Quantifying entanglement with scattering experiments

Marty, Oliver; Epping, Michael; Kampermann, Hermann; Bruß, Dagmar; Plenio, Martin B.; Cramer, M.

doi:10.1103/physrevb.89.125117

Cited by 19 publications

(17 citation statements)

References 76 publications

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“…The Schmidt gap is related to the entanglement spectrum, that is, the eigenvalues of the reduced density matrix, which can exhibit critical behav-ior [82] (however, it can be misleading, see [83]). Note that the entanglement spectrum [84], Renyi entropies for pure states [85,86] and mixed state entanglement measures [87][88][89] are experimentally accessible. For the nearest-neighbor interactions the critical point and the critical exponents can be determined exactly: One finds that with ferro-or antiferromagnetic interactions (these quantities coincide for both cases), the critical value is given by g c = 1, while the exponents are ν = z = 1 and β m = β λ = 1/8 [80].…”

Section: Equilibrium Properties Of the Lrtimmentioning

confidence: 99%

Quantum Kibble-Zurek physics in long-range transverse-field Ising models

2019

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We analyze the quantum phase transitions taking place in a one-dimensional transverse field Ising model with long-range couplings that decay algebraically with distance. We are interested in the Kibble-Zurek universal scaling laws emerging in non-equilibrium dynamics and in the potential for the unambiguous observation of such behavior in a realistic experimental setup based on trapped ions. To this end, we determine the phase diagram of the model and the critical exponents characterizing its quantum phase transitions by means of density-matrix renormalization group calculations and finite-size scaling theory, which allows us to obtain good estimates for different range of ferro-and antiferromagnetic interactions. Beyond critical equilibrium properties, we tackle a non-equilibrium scenario in which quantum Kibble-Zurek scaling laws may be retrieved. Here it is found that the predicted non-equilibrium universal behavior, i.e. the scaling laws as a function of the quench rate and critical exponents, can be observed in systems comprising an experimentally feasible number of spins. Finally, a scheme is introduced to simulate the algebraically decaying couplings accurately by means of a digital quantum simulation with trapped ions. Our results suggest that quantum Kibble-Zurek physics can be explored and observed in state-of-the-art experiments with trapped ions realizing long-range Ising models.

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Section: Equilibrium Properties Of the Lrtimmentioning

confidence: 99%

Quantum Kibble-Zurek physics in long-range transverse-field Ising models

2019

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“…If a thermal cloud of atoms (the bath) were trapped in a different potential and brought in contact with the strongly trapped atoms in the lattice, their interaction, γ , could also be tuned. Then one may potentially interrogate the trapped atoms via scattering 28,47 , and deduce the structure factor to quantify entanglement.…”

Section: Resultsmentioning

confidence: 99%

“…Our results can be tested experimentally, as scattering experiments have already proved to be useful in quantifying multipartite entanglement 28 . Structure factors are macroscopic quantities measurable in various periodic systems, e.g., Bragg scattering on ultracold atoms in optical lattices 29 or from ion chains 30 and neutron scattering from solid state systems.…”

Section: Introductionmentioning

confidence: 88%

Environment mediated multipartite and multidimensional entanglement

Lee¹,

Najafabadi²,

Schumayer³

et al. 2019

Sci Rep

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Quantum entanglement is usually considered a fragile quantity and decoherence through coupling to an external environment, such as a thermal reservoir, can quickly destroy the entanglement resource. This doesn't have to be the case and the environment can be engineered to assist in the formation of entanglement. We investigate a system of qubits and higher dimensional spins interacting only through their mutual coupling to a reservoir. We explore the entanglement of multipartite and multidimensional system as mediated by the bath and show that at low temperatures and intermediate coupling strengths multipartite entanglement may form between qubits and between higher spins, i.e., qudits. We characterise the multipartite entanglement using an entanglement witness based upon the structure factor and demonstrate its validity versus the directly calculated entanglement of formation, suggesting possible experiments for its measure.

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“…With the advent of quantum information theory, the analysis and importance of uncertainty relation got enriched. It has numerous applications like, quantum cryptography [32][33][34], entanglement detection [35,36], quantum metrology [37] and quantum speed limit [38,39]. The thermal uncertainty relation that we have derived here is a special form of general uncertainty relation.…”

Section: Introductionmentioning

confidence: 89%

Relativistic quantum heat engine from uncertainty relation standpoint

Chattopadhyay

Paul

2019

Sci Rep

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Established heat engines in quantum regime can be modeled with various quantum systems as working substances. For example, in the non-relativistic case, we can model the heat engine using infinite potential well as a working substance to evaluate the efficiency and work done of the engine. Here, we propose quantum heat engine with a relativistic particle confined in the one-dimensional potential well as working substance. The cycle comprises of two isothermal processes and two potential well processes of equal width, which forms the quantum counterpart of the known isochoric process in classical nature. For a concrete interpretation about the relation between the quantum observables with the physically measurable parameters (like the efficiency and work done), we develop a link between the thermodynamic variables and the uncertainty relation. We have used this model to explore the work extraction and the efficiency of the heat engine for a relativistic case from the standpoint of uncertainty relation, where the incompatible observables are the position and the momentum operators. We are able to determine the bounds (the upper and the lower bounds) of the efficiency of the heat engine through the thermal uncertainty relation.

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Quantifying entanglement with scattering experiments

Cited by 19 publications

References 76 publications

Quantum Kibble-Zurek physics in long-range transverse-field Ising models

Quantum Kibble-Zurek physics in long-range transverse-field Ising models

Environment mediated multipartite and multidimensional entanglement

Relativistic quantum heat engine from uncertainty relation standpoint

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