Berry phase and quantum entanglement in Majorana's stellar representation

Liu, H. D.; Fu, Libin

doi:10.1103/physreva.94.022123

Cited by 40 publications

(37 citation statements)

References 45 publications

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“…To investigate this point it is advantageous to use the Majorana stellar representation [343], which allows us to uniquely depict a spin state state living in H by 2 points on the unit sphere [344]. Several decades after its conception, this representation has recently attracted a great deal of attention in several fields [345][346][347][348][349][350][351][352][353][354][355][356][357][358].…”

Section: Majorana Representationmentioning

confidence: 99%

Quantum concepts in optical polarization

et al. 2021

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We comprehensively review the quantum theory of the polarization properties of light. In classical optics, these traits are characterized by the Stokes parameters, which can be geometrically interpreted using the Poincaré sphere. Remarkably, these Stokes parameters can also be applied to the quantum world, but then important differences emerge: now, because fluctuations in the number of photons are unavoidable, one is forced to work in the three-dimensional Poincaré space that can be regarded as a set of nested spheres. Additionally, higher-order moments of the Stokes variables might play a substantial role for quantum states, which is not the case for most classical Gaussian states. This brings about important differences between these two worlds that we review in detail. In particular, the classical degree of polarization produces unsatisfactory results in the quantum domain. We compare alternative quantum degrees and put forth that they order various states differently. Finally, intrinsically nonclassical states are explored and their potential applications in quantum technologies are discussed.

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Section: Majorana Representationmentioning

confidence: 99%

Quantum concepts in optical polarization

et al. 2021

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“…Notably, the entire constellation rotates rigidly under a polarization rotation, lending geometric intuition to multiphoton polarization states. The usefulness of the Majorana representation has been realized in topics from metrology (Bouchard et al, 2017;Chryssomalakos and Hernández-Coronado, 2017;Chryssomalakos et al, 2021;Goldberg, 2020;Goldberg and James, 2018;Goldberg et al, 2021d;Martin et al, 2020) to Bose-Einstein condensates (Cui et al, 2013;Lian et al, 2012) to non-Hermitian physics (Bartlett et al, 2021) and beyond (Björk et al, 2015a,b;Bruno, 2012;Chabaud et al, 2020;Dogra et al, 2020;Giraud et al, 2010;Hannay, 1998a,b;Kolenderski and Demkowicz-Dobrzanski, 2008;Lamacraft, 2010;Liu and Fu, 2016;Mäkelä and Messina, 2010;Martin et al, 2010;Usha Devi et al, 2012;Yang et al, 2015). We exemplify some Majorana constellations in Fig.…”

Section: A Characterizing Polarizationmentioning

confidence: 99%

Quantum Polarimetry

Goldberg

2021

Preprint

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Polarization is one of light's most versatile degrees of freedom for both classical and quantum applications. The ability to measure light's state of polarization and changes therein is thus essential; this is the science of polarimetry. It has become ever more apparent in recent years that the quantum nature of light's polarization properties is crucial, from explaining experiments with single or few photons to understanding the implications of quantum theory on classical polarization properties. We present a self-contained overview of quantum polarimetry, including discussions of classical and quantum polarization, their transformations, and measurements thereof. We use this platform to elucidate key concepts that are neglected when polarization and polarimetry are considered only from classical perspectives.

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“…The Majorana representation (MR), in which a pure state of a spin- system 1 , 2 can be precisely described as the trajectory of stars on a unit sphere, was proposed by Majorana in 1932 3 . Over the past decades, the MR has been proved to be a valuable method for many applications in quantum entanglement 4 – 10 , Bose-Einstein condensates 12 – 16 , 25 , and geometric phase 10 , 17 – 20 . In refs 10 , 20 , the Berry phase was studied by the stars and their loops on the Bloch sphere.…”

Section: Introductionmentioning

confidence: 99%

“…Over the past decades, the MR has been proved to be a valuable method for many applications in quantum entanglement 4 – 10 , Bose-Einstein condensates 12 – 16 , 25 , and geometric phase 10 , 17 – 20 . In refs 10 , 20 , the Berry phase was studied by the stars and their loops on the Bloch sphere. With the solid angles of the Majorana star loops, an intuitive relation between the Berry phase and Majorana stars’ trajectories on the Bloch sphere was given and it was shown that the Berry phase is determined by both the solid angles subtended by every Majorana star’s evolution path and the correlations between the stars 20 .…”

Section: Introductionmentioning

confidence: 99%

The Exact Curve Equation for Majorana Stars

Feng

Liu

et al. 2017

Sci Rep

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Majorana stars are visual representation for a quantum pure state. For some states, the corresponding majorana stars are located on one curve on the Block sphere. However, it is lack of exact curve equations for them. To find the exact equations, we consider a superposition of two bosonic coherent states with an arbitrary relative phase. We analytically give the curve equation and find that the curve always goes through the North pole on the Block sphere. Furthermore, for the superpositions of SU(1,1) coherent states, we find the same curve equation.

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Berry phase and quantum entanglement in Majorana's stellar representation

Cited by 40 publications

References 45 publications

Quantum concepts in optical polarization

Quantum concepts in optical polarization

Quantum Polarimetry

The Exact Curve Equation for Majorana Stars

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