Tree-size complexity of multiqubit states

Nguyen, Le Huy; Cai, Yu; Wu, Xingyao; Scarani, Valerio

doi:10.1103/physreva.88.012321

Cited by 2 publications

(1 citation statement)

References 41 publications

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“…There are other related compact objects that have been proposed with anisotropic interiors, such as gravastars [6]. Recently, it has also been found that equations of many-body astrophysical systems with spherical symmetry studied in the Post-Newtonian approach resemble those of the above-mentioned anisotropic fluid sources [7]. b) Cosmology: Spacetimes sourced by anisotropic fluids also find application in cosmology.…”

Section: Introductionmentioning

confidence: 98%

Stability analysis of a class of anisotropic spacetimes

Khamesra

Suneeta

2014

Phys. Rev. D

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We consider spherically symmetric spacetimes sourced by a fluid with pressure anisotropy in the radial direction. We use gauge-invariant perturbation theory to study the stability of this class of spacetimes under axial perturbations. We apply our results to three diverse examples. Two examples arise as endpoints of collapse of a ball of fluid -one describes a well-behaved stellar interior and the other has a naked singularity. We prove the stability of the stellar interior both with respect to Dirichlet and quasinormal mode boundary conditions on the perturbation. Surprisingly, the naked singularity is also stable under axial perturbations. Lastly, we take the example of anisotropic cosmology to show that in this case, the relevant perturbations are those in which the direction of anisotropy is also perturbed.

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Section: Introductionmentioning

confidence: 98%

Stability analysis of a class of anisotropic spacetimes

Khamesra

Suneeta

2014

Phys. Rev. D

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Maximal tree size of few-qubit states

Cai

et al. 2014

Phys. Rev. A

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Tree size (TS) is an interesting measure of complexity for multiqubit states: not only is it in principle computable, but one can obtain lower bounds for it. In this way, it has been possible to identify families of states whose complexity scales superpolynomially in the number of qubits. With the goal of progressing in the systematic study of the mathematical property of TS, in this work we characterize the tree size of pure states for the case where the number of qubits is small, namely, 3 or 4. The study of three qubits does not hold great surprises, insofar as the structure of entanglement is rather simple; the maximal TS is found to be 8, reached for instance by the |W state. The study of four qubits yields several insights: in particular, the most economic description of a state is found not to be recursive. The maximal TS is found to be 16, reached for instance by a state called |Ψ (4) which was already discussed in the context of four-photon down-conversion experiments. We also find that the states with maximal tree size form a set of zero measure: a smoothed version of tree size over a neighborhood of a state ( − TS) reduces the maximal values to 6 and 14, respectively. Finally, we introduce a notion of tree size for mixed states and discuss it for a one-parameter family of states.

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Tree-size complexity of multiqubit states

Cited by 2 publications

References 41 publications

Stability analysis of a class of anisotropic spacetimes

Stability analysis of a class of anisotropic spacetimes

Maximal tree size of few-qubit states

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