Quantum discord is significant in analyzing quantum nonclassicality beyond the paradigm of entang... more 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.
The assumption of measurement independence is required for a local deterministic model to conduct... more 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.
Steerability is a characteristic of quantum correlations lying in between entanglement and Bell n... more 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.
Kaushiki Mukherjee,1, ∗ Biswajit Paul,2, † Sumana Karmakar,3, ‡ Debasis Sarkar,3, § Amit Mukherje... more Kaushiki Mukherjee,1, ∗ Biswajit Paul,2, † Sumana Karmakar,3, ‡ Debasis Sarkar,3, § Amit Mukherjee,4, ¶ Some Sankar Bhattacharya,4, ∗∗ and Arup Roy4, †† Department of Mathematics, Government Girls’ General Degree College, Ekbalpore, Kolkata-700023, India. Department of Mathematics, South Malda College, Malda, West Bengal, India Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata-700009, India. Physics and Applied Mathematics Unit, Indian Statistical Institute, 203,B. T. Road, Kolkata 700108 , India.
Environmental influences are typical in any practical situation which in turn can have fatal effe... more 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.
In a recent work [Phys. Rev. A 86, 042113 (2012)] the question of persistency of entanglement and... more In a recent work [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.
Contrary to Bell scenario, quantum nonlocality can be exploited even when all the parties do not ... more 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.
Steerability is a characteristic nonlocal trait of quantum states lying in between entanglement a... more 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.
Quantum discord plays a pragmatic role in analyzing nonclassical feature of quantum correlations ... more 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.
Analyzing shareability of correlations arising in any physical theory may be considered as a frui... more 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.
In the present work we address the question of how bipartite steering violation takes place among... more In the present work we address the question of how bipartite steering violation takes place among multi-partite systems (where each subsystem 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 pair wise bipartite maximal steering violations, which physically can be understood as providing restrictions on the distribution of steering among sub systems. 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.
International Journal of Quantum Information, 2018
The relation between Bell-CHSH violation and factorization of Hilbert space is considered here. T... more 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 nonlocal 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 [Formula: see text], 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 conditio...
In Phys. Rev. Lett. 104,170401 (2010), Branciard e.t al. first characterized the correlations ari... more In Phys. Rev. Lett. 104,170401 (2010), Branciard 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. 104,170401 (2010) and later in Phys. Rev. A 85,032119 (2012) the authors analyzed the importance of 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 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 ≥ 4 under source independence assumption.
In [Phys. Lett. A 166, 293 (1992)] Popescu characterized nonlocality of pure n-partite entangled ... more In [Phys. Lett. A 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.
Nonlocal correlations arising from measurements on tripartite entangled states can be classified ... more 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.
Mixed states appear naturally in experiment over pure states. So for studying different notions o... more 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. 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.
Determinism, no signaling and measurement independence are some of the constraints required for f... more 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, 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 82, 062117 (2010); Phys. Rev. A 84, 022102 (2011)) for one sided relaxation scenario only.
Journal of Physics A: Mathematical and Theoretical, 2015
According to the studies of genuine tripartite nonlocality in discrete variable quantum systems c... more 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 N S2 local polytope in (J.-D. Bancal, et.al.,Phys. Rev.A 88, 014102 (2013)), to reveal genuine tripartite nonlocality of generalized GHZ(Greenberger-Horne-Zeilinger) class and a subclass of extended GHZ class states([1]) thereby proving the conjecture given by Bancal, et.al.[31] 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 .
Efficient Test to Demonstrate Genuine Nonlocality in Multipartite Scenario
According to the studies of genuine tripartite nonlocality in discrete variable quantum systems c... more 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 GGHZ class and a subclass of extended GHZ class 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 fou...
The assumption of source independence was used to reveal nonlocal (apart from standard Bell-CHSH ... more 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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