Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · quant-ph/0206067

Complete eigenstates of identical qubits arranged in regular polygons

Terry Rudolph·Itay Yavin·Helen Freedhoff
View original source ↗Read source document ↗Export metadata ↓

Abstract

We calculate the energy eigenvalues and eigenstates corresponding to coherent single and multiple excitations of an array of N identical qubits or two-level atoms (TLA's) arranged on the vertices of a regular polygon. We assume only that the coupling occurs via an exchange interaction which depends on the separation between the qubits. We include the interactions between all pairs of qubits, and our results are valid for arbitrary distances relative to the radiation wavelength. To illustrate the usefulness of these states, we plot the distance dependence of the decay rates of the n=2 (biexciton) eigenstates of an array of 4 qubits, and tabulate the biexciton eigenvalues and eigenstates, and absorption frequencies, line widths, and relative intensities for polygons consisting of N=2,...,9 qubits in the long-wavelength limit.

Explore related subjects

quant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Terry Rudolph, Itay Yavin, Helen Freedhoff. 2002-11-13. Complete eigenstates of identical qubits arranged in regular polygons. https://doi.org/10.1103/physreva.69.013815

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Measurement-Induced Local Dephasing Generates Symmetrically Located Entangled Sites in a Fermionic Tight-Binding Lattice

We investigate an odd-sized fermionic open tight-binding chain subjected to stochastic projective measurements at its central site, effectively inducing localized dephasing. Focusing initially on the single-particle regime, we demonstrate that when the system is prepared in an even-parity state, the dynamics under central-site dephasing drive it toward a nontrivial steady state, which we characterize through both analytical and numerical approaches. Remarkably, this steady state exhibits long-range quantum correlations in the form of symmetrically positioned, pairwise entangled sites across the chain. We further show that the degree of pairwise mode entanglement can be significantly enhanced by increasing the particle number, provided the system is initialized within a specific symmetry sector associated with an underlying strong symmetry operator. Our results identify a minimal measurement-induced route for generating symmetry-selected long-range pairwise mode entanglement, with possible implications for quantum communication and distributed quantum information processing.

quant-ph↗
arXiv2026

Role of scrambling and noise in temporal information processing with quantum systems

Scrambling quantum systems have attracted attention as effective substrates for temporal information processing. Here we consider a quantum reservoir processing framework that captures a broad range of physical computing models with quantum systems. We examine the scalability and memory retention of the model with scrambling reservoirs modelled by high-order unitary designs in both noiseless and noisy settings. In the former regime, we show that measurement readouts become exponentially concentrated with increasing reservoir size, yet strikingly do not worsen with the reservoir iterations. Thus, while repeatedly reusing a small scrambling reservoir with quantum data might be viable, scaling up the problem size deteriorates generalization unless one can afford an exponential shot overhead. In contrast, the memory of early inputs and initial states decays exponentially in both reservoir size and reservoir iterations. In the noisy regime, we also prove that memory decays exponentially in time for local noisy channels. These results required us to introduce new proof techniques for bounding concentration in temporal quantum models. Beyond this extreme scrambling regime, we numerically demonstrate that exponential concentration can still exist even with a physical reservoir such as an Ising model whenever the reservoir operates in a quantum-chaotic phase. In contrast, physical reservoirs in a many-body localized phase and at the edge of chaos appear to not suffer from such phenomena

quant-ph↗
arXiv2026

Superpositions of Quantum Gaussian Processes

We generalise the Gaussian formalism of Continuous Variable (CV) systems to describe their entanglement with Discrete Variable (DV) systems, leading to superpositions of CV Gaussian states. A new class of CV-DV entangled states, named Gaussian-Branched Cat States (GBCSs), yields an analytical formalism to describe quantum hybrid systems. GBCSs are fully characterised by their superposed phase-space parameters: sets of generalised complex first moments and covariance matrices, along with the DV reduced density matrix (phases and contrasts). These states arise in all the instances where Gaussian dynamics, operations, and measurements are performed conditionally on a DV state. The time evolution of the GBCS phase-space parameters allows one -- via a new set of equations in closed form -- to analytically treat a large set of unitary and open dynamics, generated by Gaussian Hamiltonians labelled by DV eigenvalues. Conditional operations, such as displacements and rotations, and Gaussian measurements (homodyne/heterodyne) jointly with DV projectors, can be both described as maps on GBCS's parameters. A phase-space perturbation theory is given to extend the analysis to non-orthogonal DV super-operators, e.g. DV decay. We showcase our general formalism with two paradigmatic examples of experimental modelling: (i) a dispersively coupled qubit to a driven parametric amplifier; (ii) a levitated nanoparticle undergoing Stern-Gerlach matter-wave interferometry in a diffusive environment. Both examples highlight the generation of novel Wigner negativities through qubit measurements.

quant-ph↗