SLOCC classification for nine families of four-qubits

Li, Dafa; Li, Xiangrong; Huang, Hongtao; Li, Xinxin

doi:10.26421/qic9.9-10-5

Cited by 21 publications

(24 citation statements)

References 8 publications

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“…Results on the classification of pure four-qubit states with respect to SLOCC can be found in [23][24][25][26]. Note that in the literature, sometimes the scaling factor λ is incorrectly ignored.…”

Section: Appendix a Entanglement Polytopesmentioning

confidence: 99%

Experimental detection of entanglement polytopes via local filters

et al. 2017

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Quantum entanglement, resulting in correlations between subsystems that are stronger than any possible classical correlation, is one of the mysteries of quantum mechanics. Entanglement cannot be increased by any local operation, and for a sufficiently large many-body quantum system there exist infinitely many different entanglement classes, i.e., states that are not related by stochastic local operations and classical communications. On the other hand, the method of entanglement polytopes results in finitely many coarse-grained types of entanglement that can be detected by only measuring single-particle spectra. We find, however, that with high probability the local spectra lie in more than one polytope, hence providing only partial information about the entanglement type. To overcome this problem, we propose to additionally use so-called local filters, which are non-unitary local operations. We experimentally demonstrate the detection of entanglement polytopes in a four-qubit system. Using local filters we can distinguish the entanglement type of states with the same single particle spectra, but which belong to different polytopes.

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Section: Appendix a Entanglement Polytopesmentioning

confidence: 99%

Experimental detection of entanglement polytopes via local filters

et al. 2017

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“…For any larger systems, there are an infinite number. In 4 qubits, for example, SLOCC classes can be described via nine canonical forms, each crucially with free parameters [79]. Thus, generating a variety of entangled states presents a difficult task in general.…”

Section: Appendixmentioning

confidence: 99%

Entangled Datasets for Quantum Machine Learning

Schatzki¹,

Arrasmith²,

Coles³

et al. 2021

Preprint

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High-quality, large-scale datasets have played a crucial role in the development and success of classical machine learning. Quantum Machine Learning (QML) is a new field that aims to use quantum computers for data analysis, with the hope of obtaining a quantum advantage of some sort. While most proposed QML architectures are benchmarked using classical datasets, there is still doubt whether QML on classical datasets will achieve such an advantage. In this work, we argue that one should instead employ quantum datasets composed of quantum states. For this purpose, we introduce the NTangled dataset composed of quantum states with different amounts and types of multipartite entanglement. We first show how a quantum neural network can be trained to generate the states in the NTangled dataset. Then, we use the NTangled dataset to benchmark QML models for supervised learning classification tasks. We also consider an alternative entanglement-based dataset, which is scalable and is composed of states prepared by quantum circuits with different depths. As a byproduct of our results, we introduce a novel method for generating multipartite entangled states, providing a use-case of quantum neural networks for quantum entanglement theory.

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“…On the other hand, it was reported in [25,26] that the number of the families is eight instead of nine for genuinely entangled states. 3 Furthermore, it was discovered in [27] that the nine families in [24] further split into 49 SLOCC entanglement classes by looking at SLOCC invariant quantities.…”

Section: -Qubit Slocc Classesmentioning

confidence: 99%

Braiding quantum gates from partition algebras

Padmanabhan,

Sugino,

Trancanelli

2020

Preprint

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Unitary braiding operators can be used as robust entangling quantum gates. We introduce a solution-generating technique to solve the (d, m, l)-generalized Yang-Baxter equation, for m 2 ≤ l ≤ m, which allows to systematically construct such braiding operators. This is achieved by using partition algebras, a generalization of the Temperley-Lieb algebra encountered in statistical mechanics. We obtain families of unitary and non-unitary braiding operators that generate the full braid group. Explicit examples are given for a 2-, 3-, and 4-qubit system, including the classification of the entangled states generated by these operators based on Stochastic Local Operations and Classical Communication.

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SLOCC classification for nine families of four-qubits

Cited by 21 publications

References 8 publications

Experimental detection of entanglement polytopes via local filters

Experimental detection of entanglement polytopes via local filters

Entangled Datasets for Quantum Machine Learning

Braiding quantum gates from partition algebras

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