Non-Gaussianity and entropy-bounded uncertainty relations: Application to detection of non-Gaussian entangled states

Baek, Kyunghyun; Nha, Hyunchul

doi:10.1103/physreva.98.042314

Cited by 15 publications

(19 citation statements)

References 44 publications

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“…Superpositions of two Fock states were studied in [8,9,39]. Various superpositions of two coherent states |α and | − α with different weights and phases were considered in papers [7,9,24,26,27,[37][38][39]. Such superpositions include, in particular, the so-called even/odd coherent states, introduced in [61] and frequently considered as simple models of the "Schrödinger cat states"; for numerous generalizations, one can consult, e.g., References [62,63].…”

Section: Introductionmentioning

confidence: 99%

Non-Gaussianity of Four-Photon Superpositions of Fock States

Freitas

Dodonov

2021

Quantum Reports

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We study two families of four-photon superpositions of the Fock states: even vacuum squeezed states (EVSS) and orthogonal-even coherent states (OECS). These families are distinguished due to several properties: for certain values of parameters, they give the fourth-order uncertainty products close to the known minimal value (which is lower than for the Gaussian states); they have equal dimensionless values of the second- and fouth-order moments of the coordinate and momentum for all values of parameters; they possess zero covariances for all values of parameters. Since these states are obviously non-Gaussian, we consider them as good candidates to compare several different measures of non-Gaussianity proposed by different authors for the past fifteen years. The reference Gaussian states in all examples are thermal states dependent on a single parameter (an effective temperature or the coordinate variance). We analyze the measures based on the normalized Hilbert–Schmidt distance and the relative entropy (introduced by Genoni–Paris–Banaszek), the fidelity measure (Ghiu–Marian–Marian) and its logarithmic analog (Baek–Nha), as well as the Mandilara–Karpov–Cerf “Gaussianity parameter”. These measures are compared with the kurtosis of the coordinate probability density and with the non-Gaussian behavior of the Wigner function.

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Section: Introductionmentioning

confidence: 99%

Non-Gaussianity of Four-Photon Superpositions of Fock States

Freitas

Dodonov

2021

Quantum Reports

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“…Superpositions of two Fock states were studied in [7,8,38]. Various superpositions of two coherent states |α and | − α with different weights and phases were considered in papers [6,8,23,25,26,[36][37][38]. Such superpositions include, in particular, the so called even/odd coherent states, introduced in [59] and frequently considered nowadays as simple models of the "Schrödinger cat states"; for numerous generalizations one can consult, e.g., Refs.…”

Section: Introductionmentioning

confidence: 99%

“…[60,61]. Various families of photon-added and photon-subtracted states were considered in papers [13,[21][22][23]26,28,[34][35][36]38,62]. Many examples related to all these states were considered in [39].…”

Section: Introductionmentioning

confidence: 99%

Non-Gaussianity of Four-Photon Superpositions of Fock States

Dodonov¹,

Citeli²

2021

Preprint

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“…These variance-based URs clearly indicate an inherent limitation to preparing a quantum state with a narrow distribution in both position and momentum observables simultaneously. In addition, they provided a useful insight into developing URs in terms of other quantum state statistical characteristics, such as mixedness [5] and non-Gaussianity [6,7,8], and into developing entanglement criteria for general quantum systems [9,10,11,12].…”

Section: Introductionmentioning

confidence: 99%

Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements

Baek

Nha

Son

2019

Entropy

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We derive an entropic uncertainty relation for generalized positive-operator-valued measure (POVM) measurements via a direct-sum majorization relation using Schur concavity of entropic quantities in a finite-dimensional Hilbert space. Our approach provides a significant improvement of the uncertainty bound compared with previous majorization-based approaches [S. Friendland, V. Gheorghiu and G. Gour, Phys. Rev. Lett. 111, 230401 (2013); A. E. Rastegin and K.Życzkowski, J. Phys. A, 49, 355301 (2016)], particularly by extending the direct-sum majorization relation first introduced in [ L. Rudnicki, Z. Pucha la and K.Życzkowski, Phys. Rev. A 89, 052115 (2014)]. We illustrate the usefulness of our uncertainty relations by considering a pair of qubit observables in a two-dimensional system and randomly chosen unsharp observables in a three-dimensional system. We also demonstrate that our bound tends to be stronger than the generalized Maassen-Uffink bound with an increase in the unsharpness effect. Furthermore, we extend our approach to the case of multiple POVM measurements, thus making it possible to establish entropic uncertainty relations involving more than two observables.

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Non-Gaussianity and entropy-bounded uncertainty relations: Application to detection of non-Gaussian entangled states

Cited by 15 publications

References 44 publications

Non-Gaussianity of Four-Photon Superpositions of Fock States

Non-Gaussianity of Four-Photon Superpositions of Fock States

Non-Gaussianity of Four-Photon Superpositions of Fock States

Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements

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