The Schwinger Representation of a Group: Concept and Applications

Chaturvedi, S.; Marmo, Giuseppe; Mukunda, N.; Simon, Richard; Zampini, Alessandro

doi:10.1142/s0129055x06002802

Cited by 39 publications

(29 citation statements)

References 14 publications

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“…Here, S applies to any two degrees of freedom, which relates to the Schwinger representation of two harmonic oscillators; see Ref. [28] for a review. We have…”

Section: Essential Quantum Correlationsmentioning

confidence: 99%

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Operational definition of quantum correlations of light

Sperling¹,

Vogel²,

Agarwal³

2016

Phys. Rev. A

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Quantum features of correlated optical modes define a major aspect of the nonclassicality in quantized radiation fields. However, the phase-sensitive detection of a two-mode light field is restricted to interferometric setups and local intensity measurements. Even the full reconstruction of the quantum state of a single radiation mode relies on such detection layouts and the preparation of a well-defined reference light field. In this work, we establish the notion of the essential quantum correlations of two-mode light fields. It refers to those quantum correlations which are measurable by a given device, i.e., the accessible part of a nonclassical Glauber-Sudarshan phase-space distribution, which does not depend on a global phase. Assuming a simple four-port interferometer and photon-number-resolving detectors, we derive the reconstruction method and nonclassicality criteria based on the Laplace-transformed moment-generating function of the essential quasiprobability. With this technique, we demonstrate that the essential quantum correlations of a polarization tomography scheme are observable even if the detectors are imperfect and cannot truly resolve the photon statistics.

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“…Here, S applies to any two degrees of freedom, which relates to the Schwinger representation of two harmonic oscillators; see Ref. [28] for a review. We have…”

Section: Essential Quantum Correlationsmentioning

confidence: 99%

“…Let us also mention that the Stokes operators have the properties of a spin angular momentum algebra [26][27][28], withĴ =Ŝ/2 andĴ 2 =Ĵ ·Ĵ = (N /2)(N /2 +1). As we restrict ourselves to linear scenarios, let us also briefly comment on other types of interference schemes.…”

Section: Essential Quantum Correlationsmentioning

confidence: 99%

Operational definition of quantum correlations of light

Sperling¹,

Vogel²,

Agarwal³

2016

Phys. Rev. A

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“…In this paper, we extend these ideas to spinlike systems, where the classical phase space is the unit sphere. We stress that this is not a mere academic curiosity, since the underlying SU(2) symmetry plays a pivotal role in numerous models in physics [27].…”

Section: Introductionmentioning

confidence: 95%

The Wigner flow on the sphere

Yang

Valtierra²,

Klimov³

et al. 2019

Phys. Scr.

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We derive a continuity equation for the evolution of the SU(2) Wigner function under nonlinear Kerr evolution. We give explicit expressions for the resulting quantum Wigner current, and discuss the appearance of the classical limit. We show that the global structure of the quantum current significantly differs from the classical one, which is clearly reflected in the form of the corresponding stagnation lines.

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“…Here we aim to devise an algorithm to construct the D-functions of arbitrary representations of SU(n) for arbitrary n. We approach the problem of limited availability of SU(n) D-functions 47,48 by presenting (i) a mapping of the weights of an irrep to a graph, (ii) a graph-theoretic algorithm to compute boson realizations of the canonical basis states of SU(n) for arbitrary n (Algorithm 2 in Subsection IV B) and (iii) an algorithm that employs the constructed boson realizations to compute expressions for D-functions as polynomials in the matrix elements of the defining representation (Algorithm 3 in Subsection IV C).…”

Section: Introductionmentioning

confidence: 99%

Algorithms for SU(n) boson realizations and D-functions

Dhand

Sanders

Guise

2015

Journal of Mathematical Physics

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Boson realizations map operators and states of groups to transformations and states of bosonic systems. We devise a graph-theoretic algorithm to construct the boson realizations of the canonical SU(n) basis states, which reduce the canonical subgroup chain, for arbitrary n. The boson realizations are employed to construct D-functions, which are the matrix elements of arbitrary irreducible representations, of SU(n) in the canonical basis. We demonstrate that our D-function algorithm offers significant advantage over the two competing procedures, namely factorization and exponentiation.

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The Schwinger Representation of a Group: Concept and Applications

Cited by 39 publications

References 14 publications

Operational definition of quantum correlations of light

Operational definition of quantum correlations of light

The Wigner flow on the sphere

Algorithms for SU(n) boson realizations and D-functions

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