Signatures of avoided energy-level crossings in entanglement indicators obtained from quantum tomograms

Sharmila, B.; Lakshmibala, S.; Balakrishnan, V.

doi:10.1088/1361-6455/abc07e

Cited by 12 publications

(7 citation statements)

References 36 publications

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“…Surprisingly, the indicator ξ pcc that captures only linear correlations, performs well, and agrees reasonably well with N(ρ ab ) (figure 4 (d)). This is in contrast to earlier results on bipartite CV and multipartite HQ systems [10],…”

Section: Nmr Experiments Icontrasting

confidence: 99%

“…Earlier work [10] indicates that ξ pcc , which captures linear correlations between the respective quadratures of the two subsystems, does not reflect very reliably the extent 0.0E+00 of entanglement. In direct contrast to this, in NMR experiment I where the state considered is a mixed bipartite state, ξ pcc is in good agreement with spin squeezing and negativity N(ρ ab ), although not with the discord.…”

Section: Discussionmentioning

confidence: 94%

“…The entanglement between the radiation fields in the output ports of a quantum beamsplitter has been identified qualitatively from tomograms [8]. Further, a quantitative analysis of entanglement using several indicators based directly on tomograms in bipartite CV and multipartite hybrid quantum (HQ) systems has been carried out [9,10], and the results have been compared with standard measures of entanglement such as ξ qmi .…”

Section: Introductionmentioning

confidence: 99%

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Tomographic entanglement indicators from NMR experiments

Sharmila,

Krithika,

Pal

et al. 2021

Preprint

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In recent years, the performance of different entanglement indicators obtained directly from tomograms has been assessed in continuous-variable and hybrid quantum systems. In this paper, we carry out this task in the case of spin systems. We compute the entanglement indicators from actual experimental data obtained from three liquid-state NMR experiments, and compare them with standard entanglement measures calculated from the corresponding density matrices, both experimentally reconstructed and numerically computed. The gross features of entanglement dynamics and spin squeezing properties are found to be reproduced by these entanglement indicators. However, the extent to which these indicators and spin squeezing track the entanglement during time evolution of the multipartite systems in the NMR experiments is very sensitive to the precise nature and strength of interactions as well as the manner in which the full system is partitioned into subsystems. We also use the IBM quantum computer to implement equivalent circuits that capture the dynamics of the multipartite system in one of the NMR experiments. We compute and compare the entanglement indicators obtained from the tomograms corresponding to the experimental execution and simulation of these equivalent circuits. This exercise shows that these indicators can estimate the degree of entanglement without necessitating detailed state reconstruction procedures, establishing the advantage of the tomographic approach.

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Section: Nmr Experiments Icontrasting

confidence: 99%

Section: Discussionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

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Tomographic entanglement indicators from NMR experiments

Sharmila,

Krithika,

Pal

et al. 2021

Preprint

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“…It is therefore advantageous to avoid detailed state reconstruction wherever possible, and to extract reliable entanglement indicators solely from tomograms. Such entanglement indicators have been proposed in the literature and their efficacy examined in CV and HQ systems by comparing them with standard entanglement measures and monotones (Sharmila et al, 2020;Sharmila et al, 2022).…”

Section: Introductionmentioning

confidence: 99%

A tomographic approach to the sum uncertainty relation and quantum entanglement in continuous variable systems

Paul¹,

Lakshmibala²,

Balakrishnan³

et al. 2023

Front. Quantum Sci. Technol.

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Entropic uncertainty relations (EURs) have been examined in various contexts, primarily in qubit systems, including their links with entanglement, as they subsume the Heisenberg uncertainty principle. With their genesis in the Shannon entropy, EURs find applications in quantum information and quantum optics. EURs are state-dependent, and the state has to be reconstructed from tomograms (which are histograms readily available from experiments). This is a challenge when the Hilbert space is large, as in continuous variable (CV) systems and certain hybrid quantum (HQ) systems. A viable alternative approach therefore is to extract as much information as possible about the unknown quantum state directly from appropriate tomograms. Many variants of EURs can be extracted from tomograms, even for CV systems. In earlier work we have defined many tomographic entanglement indicators (TEIs) that can be readily calculated from tomograms without knowledge of the density matrix, and have reported on their efficacy as entanglement indicators in various contexts in both CV and HQ systems. The specific objectives of the present work are as follows: (i) To use the tomographic approach to investigate the links between EURs and TEIs in CV and HQ systems as they evolve in time. (ii) To identify the TEI that most closely tracks the temporal evolution of EURs. We consider two generic systems. The first is a multilevel atom modeled as a nonlinear oscillator interacting with a quantized radiation field. The second is the Λ-atom interacting with two radiation fields. The former model accomodates investigations on the role of the initial state of the field and the ratio of the strengths of interaction and nonlinearity in the connection between TEIs and EURs. The second model opens up the possibility of examining the connection between mixed state bipartite entanglement and EURs, when the number of atomic levels is finite. Since the tomogram respects the requirements of classical probability theory, this effort also sheds light on the extent to which TEIs reflect the temporal behaviour of those EURs which are rooted in the Shannon entropy.

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“…The advantage of the latter has been showcased in certain continuous-variable (CV) systems as, for instance, in identifying qualitative signatures of entanglement between the radiation fields in the output ports of a quantum beam-splitter [5]. Further, detailed analysis of entanglement has been carried out theoretically using several indicators obtained directly from tomograms in different contexts, e.g., close to avoided energy-level crossings [6]. Their efficacy has been assessed by comparison with standard entanglement measures [7,8].…”

Section: Introductionmentioning

confidence: 99%

Tomographic entanglement indicators in frequency combs and Talbot carpets

Sharmila,

Lakshmibala,

Balakrishnan

2021

Preprint

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Recent theoretical investigations on tomographic entanglement indicators have showcased the advantages of the tomographic approach in the context of continuous-variable (CV), spin and hybrid quantum systems. Direct estimation of entanglement using experimental data from the IBM quantum computing platform and NMR experiments have also been carried out in earlier work. A similar investigation in the context of CV systems is necessary to fully assess the utility of our tomographic approach. In this paper, we highlight the advantages of our approach in the context of experiments reported in the literature on two CV systems, namely, entangled Talbot carpets and biphoton frequency combs. We use the tomographic entanglement indicator to assess the extent of entanglement between a pair of Talbot carpets and demonstrate that this provides a simpler and more direct procedure compared to the one suggested in the experiment. We also establish that the tomograms corresponding to the two biphoton frequency combs carry clear entanglement signatures that distinguish between the two states.

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Signatures of avoided energy-level crossings in entanglement indicators obtained from quantum tomograms

Cited by 12 publications

References 36 publications

Tomographic entanglement indicators from NMR experiments

Tomographic entanglement indicators from NMR experiments

A tomographic approach to the sum uncertainty relation and quantum entanglement in continuous variable systems

Tomographic entanglement indicators in frequency combs and Talbot carpets

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