arXiv subjects

Kaushiki Mukherjee

Publications and source records attributed to Kaushiki Mukherjee.

36 records · Page 2Linked to original sources

arXiv2019

Several Trade off Features of Quantum Steering in Distributed Scenario

In the present work, we address the question of how bipartite steering violation takes place among multi-partite systems (where each sub-system have Hilbert space dimension restricted to two) based on the maximal violations of the bipartite steering inequality of the reduced pairwise qubit systems. We have derived a trade-off relation which is satisfied by those pairwise bipartite maximal steering violations, which physically can be understood as providing restrictions on the distribution of steering among subsystems. For a three-qubit system, it is impossible that all pairs of qubits violate the steering inequality, and once a pair of qubits violates the steering inequality maximally, the other two pairs of qubits must both obey the steering inequality. We also present a complementarity relation between genuine entanglement present in a tripartite state and maximum bipartite steering violation by its reduced states.

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arXiv2019

Sharing of tripartite nonlocality by multiple observers measuring sequentially at one side

Standard tripartite nonlocality and genuine tripartite nonlocality can be detected by the violations of Mermin inequality and Svetlichny inequality, respectively. Since tripartite quantum nonlocality has novel applications in quantum information and quantum computation, it is important to investigate whether more than three observers can share tripartite nonlocality, simultaneously. In the present study we answer this question in the affirmative. In particular, we consider a scenario where three spin-$\frac{1}{2}$ particles are spatially separated and shared between Alice, Bob and multiple Charlies. Alice performs measurements on the first particle; Bob performs measurements on the second particle and multiple Charlies perform measurements on the third particle sequentially. In this scenario we investigate how many Charlies can simultaneously demonstrate standard tripartite nonlocality and genuine tripartite nonlocality with single Alice and single Bob. The interesting result revealed by the present study is that at most six Charlies can simultaneously demonstrate standard tripartite nonlocality with single Alice and single Bob. On the other hand, at most two Charlies can simultaneously demonstrate genuine tripartite nonlocality with single Alice and single Bob. Hence, the present study shows that standard tripartite nonlocality can be simultaneously shared by larger number of Charlies compared to genuine tripartite nonlocality in the aforementioned scenario, which implies that standard tripartite nonlocality is more effective than genuine tripartite nonlocality in the context of simultaneous sharing by multiple observers.

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arXiv2017

Restricted Distribution of Quantum Correlations in Bilocal Network

Analyzing shareability of correlations arising in any physical theory may be considered as a fruitful technique of studying the theory. Our present topic of discussion involves an analogous approach of studying quantum theory. For our purpose, we have deviated from the usual procedure of assessing monogamous nature of quantum correlations in standard Bell-CHSH scenario. We have considered correlations arising in a quantum network involving independent sources. Precisely speaking, we have analyzed monogamy of nonbilocal correlations by deriving a relation restricting marginals. Interestingly, restrictions constraining distribution of nonbilocal correlations remain same irrespective of whether inputs of the nodal observers are kept fixed(in different bilocal networks) while studying nonbilocal nature of marginal correlations.

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arXiv2017

Nontrilocality: Exploiting nonlocality from three particle systems

In Phys. Rev. Lett. \textbf{104},170401 (2010), Branciard \textit{e.t al.} first characterized the correlations arising in an entanglement swapping network under the assumption that the sources generating the initially uncorrelated quantum systems are independent. Precisely speaking, in Phys. Rev. Lett. \textbf{104},170401 (2010) and later in Phys. Rev. A \textbf{85},032119 (2012) the authors analyzed the importance of \textit{bilocal}(source independence) assumption to lower down the restrictions over correlations for revealing quantumness in the network where each of two sources generates a bipartite entangled state. In this context one may find interest to characterize correlations in a network involving independent sources which can correlate more than two initially uncorrelated multipartite entangled quantum systems. Our present topic of discussion basically analyzes such a network scenario. Specifically we introduce \textit{trilocal network scenario} where each of three sources independently generates a tripartite entangled quantum system thereby exploring the role of source independence assumption to exploit nonlocality in a network involving multipartite entanglement analogous to bilocal assumption in a network where only bipartite entanglement was considered. Interestingly, genuine entanglement content did not turn out to be an essential requirement for exploiting nonlocality in such a scenario. Moreover it is interesting to explore whether such a scenario can be generalized so as to characterize correlations arising in a network involving $n$ number of $n$ partite systems for any finite value of $n\geq4$ under source independence assumption.

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arXiv2017

Absolute Non-Violation of a Three-Setting Steering Inequality by Two-Qubit States

Steerability is a characteristic nonlocal trait of quantum states lying in between entanglement and Bell nonlocality. A given quantum state is considered to be steerable if it violates a suitably chosen steering inequality. A quantum state which otherwise satisfies a certain inequality can violate the inequality under a global change of basis i.e, if the state is transformed by a nonlocal unitary operation. Intriguingly there are states which preserve their non-violation(pertaining to the said inequality) under any global unitary operation. The present work explores the effect of global unitary operations on the steering ability of a quantum state which live in two qubits. We characterize such states in terms of a necessary and sufficient condition on their spectrum. Such states are also characterized in terms of some analytic characteristics of the set to which they belong. Looking back at steerability the present work also provides a relation between steerability and quantum teleportation together with the derivation of a result related to the optimal violation of steering inequality . An analytic estimation of the size of such non-violating states in terms of purity is also obtained. Interestingly the estimation in terms of purity also gives a necessary and sufficient condition in terms of bloch parameters of the state. Illustrations from some signature class of quantum states further underscore our observations.

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arXiv2017

Conditional steering under von-Neumann scenario

In [\href{http://www.sciencedirect.com/science/article/pii/037596019290711T}{Phys. Lett. A {\bf 166}, 293 (1992)}] Popescu characterized nonlocality of pure $n$-partite entangled systems by studying bipartite violation of local realism when $n-2$ number of parties perform projective measurements on their particles. A pertinent question in this scenario is whether similar characterization is possible for $n$-partite mixed entangled states also. In the present work we have followed an analogous approach so as to explore whether given a tripartite mixed entangled state the conditional bipartite states obtained by performing projective measurement on the third party, demonstrate a weaker form of nonlocality, quantum steering. We also compare this new phenomenon of conditional steering with existing notions of tripartite correlations. Interestingly the tripartite state need not be genuinely entangled to demonstrate conditional steering.

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arXiv2017

Generation of Nonlocality

Environmental influences are typical in any practical situation which in turn can have fatal effects on quantum resources. Bell nonlocality is such an important resource. Some environmental interactions can lead to nonlocality being lost. In such situations, it is vital to find possible prescriptions to retrieve nonlocality. The present work lays down one such prescription. Precisely, we have studied some well-known classes of states under the ambit of the Bell-CHSH inequality in two qubits, where we start from a Bell-CHSH local state and can transform it into a nonlocal state through our protocol. The efficacy of the protocol is further established from the fact that it can retrieve nonlocality from states admitting a LHV(local hidden variable) model. The strength of the prescription is validated by the fact that it can generate nonlocality from states when even unitary action on the composite system fails.

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arXiv2017

Bell-CHSH Violation Under Global Unitary Operations: Necessary and Sufficient conditions

The relation between Bell-CHSH violation and factorization of Hilbert space is considered here. That is, a state which is local in the sense of the Bell-CHSH inequality under a certain factorization of the underlying Hilbert space can be Bell-CHSH non-local under a different factorization. While this question has been addressed with respect to separability , the relation of the factorization with Bell-CHSH violation has remained hitherto unexplored. We find here, that there is a set containing density matrices which do not exhibit Bell-CHSH violation under any factorization of the Hilbert space brought about by global unitary operations. Using the Cartan decomposition of $ SU(4) $,we characterize the set in terms of a necessary and sufficient criterion based on the spectrum of density matrices. Sufficient conditions are obtained to characterize such density matrices based on their bloch representations. For some classes of density matrices, necessary and sufficient conditions are derived in terms of bloch parameters. Furthermore, an estimation of the volume of such density matrices is achieved in terms of purity. The criterion is applied to some well-known class of states in two qubits.Since, both local filtering and global unitary operations influence Bell-CHSH violation of a state, a comparative study is made between the two operations. The inequivalence of the two operations(in terms of increasing Bell-CHSH violation) is exemplified through their action on some classes of states.

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arXiv2017

Revealing Genuine Steering under Sequential Measurement Scenario

Genuine steering is still not well understood enough in contrast to genuine entanglement and nonlocality. Here we provide a protocol which can reveal genuine steering under some restricted operations compared to the existing witnesses of genuine multipartite steering. Our method has an impression of some sort of hidden protocol in the same spirit of hidden nonlocality, which is well understood in bipartite scenario. We also introduce a genuine steering measure which indicates the enhancement of genuine steering in the final state of our protocol compared to the initial states.

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arXiv2017

Detection of Genuine Multipartite Entanglement in Quantum Network Scenario

Experimental demonstration of entanglement needs to have a precise control of experimentalist over the system on which the measurements are performed as prescribed by an appropriate entanglement witness. To avoid such trust problem, recently device-independent entanglement witnesses (\emph{DIEW}s) for genuine tripartite entanglement have been proposed where witnesses are capable of testing genuine entanglement without precise description of Hilbert space dimension and measured operators i.e apparatus are treated as black boxes. Here we design a protocol for enhancing the possibility of identifying genuine tripartite entanglement in a device independent manner. We consider three mixed tripartite quantum states none of whose genuine entanglement can be detected by applying standard \emph{DIEW}s, but their genuine tripartite entanglement can be detected by applying the same when distributed in some suitable entanglement swapping network.

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arXiv2016

Revealing Hidden Genuine Tripartite Nonlocality

Nonlocal correlations arising from measurements on tripartite entangled states can be classified into two groups, one genuinely $3-$way nonlocal and other local with respect to some bipartition. Still, whether a genuinely tripartite entangled quantum state can exhibit genuine $3-$way nonlocality, remains a challenging problem so far as measurement context is concerned. Here we introduce a novel approach in this regard. We consider three tripartite quantum states none of which is genuinely $3-$way nonlocal in a specific Bell scenario (three parties, two measurements per party, two outcomes per measurement), but they can exhibit genuine $3-$way nonlocality when the initial states are subjected to stochastic local operations and classical communication (SLOCC). So, genuine $3-$way nonlocality is a resource, which can be revealed by using a sequence of measurements.

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arXiv2016

Persistency of Genuine Correlations Under Particle Loss

In a recent work [\href{http://journals.aps.org/pra/abstract/10.1103/PhysRevA.86.042113}{Phys. Rev. A 86, 042113 (2012)}] the question of persistency of entanglement and nonlocality of multi-party systems under particle loss has been addressed. This question is of immense importance considering the practical realization of the information theoretic tasks which make use of the power of quantum correlations. But in multipartite scenario more interesting cases arise since subsystems can also possess genuineness in correlation which is prevalently inequivalent to the bipartite scenario. In this work, we investigate the persistency of such genuine correlations under particle loss. Keeping in mind the practical importance, considerable attention has been devoted to find the multipartite states which exhibit maximal persistency of genuine correlations.

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arXiv2016

Nonlocality of three-qubit Greenberger-Horne-Zeilinger-symmetric states

Mixed states appear naturally in experiment over pure states. So for studying different notions of nonlocality and their relation with entanglement in realistic scenarios, one needs to consider mixed states. In a recent article [Phys. Rev. Lett. \textbf{108}, 020502 (2012)], a complete characterization of entanglement of an entire class of mixed three qubit states with the same symmetry as Greenberger-Horne-Zeilinger state known as GHZ-symmetric states, has been achieved. In this paper we investigate different notions of nonlocality of the same class of states. By finding the analytical expressions of maximum violation value of most efficient Bell inequalities we obtain the conditions of standard nonlocality and genuine nonlocality of this class of states. Also relation between entanglement and nonlocality is discussed for this class of states. Interestingly, genuine entanglement of GHZ-symmetric states is necessary to reveal standard nonlocality. However, it is not sufficient to exploit the same.

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arXiv2016

Revealing Quantum Advantage in a Quantum Network

The assumption of source independence was used to reveal nonlocal (apart from standard Bell-CHSH scenario) nature of correlations generated in entanglement swapping experiments. In this work, we have derived a set of sufficient criteria, imposed on the states (produced by the sources) under which source independence can reveal nonbilocal nature of correlations in a quantum network. To show this, we have considered real two qubit X states thereby discussing the various utilities of assuming source independence in a quantum network.

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arXiv2015

Efficient Test to Demonstrate Genuine Three Particle Nonlocality

According to the studies of genuine tripartite nonlocality in discrete variable quantum systems conducted so far, Svetlichny inequality is considered as the best Bell-type inequality to detect genuine (three way) nonlocality of pure tripartite genuine entangled states. In the present work, we have considered another Bell-type inequality (which has been reported as the $99$-th facet of $NS_2$ local polytope in (J.-D. Bancal, et.al.,Phys. Rev.A \textbf{88}, 014102 (2013)), to reveal genuine tripartite nonlocality of generalized GHZ(Greenberger-Horne-Zeilinger) class and a subclass of extended GHZ class states(\cite{ACN}) thereby proving the conjecture given by Bancal, et.al.\cite{BAL} for the GGHZ class and the subclass of extended GHZ states. We compare the violation of this inequality with Svetlichny inequality which reveals the efficiency of the former inequality over the latter to demonstrate genuine nonlocality using the above classes of quantum states. Even in some cases discord monogamy score can be used as a better measure of quantum correlation over Svetlichny inequality for those classes of pure states. Besides, the $99$-th facet inequality is found efficient not only for revealing genuine nonlocal behavior of correlations emerging in systems using pure entangled states but also in some cases of mixed entangled states over Svetlichny inequality and some well known measures of entanglement .

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arXiv2015

Correlations In n-local Scenario

Recently Bell-type inequalities were introduced in Phys. Rev. A \textbf{85}, 032119 (2012) to analyze the correlations emerging in an entanglement swapping scenario characterized by independence of the two sources shared between three parties. The corresponding scenario was referred to as \textit{bilocal} scenario. Here, we derive Bell-type inequalities in $n+1$ party scenario, i.e., in $n$-local scenario. Considering the two different cases with several number of inputs and outputs, we derive local and $n$-local bounds. The $n$-local inequality studied for two cases are proved to be tight. Replacing the sources by maximally entangled states for two binary inputs and two binary outputs and also for the fixed input and four outputs, we observe quantum violations of $n$-local bounds. But the resistance offered to noise cannot be increased as compared to the bilocal scenario. Thus increasing the number of parties in a linear fashion in source independent scenario does not contribute in lowering down the requirements of revealing quantumness in a network in contrast to the star configuration (Phys. Rev. A \textbf{90}, 062109 (2014)) of $n+1$ parties.

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arXiv2014

One Sided indeterminism alone is not a useful resource to simulate any nonlocal correlation

Determinism, no signaling and measurement independence are some of the constraints required for framing Bell inequality. Any model simulating nonlocal correlations must either individually or jointly give up these constraints. Recently M. J. W. Hall (Phys Review A, \textbf{84}, 022102 (2011)) derived different forms of Bell inequalities under the assumption of individual or joint relaxation of those constraints on both(i.e., two) the sides of a bipartite system. In this work we have investigated whether one sided relaxation can also be a useful resource for simulating nonlocal correlations or not. We have derived Bell-type inequalities under the assumption of joint relaxation of these constraints only by one party of a bipartite system. Interestingly we found that any amount of randomness in correlations of one party in absence of signaling between two parties is incapable of showing any sort of Bell-CHSH violation whereas signaling and measurement dependence individually can simulate any nonlocal correlations. We have also completed the proof of a recent conjecture due to Hall (Phys. Rev. A \textbf{82}, 062117 (2010); Phys. Rev. A \textbf{84}, 022102 (2011)) for one sided relaxation scenario only.

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arXiv2013

Simulating GHZ Correlations Relaxing Physical Constraints

Violation of Bell inequality (or, Bell-type inequalities) by nonlocal correlations is justified by relaxation of at least one of the plausible physical constraints used to model such inequality. Based on this fact, in this letter we present a procedure to simulate three-qubit GHZ correlation relaxing two constraints, determinism and no signaling simultaneously. We have also derived the minimum amount of indeterminism and signaling to be introduced in a system. The corresponding number of signaling and local bits of mutual information needed to communicate are also provided and thus we are able to focus on utility of relaxation of these two constraints as useful resources.

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