arXiv subjects

Amit Kundu

Publications and source records attributed to Amit Kundu.

10 recordsLinked to original sources

arXiv2025

Nonlocality in Continuous-Variable Quantum Networks

Quantum networks enable forms of nonlocality beyond the standard Bell scenario, with a multitude of potential applications. Continuous-variable (CV) platforms are particularly attractive for large-scale networks, offering deterministic entanglement generation and favorable prospects for long-distance distribution. Here we present a formalism to study CV network nonlocality using pseudospin measurements. Considering the linear chain and star configurations, we derive the maximal violations of the corresponding network locality inequalities for arbitrary two-mode states. Using two-mode squeezed vacuum states, we show that the strength of nonlocality in the star configuration remains independent of the network size. Moreover, the nonlocal correlations persist even at arbitrarily high temperatures provided the squeezing exceeds a critical threshold. Further, we demonstrate non-Gaussianity as an enhancer of network nonlocality through illustrations of various classes of non-Gaussian resources. Remarkably, a coherent superposition of single-photon subtractions across modes achieves maximal violation for vanishing squeezing. Finally, we provide schematics of an experimentally feasible implementation of CV network nonlocality based on the isomorphism between pseudospin and spatial parity observables.

quant-ph↗

arXiv2025

Measurement-device-independent Schmidt number certification of all entangled states

Bipartite quantum states with higher Schmidt numbers have been shown to outperform those with lower Schmidt numbers in various quantum information processing tasks, highlighting the operational advantage of entanglement dimensionality. Certifying the Schmidt number of such states is therefore crucial for efficient resource utilisation. Ideally, this certification should rely as little as possible on the certifying devices to ensure robustness against their potential imperfections. Fully device-independent certification via Bell-nonlocal games offers strong robustness but suffers from fundamental limitations: it cannot certify the Schmidt number of all entangled states. We demonstrate that this insufficiency of Bell-nonlocal games is not limited to entangled states that do not exhibit Bell-nonlocality. Specifically, we prove the existence of Bell-nonlocal states whose Schmidt number cannot be certified by any Bell-nonlocal game when the parties are restricted to local projective measurements. To overcome this, we develop a measurement-device-independent certification method based on semiquantum nonlocal games, which assume trusted preparation devices but treat measurement devices as black boxes. We prove that for any bipartite state with Schmidt number exceeding $r$, there exists a semiquantum nonlocal game that can certify its Schmidt number. Finally, we provide an explicit construction of such a semiquantum nonlocal game based on an optimal Schmidt number witness operator.

quant-ph↗

arXiv2024

Influence of joint measurement bases on sharing network nonlocality

Sharing network nonlocality in an extended quantum network scenario is the new paradigm in the development of quantum theory. In this paper, we investigate the influence of Elegant joint measurement(in short, EJM) bases in an extended bilocal scenario on sharing network nonlocality via sequential measurement. The work essentially based on the newly introduced[Phys. Rev. Lett. 126, 220401(2021)] bilocal inequality with ternary inputs for end parties and EJM as joint measurement bases in $Alice_n-Bob-Charlie_m$ scenario. Here, we are able to capture all simultaneous violation of this inequality for $(n,m)\in \{(2,1),(1,2),(1,1),(2,2)\}$ cases. We further observe the criteria for sharing network nonlocality where we are able to find also the dependence of the sharing on the amount of entanglement of the joint bases. The effect of the nonlinearity in this inequality is also captured in our results with the symmetrical and asymmetrical violation in this extended scenario. The work will generate further the realization of quantum correlations in network scenario.

quant-ph↗

arXiv2024

Measurement dependence can enhance security in a quantum network

Network Nonlocality is an advanced study of quantum nonlocality that comprises network structure beyond Bell's theorem. The development of quantum networks has the potential to bring a lot of technological applications in sevaral quantum information processing tasks. Here, we are focusing on how the role of the independence of the measurement choices of the end parties in a network works and can be used to enhance the security in a quantum network. In both three-parties two-sources bilocal network and four-parties three-sources star network scenarios, we are able to show, a practical way to understand the relaxation of the assumptions to enhance a real security protocol if someone wants to breach in a network communications. Theoratically, we have proved that by relaxing the independence of the measurement choices of only one end party we can create a Standard Network Nonlocality(SNN) and more stronger Full Network Nonlocality(FNN) and we can get maximum quantum violation by the classical no-signalling local model. We are able to distinguish between two types of network nonlocality in the sense that the FNN is stronger than SNN, i.e., FNN states all the sources in a network need to distribute nonlocal resources.

quant-ph↗

arXiv2023

Nature of Nonlocality in a triangle network based on EJM

Defining nonlocality in a no-input closed quantum network scenario is a new area of interest nowadays. Gisin, in[Entropy 21, 325 (2019)], proposed a possible condition for non-tri-locality of the trivial no-input closed network scenario, triangle network, by introducing a new kind of joint measurement bases and a probability bound. In[npj Quantum Information (2020) 6:70] they found a shred of numerical evidence in support of Gisin's probability bound. Now based on that probability bound, we find the nature of the correlation in a triangle network scenario. We here observe how far the probability lies from that Gisin's bound with every possible combination of entangled and local pure states distributed from three independent quantum sources. Here we use the generalized Elegant Joint Measurements bases for each party and find that there is a dependency of non-locality on the entanglement of these joint measurement bases. We also check the probability bound for the polygon structure.

quant-ph↗

arXiv2021

Arbitrary Measurement dependence in tripartite non-locality

The assumption of measurement independence is required for a local deterministic model to conduct a Bell test. The violation of a Bell inequality by such a model implies that this assumption must be relaxed. The degree to which the assumption needs to be relaxed to achieve violation of some bipartite Bell inequalities, has been investigated recently in [Phys. Rev. Lett. 105, 250404(2010), Phys. Rev. A 99, 012121(2019)]. In this work, we study the minimum degree of relaxation required to simulate violations of various well-known tripartite Bell inequalities and opens the possibility of relaxation in multipartite scenario. Local deterministic models are also provided to achieve the violations of these Bell inequalities.

quant-ph↗

arXiv2020

Monogamy Relations for Multiqubit Systems

Recently a new class of monogamy relations (actually, exponentially many) was provided by Christopher Eltschka et al. in terms of squared concurrence. Their approach restricted to the distribution of bipartite entanglement shared between different subsystems of a global state. We have critically analyzed those monogamy relations in three as well as in four qubit pure states using squared negativity. We have been able to prove that in case of pure three qubit states those relations are always true in terms of squared negativity. However, if we consider the pure four qubit states, the results are not always true. Rather, we find opposite behaviour in some particular classes of four qubit pure states where some of the monogamy relations are violated. We have provided analytical and numerical evidences in support of our claim.

quant-ph↗

arXiv2020

Maximal qubit violation of n-local inequalities in quantum network

Source independent quantum networks are considered as a natural generalization to the Bell scenario where we investigate the nonlocal properties of quantum states distributed and measured in a network. Considering the simplest network of entanglement swapping, recently Gisin et. al. and Andreoli et. al. independently provided a systematic characterization of the set of quantum states leading to violation of the so-called 'bilocality' inequality. In this work, we consider the complexities in the quantum networks with an arbitrary number of parties distributed in chain-shaped and star-shaped networks. We derive the maximal violation of the 'n-local' inequality that can be achieved by arbitrary two-qubit states for such chain and star-shaped networks. This would further provide us deeper understanding of quantum correlations in complex structures.

quant-ph↗

arXiv2020

Cosmological Correlations in Power Law Inflation models

Scalar field with non-minimal coupling to curvature scalar is studied in Robertson-Walker background. The infrared limit of two point function, and, in turn, of the energy-momentum tensor of scalar field have been considered in the power law inflation model. In this limit, within the perfect fluid model, consistent evolution of scale factor following power law inflation gives rise to growing mode solution for negative value of coupling constant. A simplified calculation for density perturbation in power law inflationary models is presented with these mode functions. Salient features of the perturbation spectra has been commented upon.

gr-qc↗

arXiv1999

Calculation of density fluctuation in inflationary epoch

Starting from an initial state of thermal equilibrium, we derive an expression for the quantum fluctuation in the energy density during the inflationary epoch in terms of the mode functions for the inflaton field. The effect of this particular initial state is not washed out in the final formula, contrary to what is usually believed. Numerically, however, the effect is completely negligible, validating the use of the two point function in the vacuum state. We also point out the requirement of conventional quantum field theory during inflation, that the quantum fluctuation in a wavelength must be evaluated, at the latest, when the wavelength crosses the Hubble length, in contrast to the usual practice in the literature.

hep-ph↗