Majorana representation for mixed states

Serrano-Ensástiga, Eduardo; Braun, Daniel

doi:10.1103/physreva.101.022332

Cited by 21 publications

(11 citation statements)

References 55 publications

(107 reference statements)

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“…Over the years much work has been done to elucidate the geometry of the state space of higher level systems, with special focus on the qutrit state space Q 3 [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. To develop an intuition for the full high-dimensional geometry of the qutrit state space, subsets, cross sections and projections onto two and three dimensions were extensively studied [6,7,10,12,15,17,18,[20][21][22][23] and multi-parameter representations of qutrit states were developed [14,21,[24][25][26]. While these approaches can reproduce many geometric properties correctly, they do not give a global view of the Bloch body.…”

Section: A Bloch-ball Analog For a Qutritmentioning

confidence: 99%

The shape of higher-dimensional state space: Bloch-ball analog for a qutrit

Eltschka

Huber

Morelli

et al. 2021

Quantum

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Geometric intuition is a crucial tool to obtain deeper insight into many concepts of physics. A paradigmatic example of its power is the Bloch ball, the geometrical representation for the state space of the simplest possible quantum system, a two-level system (or qubit). However, already for a three-level system (qutrit) the state space has eight dimensions, so that its complexity exceeds the grasp of our three-dimensional space of experience. This is unfortunate, given that the geometric object describing the state space of a qutrit has a much richer structure and is in many ways more representative for a general quantum system than a qubit. In this work we demonstrate that, based on the Bloch representation of quantum states, it is possible to construct a three dimensional model for the qutrit state space that captures most of the essential geometric features of the latter. Besides being of indisputable theoretical value, this opens the door to a new type of representation, thus extending our geometric intuition beyond the simplest quantum systems.

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Section: A Bloch-ball Analog For a Qutritmentioning

confidence: 99%

The shape of higher-dimensional state space: Bloch-ball analog for a qutrit

Eltschka

Huber

Morelli

et al. 2021

Quantum

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“…The denominator in the l.h.s. of (32) is just the product of the eigenvalues of the matrix − ( ) ( ), i.e., its determinant, so that a generating function for the multiplicities ( , ) , for fixed , , and all values of , may be obtained in the form of an integral formula,…”

Section: Generating Functionsmentioning

confidence: 99%

“…The stellar representation of Majorana, originally designed for pure states of a monopartite system [1], can be also generalized for mixed quantum states [32]. In the case of multipartite systems, the stellar representation is directly applicable to symmetric states of a system composed of several qubits, but a generalization applicable to antisymmetric states has also been established [33].…”

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confidence: 99%

Symmetric Multiqudit States: Stars, Entanglement, Rotosensors

Chryssomalakos,

Hanotel,

Guzmán-González

et al. 2021

Preprint

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A constellation of= − 1 Majorana stars represents an arbitrary pure quantum state of dimension or a permutation-symmetric state of a system consisting of qubits. We generalize the latter construction to represent in a similar way an arbitrary symmetric pure state of subsystems with levels each. For ≥ 3, such states are equivalent, as far as rotations are concerned, to a collection of various spin states, with definite relative complex weights. Following Majorana's lead, we introduce a multiconstellation, consisting of the Majorana constellations of the above spin states, augmented by an auxiliary, "spectator" constellation, encoding the complex weights. Examples of stellar representations of symmetric states of four qutrits, and two spin-3/2 systems, are presented. We revisit the Hermite and Murnaghan isomorphisms, which relate multipartite states of various spins, number of parties, and even symmetries. We show how the tools introduced can be used to analyze multipartite entanglement and to identify optimal quantum rotosensors, i.e., pure states which are maximally sensitive to rotations around a specified axis, or averaged over all axes.

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“…Consequently, ρ nc must commute with F z , and hence share the same eigenvectors |1, m . A useful visual way to infer the rotational symmetries over the quantum states, which allows to simplify the degrees of freedom, is through the stellar Majorana representation for pure [51] and mixed states [52]. The eigenvalues of A (B7) are described by…”

Section: P Phasementioning

confidence: 99%

Metastable spin-phase diagrams in antiferromagnetic Bose-Einstein condensates

Serrano-Ensástiga,

Mireles

2021

Preprint

Self Cite

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Spinor Bose-Einstein condensates under external magnetic fields exhibit well-characterized spin domains of its ground state due to spin-dependent interactions. At low temperatures, collisioninduced spin-mixing instabilities may promote the condensate to dwell into metastable states occurring near the phase boundaries. In this work, we study theoretically the metastable spin-phase diagram of a spin-1 antiferromagnetic Bose-Einstein condensate at zero and finite temperatures. The approach makes use of Hartree-Fock theory and exploits the symmetry of the Hamiltonian and of the order parameters yielding a closed system of transcendental equations for the free energy, fully avoiding the use of selfconsistency. Our results are consistent with recent experiments and allow us to explain qualitatively the different types of observed quench dynamics. In addition, we found that similar phenomena should occur in antiferromagnetic spinor condensates with a sudden change in the temperature. It is shown also that the increase of temperature induces a traceable shift of the Ferromagnetic-Polar transition boundary, behavior previously not noticed by selfconsistent mean-field calculations.

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Majorana representation for mixed states

Cited by 21 publications

References 55 publications

The shape of higher-dimensional state space: Bloch-ball analog for a qutrit

The shape of higher-dimensional state space: Bloch-ball analog for a qutrit

Symmetric Multiqudit States: Stars, Entanglement, Rotosensors

Metastable spin-phase diagrams in antiferromagnetic Bose-Einstein condensates

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