Geometry of spin coherent states

Chryssomalakos, Chryssomalis; Guzmán-González, Edgar; Serrano-Ensástiga, Eduardo

doi:10.1088/1751-8121/aab349

Cited by 24 publications

(13 citation statements)

References 50 publications

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“…where | n and | n are assumed to be normalized. While any set of 2j +1 distinct coherent states already spans the full spin Hilbert space [33], the standard overcompleteness relation from the general group theoretical construction of coherent states is most commonly used [34]…”

Section: Properties Of Spin Coherent Statesmentioning

confidence: 99%

Non-Markovian Quantum State Diffusion for Spin Environments

Link¹,

Luoma²,

Strunz³

2022

Preprint

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We introduce a theory of non-Markovian quantum state diffusion (NMQSD) for quantum systems coupled to a class of non-Gaussian environments consisting of spins. This allows us to express the time evolved reduced state of the system as the average of an ensemble of stochastically evolving pure states. We develop the theory for arbitrary linear spin environments at zero and also at finite temperature. Moreover, we introduce a hierarchical expansion which constitutes a method to numerically compute the time evolution of the stochastic pure states, and thus to solve the open system problem.

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Section: Properties Of Spin Coherent Statesmentioning

confidence: 99%

Non-Markovian Quantum State Diffusion for Spin Environments

Link¹,

Luoma²,

Strunz³

2022

Preprint

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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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“…The restriction of product states to the symmetric subspace leads to N -qubit states of the form |ψ = |φ ⊗N with |φ = α|+ +β|− a normalized single qubit state. In the spin picture, this corresponds to spin-coherent (SC) states [25,26]. The convex hull of SC states defines the set of classical spin-states C [27,28].…”

Section: A Separable States Of Multiqubit Systemsmentioning

confidence: 99%

Maximally entangled mixed symmetric states of two qubits

Serrano-Ensástiga¹,

Martin²

2021

Preprint

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In this work, a variation of the problem originally solved by Verstraete, Audenaert, and De Moor [Phys. Rev. A 64, 012316 (2001)] on what is the maximum entanglement that can be created in a two-qubit system by a global unitary transformation is considered and solved when permutation invariance in the state is imposed. The additional constraint of permutation symmetry appears naturally in the context of bosonic systems or spin states. We also characterise symmetric two-qubit states that remain separable after any global unitary transformation, called symmetric absolutely separable states (SAS), or absolutely classical for spin states. This allows us to determine the maximal radius of a ball of SAS states around the maximally mixed state in the symmetric sector, and the minimal radius of a ball that includes the set of SAS states. For three-qubit systems, a necessary condition for absolute separability of symmetric states is given, which leads us to upper bounds on the ball radii similar to those studied for the two-qubit system.

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Geometry of spin coherent states

Cited by 24 publications

References 50 publications

Non-Markovian Quantum State Diffusion for Spin Environments

Non-Markovian Quantum State Diffusion for Spin Environments

Quantum concepts in optical polarization

Maximally entangled mixed symmetric states of two qubits

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