lattice models, and have been proposed for topological quantum computing schemes due to their resilience to noise. Here we use parametric down-conversion in an integrated semiconductor chip to generate biphoton states simulating anyonic particle statistics in a reconfigurable manner. Our scheme exploits the frequency entanglement of the photon pairs, which is directly controlled through the spatial shaping of the pump beam. These results, demonstrated at room temperature and telecom wavelength on a chip-integrated platform, pave the way to the practical implementation of quantum simulation tasks with tailored particle statistics.
Anyons, particles displaying a fractional exchange statistics intermediate between bosons and fermions, play a central role in the fractional quantum Hall effect and various spin lattice models, and have been proposed for topological quantum computing schemes due to their resilience to noise. Here we use parametric down-conversion in an integrated semiconductor chip to generate biphoton states simulating anyonic particle statistics, in a reconfigurable manner. Our scheme exploits the frequency entanglement of the photon pairs, which is directly controlled through the spatial shaping of the pump beam. These results, demonstrated at room temperature and telecom wavelength on a chip-integrated platform, pave the way to the practical implementation of quantum simulation tasks with tailored particle statistics.
We investigate quantum superposition effects in two-dimensional quantum walks of identical particles with different statistics under particle exchange, starting from various different initial configurations. To characterize interparticle correlation dynamics, we focus on joint properties such as two-particle coincidence probabilities and the spread velocity of the interparticle distance. Regarding spatial modes as an environment for the particles internal degrees of freedom, we study the role played by the particle statistics using standard entanglement witnesses, showing that particles possessing fermionic statistics are more resistant to thermalize with their environment. We analyze the presence of multipartite entanglement in the system's degrees of freedom through the Quantum Fisher Information, revealing that fermionic states generated during the walk are better suited to perform quantum metrology tasks. Finally, we discuss the potential for implementing this model using integrated photonic circuits by exploiting N -partite entanglement between individual photons.
We describe an efficient theoretical criterion suitable for the evaluation of the tripartite entanglement of any mixed three-boson or three-fermion state, based on the notion of the entanglement of particles for bipartite systems of identical particles. Our approach allows one to quantify the accessible number of quantum correlations in the systems without any violation of the local particle number superselection rule. A generalization of the tripartite negativity is here applied to some correlated systems including the continuous-time quantum walks of identical particles (for both bosons and fermions) and compared with other criteria recently proposed in the literature. Our results show the dependence of the entanglement dynamics upon the quantum statistics: The bosonic bunching results in a low number of quantum correlations while Fermi-Dirac statistics allows for higher values of the entanglement.
Progress in the reliable preparation, coherent propagation and efficient detection of many-body states has recently brought collective quantum phenomena of many identical particles into the spotlight. This tutorial introduces the physics of many-boson and many-fermion interference required for the description of current experiments and for the understanding of novel approaches to quantum computing. The field is motivated via the two-particle case, for which the uncorrelated, classical dynamics of distinguishable particles is compared to the quantum behaviour of identical bosons and fermions. Bunching of bosons is opposed to anti-bunching of fermions, while both species constitute equivalent sources of bipartite two-level entanglement. The realms of indistinguishable and distinguishable particles are connected by a monotonic transition, on a scale defined by the coherence length of the interfering particles. As we move to larger systems, any attempt to understand many particles via the two-particle paradigm fails: In contrast to two-particle bunching and anti-bunching, the very same signatures can be exhibited by bosons and fermions, and coherent effects dominate over statistical behaviour. The simulation of many-boson interference, termed Boson-Sampling, entails a qualitatively superior computational complexity when compared to fermions. The hierarchy between bosons and fermions also characterises multipartite entanglement generation, for which bosons again clearly outmatch fermions. Finally, the quantum-to-classical transition between many indistinguishable and many distinguishable particles features non-monotonic structures. While the same physical principles govern small and large systems, the deployment of the intrinsic complexity of collective many-body interference makes more particles behave differently.