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Relevant bibliographies by topics / Absolutely Maximally Entangled states

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Academic literature on the topic 'Absolutely Maximally Entangled states'

Author: Grafiati

Published: 24 April 2022

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Journal articles on the topic "Absolutely Maximally Entangled states"

1

Mansour, M., M. Daoud, and L. Bouhouch. "Absolutely maximally entangled states from phase states." International Journal of Quantum Information 17, no. 01 (2019): 1950009. http://dx.doi.org/10.1142/s0219749919500096.

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We derive absolutely maximally entangled (AME) states from phase states for a multi-qudit system whose dynamics is governed by a two-qudit interaction Hamiltonian of Heisenberg type. AME states are characterized by being maximally entangled for all bipartitions of the multi-qudit system and present absolute multipartite entanglement. The key ingredient of this approach is the theory of phase states for finite-dimensional systems (qudits). We define further the unitary phase operators of [Formula: see text]-qudit systems and we give next the corresponding separable phase states. Using a qudit–q

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2

Raissi, Zahra, Christian Gogolin, Arnau Riera, and Antonio Acín. "Optimal quantum error correcting codes from absolutely maximally entangled states." Journal of Physics A: Mathematical and Theoretical 51, no. 7 (2018): 075301. http://dx.doi.org/10.1088/1751-8121/aaa151.

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3

Bernal, Antonio. "On the Existence of Absolutely Maximally Entangled States of Minimal Support II." Quantum Physics Letters 8, no. 1 (2019): 1–4. http://dx.doi.org/10.18576/qpl/080101.

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4

Huber, Felix, Christopher Eltschka, Jens Siewert, and Otfried Gühne. "Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity." Journal of Physics A: Mathematical and Theoretical 51, no. 17 (2018): 175301. http://dx.doi.org/10.1088/1751-8121/aaade5.

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5

Huber, Felix, and Markus Grassl. "Quantum Codes of Maximal Distance and Highly Entangled Subspaces." Quantum 4 (June 18, 2020): 284. http://dx.doi.org/10.22331/q-2020-06-18-284.

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We present new bounds on the existence of general quantum maximum distance separable codes (QMDS): the length n of all QMDS codes with local dimension D and distance d≥3 is bounded by n≤D2+d−2. We obtain their weight distribution and present additional bounds that arise from Rains' shadow inequalities. Our main result can be seen as a generalization of bounds that are known for the two special cases of stabilizer QMDS codes and absolutely maximally entangled states, and confirms the quantum MDS conjecture in the special case of distance-three codes. As the existence of QMDS codes is linked to

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6

Reuvers, R. "An algorithm to explore entanglement in small systems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2214 (2018): 20180023. http://dx.doi.org/10.1098/rspa.2018.0023.

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A quantum state’s entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms. Depending on the choice of norm, the optimizing states maximize or minimize entanglement, possibly across several bipartite cuts at the same time and possibly only among states in a specified subspace. Recognizing that convergence but not success is certain, we use the algorithm to explore topics ranging from fermionic reduced density matrices and varieties of pu

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7

I. Latorre, Jose, and German Sierra. "Platonic entanglement." Quantum Information and Computation 21, no. 13&14 (2021): 1081–90. http://dx.doi.org/10.26421/qic21.13-14-1.

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We present a construction of highly entangled states defined on the topology of a platonic solid using tensor networks based on ancillary Absolute Maximally Entangled (AME) states. We illustrate the idea using the example of a quantum state based on AME(5,2) over a dodecahedron. We analyze the entropy of such states on many different partitions, and observe that they come on integer numbers and are almost maximal. We also observe that all platonic solids accept the construction of AME states based on Reed-Solomon codes since their number of facets, vertices and edges are always a prime number

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8

Bernal, Antonio. "On the Existence of Absolutely Maximally Entangled States of Minimal Support Physical Consistency of Theories with Fermions in the Division Algebra Modules." Quantum Physics Letters 6, no. 1 (2017): 1–3. http://dx.doi.org/10.18576/qpl/060101.

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9

Revzen, M. "Universal maximally entangled states." Quantum Studies: Mathematics and Foundations 2, no. 1 (2014): 77–88. http://dx.doi.org/10.1007/s40509-014-0016-4.

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10

Li, Z. G., M. G. Zhao, S. M. Fei, H. Fan, and W. M. Liu. "Mixed maximally entangled states." Quantum Information and Computation 12, no. 1&2 (2012): 63–73. http://dx.doi.org/10.26421/qic12.1-2-5.

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We find that the mixed maximally entangled states exist and prove that the form of the mixed maximally entangled states is unique in terms of the entanglement of formation. Moreover, even if the entanglement is quantified by other entanglement measures, this conclusion is still proven right. This result is a supplementary to the generally accepted fact that all maximally entangled states are pure. These states possess important properties of the pure maximally entangled states, for example, these states can be used as a resource for faithful teleportation and they can be distinguished perfectl

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