Bound Entanglement

Horodecki, Paweł

doi:10.1002/9783527805785.ch13

Cited by 172 publications

(297 citation statements)

References 118 publications

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“…From this it follows that the states ghz have, for any convex entanglement measure obeying the additional constraint of being permutation-invariant [14], the minimal entanglement among all states with the same GHZ fidelities f + and f − . This can be seen as follows: The transformations (i), (ii) and (iii) from above do not change the amount of entanglement.…”

Section: Figurementioning

confidence: 89%

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Evaluating the geometric measure of multiparticle entanglement

2015

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We present an analytical approach to evaluate the geometric measure of multiparticle entanglement for mixed quantum states. Our method allows the computation of this measure for a family of multiparticle states with a certain symmetry and delivers lower bounds on the measure for general states. It works for an arbitrary number of particles, for arbitrary classes of multiparticle entanglement, and can also be used to determine other entanglement measures.

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Section: Figurementioning

confidence: 89%

“…From this property and Eq. (14) it follows that the geometric measure for a state decreases under a positive map , if the nearest separable state σ is mapped onto a separable states, i.e.…”

Section: Connections To Other Entanglement Measuresmentioning

confidence: 99%

Evaluating the geometric measure of multiparticle entanglement

2015

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“…others include the more general one-parameter family of R enyi entropies [225,226,229] for parameter lower than 1, the Hartley entropy lnr Sch (which can be considered as the R enyi entropy in the limit when its parameter tends to 0), the Schmidt rank r Sch itself, the one-parameter family of Tsallis entropies, [230] the concurrence-squared, or linear entropy (the latter two are, up to normalization, the Tsallis entropy for parameter 2). On the other hand, the von Neumann entropy is the R enyi or Tsallis entropy in the limit when their parameters tend to 1.…”

Section: Svd and Entanglementmentioning

confidence: 99%

Tensor product methods and entanglement optimization for ab initio quantum chemistry

Szalay

Pfeffer

Murg

et al. 2015

Int J of Quantum Chemistry

282

395

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The treatment of high-dimensional problems such as the Schr€ odinger equation can be approached by concepts of tensor product approximation. We present general techniques that can be used for the treatment of high-dimensional optimization tasks and time-dependent equations, and connect them to concepts already used in many-body quantum physics. Based on achievements from the past decade, entanglement-based methods-developed from different perspectives for different purposes in distinct communities already matured to provide a variety of tools-can be combined to attack highly challenging problems in quantum chemistry. The aim of the present paper is to give a pedagogical introduction to the theoretical background of this novel field and demonstrate the underlying benefits through numerical applications on a text book example. Among the various optimization tasks, we will discuss only those which are connected to a controlled manipulation of the entanglement which is in fact the key ingredient of the methods considered in the paper. The selected topics will be covered according to a series of lectures given on the topic "New wavefunction methods and entanglement optimizations in quantum

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“…The robustness of the presented results is ensured by exploring settings that involve a higher number of orbitals thereby supporting the validity of our approximation and of the observed beyond mean-field excitations (see also appendix B). Within the employed multi-orbital approximation bipartite entanglement (see [49,50] and references therein) between the distinguishable species resulting from the spontaneous fragmentation of the DBs is generally present. More importantly it is the interplay between fragmentation and the resulting entanglement which gives rise to the observed dynamical structures.The dynamics of a single DB soliton being initialized off-center in the parabolic trap is first analyzed.…”

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confidence: 99%

Dark–bright soliton dynamics beyond the mean-field approximation

et al. 2017

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The dynamics of dark-bright (DB) solitons beyond the mean-field approximation is investigated. We first examine the case of a single DB soliton and its oscillations within a parabolic trap. Subsequently, we move to the setting of collisions, comparing the mean-field approximation to that involving multiple orbitals in both the dark and the bright component. Fragmentation is present and significantly affects the dynamics, especially in the case of slower solitons and in that of lower atom numbers. It is shown that the presence of fragmentation allows for bipartite entanglement between the distinguishable species. Most importantly the interplay between fragmentation and entanglement leads to the splitting of each of the parent mean-field DB solitons, placed off-center within the parabolic trap, into a fast and a slow daughter solitary wave. The latter process is in direct contrast to the predictions of the mean-field approximation. A variety of excitations including DB solitons in multiple (concurrently populated) orbitals is observed. Dark-antidark states and domain-wall-bright soliton complexes can also be observed to arise spontaneously in the beyond mean-field dynamics. that slower solitons and smaller atom numbers result in significant deviations from the mean-field, Gross-Pitaevskii (GP) limit.However, to the best of our knowledge, such studies have not been performed in a systematic fashion in multi-component settings and for associated solitary wave structures. In that light, herein we explore the case of DB solitons and their dynamics, as well as collisions both at and beyond the mean-field limit. To incorporate the quantum fluctuations stemming from the correlations in the DB soliton dynamics, we employ the multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB) [47,48] designed for simulating the quantum dynamics of bosonic mixtures. We consider both the oscillation of a single DB solitary wave in a trap, as well as the interaction of two symmetric solitary waves inside a parabolic trap. We compare and contrast the findings of the mean-field case (where a single orbital is effectively used in the dark-and brightcomponents) with cases where multiple orbitals are used. In all cases it is found that the initial mean-field DB solitons split into daughter DB solitary waves, in contrast to the well-known mean-field predictions. The robustness of the presented results is ensured by exploring settings that involve a higher number of orbitals thereby supporting the validity of our approximation and of the observed beyond mean-field excitations (see also appendix B). Within the employed multi-orbital approximation bipartite entanglement (see [49,50] and references therein) between the distinguishable species resulting from the spontaneous fragmentation of the DBs is generally present. More importantly it is the interplay between fragmentation and the resulting entanglement which gives rise to the observed dynamical structures.The dynamics of a single DB soliton being initialized off-ce...

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Bound Entanglement

Cited by 172 publications

References 118 publications

Evaluating the geometric measure of multiparticle entanglement

Evaluating the geometric measure of multiparticle entanglement

Tensor product methods and entanglement optimization for ab initio quantum chemistry

Dark–bright soliton dynamics beyond the mean-field approximation

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