Information diagrams in the study of entanglement in symmetric multi-quDit systems and applications to quantum phase transitions in Lipkin–Meshkov–Glick D-level atom models

Guerrero, Julio Becerra; Mayorgas, Alberto; Calixto, M.

doi:10.1007/s11128-022-03524-7

Cited by 5 publications

(13 citation statements)

References 27 publications

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“…First, we will review the concept of information diagrams and its main properties. We will limit our scope since most details have already been given in [1] (and references therein).…”

Section: Information Diagrams and Entropic Measuresmentioning

confidence: 99%

“…This makes possible the classification of density matrices within each subregion by the minimum rank they have. Details about the explicit meaning of these curves and their parametrization can be found on [1].…”

Section: Information Diagrams and Entropic Measuresmentioning

confidence: 99%

“…On previous papers [1], we applied them to characterize the entanglement of parity adapted U(D)-spin coherent states (CSs) or DCATs. This work extends this analysis, computing information diagrams for the generalization to different parities of the purely even DCAT already studied.…”

Section: Introductionmentioning

confidence: 99%

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Study of entanglement in symmetric multi-quDits systems through information diagrams

Guerrero,

Sojo,

Mayorgas

et al. 2023

SciPost Phys. Proc.

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Along this paper, we analyze the entanglement properties of symmetric multi-quDits systems in a special type of states created from the generalization to U(D) of the usual spin coherent states. By means of parity operators, we define what we call multicomponent Schrödinger cat states as parity adapted coherent states. Introducing the tool of information diagrams, i.e. representations of pairs of entropy measures, we analyze the correlation structure of this type of states and their M-wise reduced density matrices.

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“…First, we will review the concept of information diagrams and its main properties. We will limit our scope since most details have already been given in [1] (and references therein).…”

Section: Information Diagrams and Entropic Measuresmentioning

confidence: 99%

Section: Information Diagrams and Entropic Measuresmentioning

confidence: 99%

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Study of entanglement in symmetric multi-quDits systems through information diagrams

Guerrero,

Sojo,

Mayorgas

et al. 2023

SciPost Phys. Proc.

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“…The coefficients of this decomposition (Schmidt coefficients) and their squares (Schmidt eigenvalues) are determined for all N and M , and the main features of them and their behaviour under various limits are estudied. For a detailed account of these features, a variety of graphical tools are used, like contour plots, angular plots, etc., but, in the case of a large D, information diagrams (see [10] and references therein) prove to be a valuable tool when appropriate colormaps are used (see the Supplementary Material).…”

Section: Introductionmentioning

confidence: 99%

Schmidt decomposition of parity adapted coherent states for symmetric multi-quDits

Guerrero¹,

Sojo²,

Mayorgas³

et al. 2023

Preprint

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In this paper we study the entanglement in symmetric N -quDit systems. In particular we use generalizations to U (D) of spin U (2) coherent states and their projections on definite parity c ∈ Z D−1 2 (multicomponent Schrödinger cat) states and we analyse their reduced density matrices when tracing out M < N quDits. The eigenvalues (or Schmidt coefficients) of these reduced density matrices are completely characterized, allowing to proof a theorem for the decomposition of a N -quDit Schrödinger cat state with a given parity c into a sum over all possible parities of tensor products of Schrödinger cat states of N − M and M particles. Diverse asymptotic properties of the Schmidt eigenvalues are studied and, in particular, for the (rescaled) double thermodynamic limit (N, M → ∞, M/N fixed), we reproduce and generalize to quDits known results for photon loss of parity adapted coherent states of the harmonic oscillator, thus providing an unified Schmidt decomposition for both multi-quDits and (multi-mode) photons. These results allow to determine the entanglement properties of these states and also their decoherence properties under quDit loss, where we demonstrate the robustness of these states.

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“…The coefficients of this decomposition (Schmidt coefficients) and their squares (Schmidt eigenvalues) are determined for all N and M, and the main features of them and their behaviour under various limits are studied. For a detailed account of these features, a variety of graphical tools are used, like contour plots, angular plots, etc but, in the case of a large D, information diagrams (see [16] and references therein) prove to be a valuable tool when appropriate colormaps are used (see the supplementary material).…”

Section: Introductionmentioning

confidence: 99%

Schmidt decomposition of parity adapted coherent states for symmetric multi-quDits

Guerrero¹,

Sojo²,

Mayorgas³

et al. 2023

J. Phys. A: Math. Theor.

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In this paper we study the entanglement in symmetric $N$-quDit systems. In particular we use generalizations to $U(D)$ of spin $U(2)$ coherent states and their projections on definite parity $\mathbbm{c}\in\mathbb{Z}_2^{D-1}$ (multicomponent Schrödinger cat) states and we analyse their reduced density matrices when tracing out $M<N$ quDits. The eigenvalues (or Schmidt coefficients) of these reduced density matrices are completely characterized, allowing to proof a theorem for the decomposition of a $N$-quDit Schr"odinger cat state with a given parity $\mathbbm{c}$ into a sum over all possible parities of tensor products of Schr"odinger cat states of $N-M$ and $M$ particles. Diverse asymptotic properties of the Schmidt eigenvalues are studied and, in particular, for the (rescaled) double thermodynamic limit ($N,M\rightarrow\infty,\,M/N$ fixed), we reproduce and generalize to quDits known results for photon loss of parity adapted coherent states of the harmonic oscillator, thus providing an unified Schmidt decomposition for both multi-quDits and (multi-mode) photons. These results allow to determine the entanglement properties of these states and also their decoherence properties under quDit loss, where we demonstrate the robustness of these states.

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Information diagrams in the study of entanglement in symmetric multi-quDit systems and applications to quantum phase transitions in Lipkin–Meshkov–Glick D-level atom models

Abstract: In this paper we pursue the use of information measures (in particular, information diagrams) for the study of entanglement in symmetric multi-quDit systems. We use generalizations to $${U}(D)$$ U ( D ) of spin $${U}(2)$$ U ( 2 ) coherent states… Show more

Cited by 5 publications

References 27 publications

Study of entanglement in symmetric multi-quDits systems through information diagrams

Study of entanglement in symmetric multi-quDits systems through information diagrams

Schmidt decomposition of parity adapted coherent states for symmetric multi-quDits

Schmidt decomposition of parity adapted coherent states for symmetric multi-quDits

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