arXiv subjects

Kaushiki Mukherjee

Publications and source records attributed to Kaushiki Mukherjee.

At least 19 recordsLinked to original sources

arXiv2026

Full Network Nonlocality Based Security In Quantum Key Distribution

In the last decade research of quantum nonlocality has moved beyond the regime of standard Bell nonlocality to consider network-based experimental set-ups involving multiple independent sources. Notion of full network nonlocality has emerged as some truly network phenomena that cannot be realized in traditional Bell experiments. Present work manifests utility of such form of truly network non-classicality in designing a four partite network-based entanglement assisted quantum key distribution protocol. To be more precise, security of the protocol relies upon full network nonlocality detection via violation of some suitable trilocal inequality. Based on the quantum bit error rate and violation of trilocal inequality, arbitrary two qubit entangled states are characterized in accordance with their utility in successfully executing the protocol. Intuitively, owing to connected structure of entangled sources, any genuine form of network nonlocality may offer advantage over standard Bell nonlocality for designing secure key distribution protocols. To establish that as a fact, another QKD protocol relying upon Bell-CHSH nonlocality detection in all pairs of sender and a receiver party is designed. The former turns out to be more secure compared to the latter. Importantly, while the quantum bit error rate can be less than 14.6% exploiting Bell-CHSH nonlocality, it can be reduced below 13.7% by exploiting full network nonlocality.

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arXiv2025

Network nonlocality breaking channels

Network nonlocality, a recently noted form of nonlocality has been shown to have distinctive features, marking a significant departure from the notion of standard Bell nonlocality in the context of quantum correlations. On a pragmatic front, it has gained significant importance as researchers worldwide actively engage in the study on quantum networks. However, as typical to any quantum resource, network nonlocality is also vulnerable to environmental noise, which sometimes prove to be detrimental. Environmental interactions are modeled in terms of quantum channels. In the present study, we introduce and characterize network nonlocality breaking channels. Network nonlocality breaking channels model environmental influences which results in the loss of resource, i.e., the system loses its nonlocal resource due to such interactions. The study is done in the ambit of some suitably chosen inequalities in (i) linear networks and (ii) star-shaped networks. Further, the loss in full network nonlocality is also studied. Furthermore, we also characterize quantum channels according to their ability in preserving quantum resources, i.e., they do not break network nonlocality, which enables one to identify useful quantum channels in networks. The study is vindicated by illustrations from various noise models like depolarizing and dephasing channels.

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arXiv2025

Measurement Incompatibility Based In-equivalence Between Bell and Network Nonlocality

It is a well-known fact that measurement incompatibility is a necessary resource to generate nonlocal correlations in usual Bell scenario that typically involves single quantum source. We can provide with some contrasting findings if we consider connected structure of multiple quantum sources. Precisely, we demonstrate that non n-locality can be detected in standard quantum network even when only a single party performs incompatible measurements. More interestingly, for any finite n greater than 2, non n-local correlations can be generated in any standard linear n-local network when all the parties perform compatible measurements. Such an observation is topology specific as one of the parties must perform incompatible measurement to exhibit non n-locality in any non-linear network endowed with star topology. However, we observe that in any non-standard network(all sources independent and nonlocal), to generate genuine non n-local correlations, all the parties must perform incompatible measurements. Such a finding is intuitive as more resource is required to generate stronger form of quantum non-classicality. We also demonstrate that merely providing resource of measurement incompatibility to all the parties is not sufficient for non n-locality detection in any quantum network

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arXiv2025

Revealing Hidden Non n-Locality In n-Local Star Network

Keeping pace with technological advancement, in the past decade, use of scalable networks have extended the study of quantum non-classicality beyond the regime of Bell-CHSH nonlocality. Present work provide characterization of non n-locality that can be exploited by incorporating filtering operations in star-shaped n-local networks. This in turn provide a framework of sequential n-local networks capable of generating non n-local correlations by involving some suitable form of stochastic local operations assisted with classical communications(SLOCC). It is observed that for effectiveness of such sequential networks, Bell-CHSH nonlocality(upto SLOCC operations) of every individual two-qubit state, distributed in the network, is not mandatory. However, there does not exist any separable local filter, which when applied in n-local network involving only Bell local states(upto SLOCC operations), can reveal non n-locality. Interestingly, instances revealing advantage of nonseparable mutli-qubit local filters over separable mutli-qubit local filters(by central node) are obtained. Such an advantage is attributable to the specific topology of star-shaped n-local networks and thus can never be reflected in Bell scenario.

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arXiv2024

Network Nonlocality Without Entanglement Of All Sources

Entanglement and nonlocality are two important nonclassical features of quantum correlations. Recently the study of quantum correlations in networks has undergone remarkable progress owing to technological development towards scalable quantum networks. However, compared to standard Bell scenario, manifestation of the interplay between these two aspects has received less attention in network scenarios featuring independent sources. In this work we have analyzed the relation between entanglement content of the sources and detectable non n-locality in two distinct network topologies(linear and star). We have studied the extremal violations of n-local inequalities(compatible with linear and star network) for any fixed amount of entanglement(in terms of concurrence) of the independent sources. It is observed that each of the sources must be entangled for detecting non n-locality in linear network. However, the same is not true for star n-local network. Present analysis is revealing that entanglement of all the independent sources is not a necessity for generation of non n-local correlations in star topology. Characterization of sources in terms of minimum entanglement requirement for any fixed violation amount of the n-local inequalities is also provided. Interestingly, detection of non n-locality is ensured in the network if product of concurrence of all the sources involved exceeds 1/2. .

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arXiv2024

Quantum channels and some absolute properties of quantum states

Environmental interactions are ubiquitous in any real-world application of a quantum information processing protocol. Such interactions result in depletion of quantum resources. Two important figure of merits in the context of quantum information are the fully entangled fraction (FEF) and conditional entropy of a composite quantum system. FEF has a key role to play in tasks like teleportation. Conditional entropy on the other hand can be negative for certain quantum states and thus the negativity remains a resource for tasks like dense coding and state merging. FEF $ > 1/d $ for a $ d \otimes d $ quantum system is a significant threshold, however for some quantum states it remains less than the threshold even with global unitary operations, consequently being known as states having absolute fully entangled fraction (AFEF). Pertaining to conditional von Neumann entropy, there are some states which retains the nonnegativity of the conditional entropy under global unitary action, to be called as states with absolute conditional von Neumann entropy nonnegative (ACVENN) property. In the present submission, we probe the action of some quantum channels in two qubits and two qudits and find that some quantum states move from the non-absolute regime to the absolute regime under the action. Since, global unitary operations are unable to retrieve them back to the non-absolute regime, we provide a prescription for the retrieval using an entanglement swapping network. Furthermore, we extend the notion of absoluteness to conditional Rényi entropies and find the required condition for a state to have absolute conditional Rényi entropy non-negative (ACRENN) property. We then extend the work to include the marginals of a tripartite system and provide for their characterization with respect to the aforementioned absolute properties.

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arXiv2023

Hidden Non n-locality In Linear Networks

We study hidden nonlocality in a linear network with independent sources. In the usual paradigm of Bell nonlocality, there are certain states which exhibit nonlocality only after the application of suitable local filtering operations, which, in turn, are some special stochastic local operations assisted with classical communication (SLOCC). In the present work, we introduce the notion of hidden non n-locality. The notion is detailed using a bilocal network. We provide instances of hidden nonbilocality and nontrilocality, where we notice quite intriguingly that nonbilocality is observed even when one of the sources distributes a mixed two-qubit separable state. Furthermore, a characterization of hidden nonbilocality is also provided in terms of the Bloch-Fano decomposition, wherein we conjecture that, to witness hidden nonbilocality, one of the two states (used by the sources) must have nonnull local Bloch vectors. Noise is inevitable in practical scenarios, which makes it imperative to study any possible method to enhance the possibility of detecting nonclassicality in the presence of noise in the network. We find that local filtering enhances the robustness to noise, which we demonstrate using bit-flip and amplitude-damping channels.

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arXiv2023

Entanglement and Teleportation in a 1-D Network with Repeaters

The most simplest form of quantum network is an one dimensional quantum network with a single player in each node. In remote entanglement distribution each of the players carry out measurement at the intermediate nodes to produce an entangled state between initial and final node which are remotely separated. It is imperative to say that the flow of information as well as the percolation of entanglement in a network between the source and target node is an important area of study. This will help us to understand the limits of the resource states as well as the measurements that are carried out in the process of remote entanglement distribution. In this article we investigate how the concurrence of the final entangled state obtained is connected with the concurrences of the initial entangled states present in a 1-D chain. We extend the works done for the pure entangled states for mixed entangled states like Werner states, Bell diagonal states and for general mixed states. We did not limit ourselves to a situation where the measurements are happening perfectly. We also investigate how these relations change when we consider imperfect swapping. We obtain the limits on the number of swappings as well as the success probability measurements to ensure the final state to be entangled state after swapping. In addition to these we also investigate on how much quantum information can be sent from the initial node to the final node (by computing the teleportation fidelity) when the measurement is perfect and imperfect with the same set of examples. Here also we obtain the limits on the number of swapping and the success probability of measurement to ensure that the final state obtained is capable of transferring the information . These results have tremendous future applications in sending quantum information between two quantum processors in remote entangled distribution.

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arXiv2023

Persistency of non-n-local correlations in noisy linear networks

Linear n-local networks are compatible with quantum repeaters based entanglement distribution protocols. Different sources of imperfections such as error in entanglement generation, communication over noisy quantum channels and imperfections in measurements result in decay of quantumness across such networks. From practical perspectives it becomes imperative to analyze non classicality of quantum network correlations in presence of different types of noise. Present discussion provides a formal characterization of non n-local feature of quantum correlations in noisy network scenario. In this context, persistency of non n-locality has been introduced. Such a notion helps in analyzing decay of non n-local feature of network correlations with increasing length of the linear network in presence of one or more causes of imperfections.

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arXiv2023

Hidden Steering Nonlocality in Quantum Networks

By combining two objects with no quantum effect one can get an object with quantum effect. Such a phenomenon, often referred to as activation has been analyzed for the notion of steering nonlocality. Activation of steering nonlocality is observed for different classes of mixed entangled states in linear network scenarios. Characterization of arbitrary two qubit states, in ambit of steering activation in network scenarios has been provided in this context. Using the notion of reduced steering, instances of steerability activation are also observed in nonlinear network. Present analysis involves three measurement settings scenario(for both trusted and untrusted parties) where steering nonlocality is distinguishable from Bell nonlocality.

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arXiv2023

Detecting Nontrilocal Correlations In Triangle Networks

Correlations in quantum networks with independent sources exhibit a completely novel form of nonclassicality in the sense that the nonlocality of such correlations can be demonstrated in fixed local input scenarios. Before the pioneering work by M.O.Renou, et al., in [1], the nonlocal feature of such network correlations was directly attributable to standard Bell nonlocality. In [1], the authors provided some of the first examples of triangle network correlations, whose nonlocality cannot be deduced from Bell-CHSH nonlocality. To date, a complete characterization of such scenarios is yet to be provided. Present work characterizes correlations arising due to fixed local measurements in a triangle network under a source independence assumptions. Precisely speaking, a set of criteria is framed in the form of Bell-type inequalities, each of which is necessarily satisfied by trilocal correlations. Possible quantum violation of at least one criterion from the set is analyzed, which in turn points out the utility of the set of criteria to detect nonlocality (nontrilocality) in quantum triangle networks. Interestingly, measurement on a local product state basis turns out to be sufficient to generate nontrilocal correlations in some quantum networks. Noise tolerance of the detection criteria is discussed followed by a generalization of the framework for demonstrating correlations in any n-sided polygon where n is finite.

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arXiv2022

Role of Steering Inequality In Quantum Key Distribution Protocol

Violation of Bell's inequality has been the mainspring for secure key generation in an entanglement assisted Quantum Key Distribution(QKD) protocol. Various contributions have relied on the violation of appropriate Bell inequalities to build an appropriate QKD protocol. Residing between Bell nonlocality and entanglement, there exists a hybrid trait of correlations, namely correlations exhibited through the violation of steering inequalities. However, such correlations have not been put to use in QKD protocols as much as their stronger counterpart, the Bell violations. In the present work, we show that the violations of the CJWR(E.G.Cavalcanti,S.J. Jones,H.M Wiseman and M.D. Reid, Phys.Rev.A 80,032112(2009))steering inequalities can act as key ingredients in an entanglement assisted QKD protocol. We work with arbitrary two qubit entangled states, characterize them in accordance with their utility in such protocols. The characterization is based on the quantum bit error rate and violation of a CJWR inequality. Furthermore, we show that subsequent applications of local filtering operations on initially entangled states exhibiting non violation, lead to violations necessary for the successful implementation of the protocol. An additional vindication of our protocol is provided by the use of absolutely Bell-CHSH local states, states which remain Bell-CHSH local even under global unitary operations.

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arXiv2022

Absolute fully entangled fraction from spectrum

Fully entangled fraction (FEF) is a significant figure of merit for density matrices. In bipartite $ d \otimes d $ quantum systems, the threshold value FEF $ > 1/d $, carries significant implications for quantum information processing tasks. Like separability, the value of FEF is also related to the choice of global basis of the underlying Hilbert space. A state having its FEF $ \le 1/d $, might give a value $ > 1/d $ in another global basis. A change in the global basis corresponds to a global unitary action on the quantum state. In the present work, we find that there are quantum states whose FEF remains less than $ 1/d $, under the action of any global unitary i.e., any choice of global basis. We invoke the hyperplane separation theorem to demarcate the set from states whose FEF can be increased beyond $ 1/d $ through global unitary action. Consequent to this, we probe the marginals of a pure three party system in qubits. We observe that under some restrictions on the parameters, even if two parties collaborate (through unitary action on their combined system) they will not be able to breach the FEF threshold. The study is further extended to include some classes of mixed three qubit and three qutrit systems. Furthermore, the implications of our work pertaining to $ k- $copy nonlocality and teleportation are also investigated.

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arXiv2020

Shareability of Quantum Steering and its Relation with Entanglement

Steerability is a characteristic of quantum correlations lying in between entanglement and Bell nonlocality. Understanding how these steering correlations can be shared between different parties has profound applications in ensuring security of quantum communication protocols. Here we show that at most two bipartite reduced states of a three qubit state can violate the three settings CJWR linear steering inequality contrary to two settings linear steering inequality. This result explains that quantum steering correlations have limited shareability properties and can sometimes even be nonmonogamous. In contrast to the two setting measurement scenario, three setting scenario turns out to be more useful to develop deeper understanding of shareability of tripartite steering correlations. Apart from distribution of steering correlations, several relations between reduced bipartite steering, different measures of bipartite entanglement of reduced states and genuine tripartite entanglement are presented here. The results enable detection of different kind of tripartite entanglement.

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arXiv2020

Any Two Qubit State Has Non Zero Quantum Discord Under Global Unitary Operations

Quantum discord is significant in analyzing quantum nonclassicality beyond the paradigm of entanglement. Presently we have explored the effectiveness of global unitary operations in manifesting quantum discord from a general two qubit zero discord state. Apart from the emergence of some obvious concepts such as absolute classical-quantum, absolute quantum-classical states, more interestingly, it is observed that set of states characterized by absoluteness contains only maximally mixed state. Consequently this marks the peak of effectiveness of global unitary operations in purview of manifesting nonclassicality from arbitrary two qubit state when other standard methods fail to do so. Set of effective global unitaries has been provided in this context. Our observations have direct implications in remote state preparation task.

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arXiv2020

Characterizing Quantum Correlations In Fixed Input $n$-Local Network Scenario

Contrary to Bell scenario, quantum nonlocality can be exploited even when all the parties do not have freedom to select inputs randomly. Such manifestation of nonlocality is possible in networks involving independent sources. One can utilize such a feature of quantum networks for purpose of entanglement detection of bipartite quantum states. In this context, we characterize correlations simulated in networks involving finite number of sources generating quantum states when some parties perform fixed measurement. Beyond bipartite entanglement, we enquire the same for networks involving sources now generating pure tripartite quantum states. Interestingly, here also randomness in input selection is not necessary for every party to generate nonlocal correlation.

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arXiv2019

Environmental effects on nonlocal correlations

Environmental interactions are ubiquitous in practical instances of any quantum information processing protocol. The interaction results in depletion of various quantum resources and even complete loss in numerous situations. Nonlocality, which is one particular quantum resource marking a significant departure of quantum mechanics from classical mechanics, meets the same fate. In the present work we study the decay in nonlocality to the extent of the output state admitting a local hidden state model. Using some fundamental quantum channels we also demonstrate the complete decay in the resources in the purview of the Bell-CHSH inequality and a 3-settings steering inequality. We also obtain bounds on the parameter of the depolarizing map for which it becomes steerability breaking pertaining to a general class of two qubit states.

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arXiv2019

Detecting Two Qubit Both-Way Positive Discord States

Quantum discord plays a pragmatic role in analyzing nonclassical feature of quantum correlations beyond entanglement. It is used in several information processing protocols which lacks sufficient amount of entanglement to be used as a resource. We have provided with an analytical method of detecting quantum discord of an arbitrary two qubit state. We have formulated a set of necessary and sufficient conditions for any two qubit state to be a both-way non-zero quantum discord state. As quantum discord is asymmetric in nature, we have framed the set of if and only if conditions for a two qubit state to be classical-quantum as well for it to be quantum-classical. Interestingly, not only correlation tensor but also local Bloch vector(corresponding to the classical party) plays a role for detecting the state to be a positive discord state.

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