Symplectic group methods and the Arthurs Kelly model of measurement in quantum mechanics

Arvind, .; Chaturvedi, S.; Mukunda, N.

doi:10.1016/j.physleta.2020.126543

Cited by 2 publications

(1 citation statement)

References 18 publications

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“…Here the results show that the optimal performance of the scheme can only be obtained when the meters are uncorrelated. Since the Hamiltonians involved in the sequential measurement and the Arthurs-Kelly scheme are quadratic expressions in quadrature operators, the corresponding symplectic transformations acting on the quadrature operators or the phase space variables belong to the real symplectic group Sp(4, R) and Sp(6, R) [39], respectively. We exploit this fact and explicitly work in phase space for calculational simplicity.…”

Section: Introductionmentioning

confidence: 99%

Estimation of Wigner distribution of single mode Gaussian states: a comparative study

Kumar

2021

Preprint

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In this work, we consider the estimation of single mode Gaussian states using four different measurement schemes namely: i) homodyne measurement, ii) sequential measurement, iii) Arthurs-Kelly scheme, and iv) heterodyne measurement, with a view to compare their relative performance. To this end, we work in the phase space formalism, specifically at the covariance matrix level, which provides an elegant and intuitive way to explicitly carry out involved calculations. We show that the optimal performance of the Arthurs-Kelly scheme and the sequential measurement is equal to the heterodyne measurement. While the heterodyne measurement outperforms the homodyne measurement in the mean estimation of squeezed state ensembles, the homodyne measurement outperforms the heterodyne measurement for variance estimation of squeezed state ensembles up to a certain range of the squeezing parameter. We then modify the Hamiltonian in the Arthurs-Kelly scheme, such that the two meters can have correlations and show that the optimal performance is achieved when the meters are uncorrelated. We expect that these results will be useful in various quantum information and quantum communication protocols.

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Section: Introductionmentioning

confidence: 99%

Estimation of Wigner distribution of single mode Gaussian states: a comparative study

Kumar

2021

Preprint

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Estimation of the Wigner distribution of single-mode Gaussian states: A comparative study

Kumar

Arvind

2022

Phys. Rev. A

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Symplectic group methods and the Arthurs Kelly model of measurement in quantum mechanics

Cited by 2 publications

References 18 publications

Estimation of Wigner distribution of single mode Gaussian states: a comparative study

Estimation of Wigner distribution of single mode Gaussian states: a comparative study

Estimation of the Wigner distribution of single-mode Gaussian states: A comparative study

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