arXiv subjects

Andreas Osterloh

Publications and source records attributed to Andreas Osterloh.

At least 19 recordsLinked to original sources

arXiv2026

The exact convex roof for GHZ-W mixtures for three qubits and beyond

I present an exact solution for the convex roof of the square root of the threetangle for rank two density matrices and for all states within the Bloch sphere. Aside the formerly known two tetrahedra it contains three additional optimal tetrahedra and connecting triangular optimal decompositions. The remaining optimal decompositions are one-dimensional. Optimal decompositions are proved to contain as many states from the zero-polytope as possible, a property that is called zero-state locking; it will be the working horse throughout this work. In addition, an inequality is derived which decides about the optimality of the decompositions under consideration. The footprint of the measure of entanglement consists in a characteristic pattern for the fixed pure states on the Bloch sphere surface which constitute the optimal solution. This solution is subject to transformation properties due to the SL-invariance of the entanglement measure which renders the optimal decomposition found here to all the states within the SL-class of GHZ and W. The method presented here is directly applicable to the symmetric mixture of generalized GHZ and W states for arbitrary number of qubits but the main structure of the 3-dimensional tetrahedra is general for all rank-two mixtures of states.

quant-ph↗

arXiv2025

Static impurity in a mesoscopic system of SU($N$) fermionic matter-waves

We investigate the effects of a static impurity, modeled by a localized barrier, in a one-dimensional mesoscopic system comprised of strongly correlated repulsive SU($N$)-symmetric fermions. For a mesoscopic sized ring under the effect of an artificial gauge field, we analyze the energy spectrum, the particle density and the current flowing through the impurity at varying interaction strengths, barrier heights, and number of components. We find that the physics of the system is governed by the competition between effective single-particle process and the formation of a high-stiffness spin-correlated state associated to the phenomenon of fractionalization of the flux quantum characterizing the $N$-component fermionic system. Our findings provide a route to probe the response of SU($N$) fermions to effective magnetic fields; at the same time, they hold significance for fundamental understanding of localized impurity problems.

cond-mat.quant-gas↗

arXiv2025

Threetangle in the XY-model class with a non-integrable field background

The square root of the threetangle is calculated for the transverse XY-model with an integrability-breaking in-plane field component. To be in a regime of quasi-solvability of the convex roof, here we concentrate here on a 4-site model Hamiltonian. In general, the field and hence a mixing of the odd/even sectors, has a detrimental effect on the threetangle, as expected. Only in a particular spot of models with no or weak inhomogeneity $γ$ does a finite value of the tangle prevail in a broad maximum region of the field strength $h\approx 0.3\pm 0.1$. There, the threetangle is basically independent of the non-zero angle $α$. This system could be experimentally used as a quasi-pure source of threetangled states or as an entanglement triggered switch depending on the experimental error in the field orientation.

quant-ph↗

arXiv2023

Perspective on new implementations of atomtronic circuits

In this article, we provide perspectives for atomtronics circuits on quantum technology platforms beyond simple bosonic or fermionic cold atom matter-wave currents. Specifically, we consider (i) matter-wave schemes with multi-component quantum fluids; (ii) networks of Rydberg atoms that provide a radically new concept of atomtronics circuits in which the flow, rather than in terms of matter, occurs through excitations; (iii) hybrid matter-wave circuits - cavities systems that can be used to study atomtronic circuits beyond the standard solutions and provide new schemes for integrated matter-wave networks. We also sketch how driving these systems can open new pathways for atomtronics.

cond-mat.quant-gas↗

arXiv2023

Interference dynamics of matter-waves of SU($N$) fermions

We analyze the two main physical observables related to the momenta of strongly correlated SU($N$) fermions in ring-shaped lattices pierced by an effective magnetic flux: homodyne (momentum distribution) and self-heterodyne interference patterns. We demonstrate how their analysis allows us to monitor the persistent current pattern. We find that both homodyne and self-heterodyne interference display a specific dependence on the structure of the Fermi distribution and particles' correlations. For homodyne protocols, the momentum distribution is affected by the particle statistics in two distinctive ways. The first effect is a purely statistical one: at zero interactions, the characteristic hole in the momentum distribution around the momentum $\mathbf{k}=0$ opens up once half of the SU($N$) Fermi sphere is displaced. The second effect originates from interaction: the fractionalization in the interacting system manifests itself by an additional `delay' in the flux for the occurrence of the hole, that now becomes a depression at $\mathbf{k}=0$. In the case of self-heterodyne interference patterns, we are not only able to monitor, but also observe the fractionalization. Indeed, the fractionalized angular momenta, due to level crossings in the system, are reflected in dislocations present in interferograms. Our analysis demonstrate how the study of the interference fringes grants us access to both number of particles and number of components of SU($N$) fermions.

cond-mat.quant-gas↗

arXiv2023

Probe for bound states of SU(3) fermions and colour deconfinement

Fermionic artificial matter realized with cold atoms grants access to an unprecedented degree of control on sophisticated many-body effects with an enhanced flexibility of the operating conditions. We consider three-component fermions with attractive interactions to study the formation of complex bound states whose nature goes beyond the standard fermion pairing occurring in quantum materials. Such systems display clear analogies with quark matter. Here, we address the nature of the bound states of a three-component fermionic system in a ring-shaped trap through the persistent current. In this way, we demonstrate that we can distinguish between color superfluid and trionic bound states. By analyzing finite temperature effects, we show how finite temperature can lead to the deconfinement of bound states. For weak interactions the deconfinement occurs because of scattering states. In this regime, the deconfinement depends on the trade-off between interactions and thermal fluctuations temperature. For strong interactions the features of the persistent current result from the properties of a suitable gas of bound states.

cond-mat.quant-gas↗

arXiv2023

Exact one-particle density matrix for SU($N$) fermionic matter-waves in the strong repulsive limit

We consider a gas of repulsive $N$-component fermions confined in a ring-shaped potential, subject to an effective magnetic field. For large repulsion strengths, we work out a Bethe ansatz scheme to compute the two-point correlation matrix and then the one-particle density matrix. Our results holds in the mesoscopic regime of finite but sufficiently large number of particles and system size that are not accessible by numerics. We access the momentum distribution of the system and analyse its specific dependence of interaction, magnetic field and number of components $N$. In the context of cold atoms, the exact computation of the correlation matrix to determine the interference patterns that are produced by releasing cold atoms from ring traps is carried out.

cond-mat.quant-gas↗

arXiv2017

Generalized W-state of four qubits with exclusively threetangle

We single out a class of states possessing only threetangle but distributed all over four qubits. This is a three-site analogue of states from the $W$-class, which only possess globally distributed pairwise entanglement as measured by the concurrence. We perform an analysis for four qubits, showing that such a state indeed exists. To this end we analyze specific states of four qubits that are not convexly balanced as for $SL$ invariant families of entanglement, but only affinely balanced. For these states all possible $SL$-invariants vanish, hence they are part of the $SL$ null-cone. Instead, they will possess at least a certain unitary invariant. As an interesting byproduct it is demonstrated that the exact convex roof is reached in the rank-two case of a homogeneous polynomial $SL$-invariant measure of entanglement of degree $2m$, if there is a state which corresponds to a maximally $m$-fold degenerate solution in the zero-polytope that can be combined with the convexified minimal characteristic curve to give a decomposition of $ρ$. If more than one such state does exist in the zero polytope, a minimization must be performed. A better lower bound than the lowest convexified characteristic curve is obtained if no decomposition of $ρ$ is obtained in this way.

quant-ph↗

arXiv2017

Exact zeros of entanglement for arbitrary rank-two mixtures: how a geometric view of the zero-polytope makes life more easy

Here I present a method how intersections of a certain density matrix of rank two with the zero-polytope can be calculated exactly. This is a purely geometrical procedure which thereby is applicable to obtaining the zeros of SL- and SU-invariant entanglement measures of arbitrary polynomial degree. I explain this method in detail for a recently unsolved problem. In particular, I show how a three-dimensional view, namely in terms of the Boch-sphere analogy, solves this problem immediately. To this end, I determine the zero-polytope of the three-tangle, which is an exact result up to computer accuracy, and calculate upper bounds to its convex roof which are below the linearized upper bound. The zeros of the three-tangle (in this case) induced by the zero-polytope (zero-simplex) are exact values. I apply this procedure to a superposition of the four qubit GHZand W-state. It can however be applied to every case one has under consideration, including an arbitrary polynomial convex-roof measure of entanglement and for arbitrary local dimension.

quant-ph↗

arXiv2016

Upper bound for SL-invariant entanglement measures of mixed states

An algorithm is proposed that serves to handle full rank density matrices, when coming from a lower rank method to compute the convex-roof. This is in order to calculate an upper bound for any polynomial SL invariant multipartite entanglement measure E. Here, it is exemplifyed how this algorithm works, based on a method for calculating convex-roofs of rank two density matrices. It iteratively considers the decompositions of the density matrix into two states each, exploiting the knowledge for the rank-two case. The algorithm is therefore quasi exact as far as the two rank case is concerned, and it also gives hints where it should include more states in the decomposition of the density matrix. Focusing on the threetangle, I show the results the algorithm gives for two states, one of which being the $GHZ$-Werner state, for which the exact convex roof is known. It overestimates the threetangle in the state, thereby giving insight into the optimal decomposition the $GHZ$-Werner state has. As a proof of principle, I have run the algorithm for the threetangle on the transverse quantum Ising model. I give qualitative and quantitative arguments why the convex roof should be close to the upper bound found here.

quant-ph↗

arXiv2016

The nine ways of four qubit entanglement and their threetangle

I calculate the mixed threetangle $τ_3[ρ]$ for the reduced density matrices of the four-qubit representant states found in Phys. Rev. A {\bf 65}, 052112 (2002). In most of the cases, the convex roof is obtained, except for one class, where I provide with a new upper bound, which is assumed to be very close to the convex roof. I compare with results published in Phys. Rev. Lett. {\bf 113}, 110501 (2014). Since the method applied there usually results in higher values for the upper bound, in certain cases it can be understood that the convex roof is obtained exactly, namely when the zero-polytope where $τ_3$ vanishes shrinks to a single point.

quant-ph↗

arXiv2016

Avalanche of entanglement and correlations at quantum phase transitions

We study the ground-state entanglement in the quantum Ising model with nearest neighbor ferromagnetic coupling $J$ and find a sequential increase of entanglement depth with growing $J$. This entanglement avalanche starts with two-point entanglement, as measured by the concurrence, and continues via the three-tangle and four-tangle, until finally, deep in the ferromagnetic phase for $J=\infty$, arriving at pure $\ell$-partite (GHZ type) entanglement of all $\ell$ spins. Comparison with the two, three, and four-point correlations reveals a similar sequence and shows strong ties to the above entanglement measures for small $J$. However, we also find a partial inversion of the hierarchy, where the four-point correlation exceeds the three- and two-point correlations, well before the critical point is reached. Qualitatively similar behavior is also found for the Bose-Hubbard model, suggesting that this is a general feature of a quantum phase transition. This should have far reaching consequences for approximations starting from a mean-field limit.

quant-ph↗

arXiv2016

Strong monogamy inequalities for four qubits

We investigate possible generalizations of the Coffman-Kundu-Wootters monogamy inequality to four qubits, accounting for multipartite entanglement in addition to the bipartite terms. We show that the most natural extension of the inequality does not hold in general, and we describe the violations of this inequality in detail. We investigate alternative ways to extend the monogamy inequality to express a constraint on entanglement sharing valid for all four-qubit states, and perform an extensive numerical analysis of randomly generated four-qubit states to explore the properties of such extensions.

quant-ph↗

arXiv2015

The fourtangle in the transverse XY model

We analyze the entanglement measure $C_4$ for mixed states in general and for the transverse XY model. We come to the conclusion that it cannot serve alone for guaranteeing an entanglement of $GHZ_4$-type. The genuine negativity calculated in Ref.~\cite{Hofmann14} isn't sufficient for that either and some additional measure of entanglement must be considered. In particular we study the transverse XY-model and find a non-zero $C_4$ measure which is of the same order of magnitude than the genuine negativity. Furthermore, we observe a feature in the $C_4$ values that resembles a destructive interference with the underlying concurrence.

quant-ph↗

arXiv2014

Genuinely multipartite entangled states in higher dimensions: a generalization of balancedness

I generalize the concept of balancedness to qudits with arbitrary dimension $d$. It is an extension of the concept of balancedness in New J. Phys. {\bf 12}, 075025 (2010) [1]. At first, I define maximally entangled states as being the stochastic states (with local reduced density matrices $\id/d$ for a $d$-dimensional local Hilbert space) that are not product states and show that every so-defined maximal genuinely multi-qudit entangled state is balanced. Furthermore, all irreducibly balanced states are genuinely multi-qudit entangled and are locally equivalent with respect to $SL(d)$ transformations (i.e. the local filtering transformations (LFO)) to a maximally entangled state. In particular the concept given here gives the maximal genuinely multi-qudit entangled states for general local Hilbert space dimension $d$. All genuinely multi-qudit entangled states are an element of the partly balanced $SU(d)$-orbits.

quant-ph↗

arXiv2014

SL-invariant entanglement measures in higher dimensions: the case of spin $1$ and $3/2$

An SL-invariant extension of the concurrence to higher local Hilbert-space dimension is due to its relation with the determinant of the matrix of a $d\times d$ two qudits state, which is the only SL-invariant of polynomial degree $d$. This determinant is written in terms of antilinear expectation values of the local $SL(d)$ operators. We use the permutation invariance of the comb-condition for creating further local antilinear operators which are orthogonal to the original operator. It means that the symmetric group acts transitively on the space of combs of a given order. This extends the mechanism for writing $SL(2)$-invariants for qubits to qudits. I outline the method, that in principle works for arbitrary dimension $d$, explicitely for spin 1, and spin 3/2. There is an odd-even discrepancy: whereas for half odd integer spin a situation similar to that observed for qubits is found, for integer spin the outcome is an asymmetric invariant of polynomial degree $2d$.

quant-ph↗

arXiv2014

Monogamy of entanglement and improved mean-field ansatz for spin lattices

We consider rather general spin-$1/2$ lattices with large coordination numbers $Z$. Based on the monogamy of entanglement and other properties of the concurrence $C$, we derive rigorous bounds for the entanglement between neighboring spins, such as $C\leq 1/\sqrt{Z}$, which show that $C$ decreases for large $Z$. In addition, the concurrence $C$ measures the deviation from mean-field behavior and can only vanish if the mean-field ansatz yields an exact ground state of the Hamiltonian. Motivated by these findings, we propose an improved mean-field ansatz by adding entanglement.

quant-ph↗

arXiv2014

Scaling of genuine multiparticle entanglement at a quantum phase transition

We investigate the scaling and spatial distribution of genuine multiparticle entanglement in three- and four-spin reduced states of the one-dimensional XY-model at the quantum phase transition. We observe a logarithmic divergence and show that genuine three- and four-particle entanglement obeys finite-size scaling.

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