arXiv subjects

Nirman Ganguly

Publications and source records attributed to Nirman Ganguly.

At least 37 records · Page 2Linked to original sources

arXiv2020

Broadcasting of NPT Entanglement in Two Qutrit Systems

It is known that beyond $2 \otimes 2$ and $2 \otimes 3$ dimensional quantum systems, Peres-Hordecki criterion is no longer sufficient as an entanglement detection criterion as there are entangled states with both positive and negative partial transpose (PPT and NPT). Further, it is also true that all PPT entangled states are bound entangled states. However, in the class of NPT states, there can exist bound entangled states as well as free entangled states. All free/useful/distillable entanglement is a part of the class of NPT entangled states. In this article, we ask the question that given an NPT entangled state in $3 \otimes3$ dimensional system as a resource, how much entanglement can we broadcast so that resource still remains NPT. We have chosen $3 \otimes 3$ system as a first step to understand broadcasting of NPT states in higher dimensional systems. In particular, we find out the range of broadcasting of NPT entanglement for Two parameter Class of States (TPCS) and Isotropic States (IS). Interestingly, as a derivative of this process we are also able to locate the existence of absolute PPT states (ABPPT) in $3 \otimes 3$ dimensional system. Here we implement the strategy of broadcasting through approximate cloning operations.

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arXiv2020

Generating and detecting bound entanglement in two-qutrits using a family of indecomposable positive maps

The problem of bound entanglement detection is a challenging aspect of quantum information theory for higher dimensional systems. Here, we propose an indecomposable positive map for two-qutrit systems, which is shown to generate a class of positive partial transposed (PPT) states. A corresponding witness operator is constructed and shown to be weakly optimal and locally implementable. Further, we perform a structural physical approximation of the indecomposable map to make it a completely positive one, and find a new PPT entangled state which is not detectable by certain other well-known entanglement detection criteria.

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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

Two-Qubit Pure Entanglement as Optimal Social Welfare Resource in Bayesian Game

Entanglement is of paramount importance in quantum information theory. Its supremacy over classical correlations has been demonstrated in numerous information theoretic protocols. Here we study possible adequacy of quantum entanglement in Bayesian game theory, particularly in social welfare solution (SWS), a strategy which the players follow to maximize the sum of their payoffs. Given a multi-partite quantum state as an advice, players can come up with several correlated strategies by performing local measurements on their parts of the quantum state. A quantum strategy is called quantum-SWS if it is advantageous over a classical equilibrium (CE) strategy in the sense that none of the players has to sacrifice their CE-payoff rather some have incentive and at the same time it maximizes the sum of all players' payoffs over all possible quantum advantageous strategies. Quantum state yielding such a quantum-SWS is called a quantum social welfare advice (SWA). We show that any two-qubit pure entangled state, even if it is arbitrarily close to a product state, can serve as quantum-SWA in some Bayesian game. Our result, thus, gives cognizance to the fact that every two-qubit pure entanglement is the best resource for some operational task.

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arXiv2019

Broadcasting of quantum correlations in qubit-qudit systems

Quantum mechanical properties like entanglement, discord and coherence act as fundamental resources in various quantum information processing tasks. Consequently, generating more resources from a few, typically termed as broadcasting is a task of utmost significance. One such strategy of broadcasting is through the application of cloning machines. In this article, broadcasting of quantum resources beyond $2 \otimes 2$ systems is investigated. In particular, in $2\otimes3$ dimension, a class of states not useful for broadcasting of entanglement is characterized for a choice of optimal universal Heisenberg cloning machine. The broadcasting ranges for maximally entangled mixed states (MEMS) and two parameter class of states (TPCS) are obtained to exemplify our protocol. A significant derivative of the protocol is the generation of entangled states with positive partial transpose in $3 \otimes 3$ dimension and states which are absolutely separable in $2 \otimes 2$ dimension. Moving beyond entanglement, in $2 \otimes d$ dimension, the impossibility to optimally broadcast quantum correlations beyond entanglement (QCsbE) (discord) and quantum coherence ($l_{1}$-norm) is established. However, some significant illustrations are provided to highlight that non-optimal broadcasting of QCsbE and coherence are still possible.

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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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arXiv2018

Non-negativity of conditional von Neumann entropy and global unitary operations

Conditional von Neumann entropy is an intriguing concept in quantum information theory. In the present work, we examine the effect of global unitary operations on the conditional entropy of the system. We start with the set containing states with non-negative conditional entropy and find that some states preserve the non-negativity under unitary operations on the composite system. We call this class of states as Absolute Conditional von Neumann entropy Non Negative class (\textbf{ACVENN}). We are able to characterize such states for $2\otimes 2$ dimensional systems. On a different perspective the characterization accentuates the detection of states whose conditional entropy becomes negative after the global unitary action. Interestingly, we are able to show that this \textbf{ACVENN} class of states forms a set which is convex and compact. This feature enables for the existence of hermitian witness operators the measurement of which could distinguish unknown states which will have negative conditional entropy after the global unitary operation. This has immediate application in super dense coding and state merging as negativity of conditional entropy plays a key role in both these information processing tasks. Some illustrations are also provided to probe the connection of such states with Absolute separable (AS) states and Absolute local (AL) states.

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arXiv2017

Characterization of Nonlocal Resources Under Global Unitary Action

The task of device independent secure key distribution requires preparation and subsequently distribution of nonlocal resources. For secured practical implementation, one needs to take two initially uncorrelated quantum systems and perform a unitary on the composite system to generate the nonlocal resource, which is supposed to violate a Bell inequality (say, Bell-CHSH). States which do not violate Bell-CHSH inequality, but violate it when transformed by a global unitary, can be deemed useful for the preparation of nonlocal resource. One may then start from a state which is Bell-CHSH local (take for example, a pure product state) and apply an appropriate global unitary on it which results in a Bell-CHSH non-local state. However, an intriguing fact is the existence of useless states from which no Bell-CHSH non-local resource can be generated with a global unitary. This is due to the purity preserving nature of unitary operators which bound the amount of correlation in the set of final states depending on the purity of the initial (possibly uncorrelated) states. The present work confirms the existence of such a set, pertaining to two qubit systems. The set exhibits counter intuitive features by containing within it some entangled states which remain Bell-CHSH local on the action of any unitary. From practical perspective, this work draws a line between useful and useless states for the task of preparing nonlocal resource using global unitary transformations. Furthermore through an analytic characterization of the set we lay down a generic prescription through which one can operationally identify the useful states. It has also been shown that our prescription remains valid for any linear Bell inequality.

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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

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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arXiv2016

A cloned qutrit and its utility in information processing tasks

We, in this paper, analyze the efficacy of an output as a resource from a universal quantum cloning machine in information processing tasks such as teleportation and dense coding. For this, we have considered the $3\otimes 3$ dimensional system (or qutrit system). The output states are found to be NPT states for certain ranges of machine parameters. Using the output state as an entangled resource, we have also studied the optimal fidelities of teleportation and capacities of dense coding protocols with respect to the machine parameters and have made a few interesting observations. Our work is mainly motivated from the fact that the cloning output can be used as a resource in quantum information processing and adds a valuable dimension to the applications of cloning machines.

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arXiv2014

Witness of mixed separable states useful for entanglement creation

Absolutely separable states form a special subset of the set of all separable states, as they remain separable under any global unitary transformation unlike other separable states. In this work we consider the set of absolutely separable bipartite states and show that it is convex and compact in any arbitrary dimensional Hilbert space. Through a generic approach of construction of suitable hermitian operators we prove the completeness of the separation axiom for identifying any separable state that is not absolutely separable. We demonstrate the action of such witness operators in different qudit systems. Examples of mixed separable systems are provided, pointing out the utility of the witness in entanglement creation using quantum gates. Decomposition of witnesses in terms of spin operators or photon polarizations facilitates their measureability for qubit states.

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arXiv2012

Construction of optimal teleportation witness operators from entanglement witnesses

Teleportation witnesses are hermitian operators which can identify useful entanglement for quantum teleportation. Here we provide a systematic method to construct teleportation witnesses from entanglement witnesses corresponding to general qudit systems. The witnesses so constructed are shown to be optimal for qubit and qutrit systems, and therefore detect the largest set of states useful for teleportation within a given class. We demonstrate the action of the witness pertaining to different classes of states in qubits and qutrits. Decomposition of the witness in terms of spin operators facilitiates experimental identification of useful resources for teleportation.

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arXiv2011

Entanglement witness operator for quantum teleportation

The ability of entangled states to act as resource for teleportation is linked to a property of the fully entangled fraction. We show that the set of states with their fully entangled fraction bounded by a threshold value required for performing teleportation is both convex and compact. This feature enables for the existence of hermitian witness operators the measurement of which could distinguish unknown states useful for performing teleportation. We present an example of such a witness operator illustrating it for different classes of states.

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arXiv2011

Common entanglement witnesses and their characteristics

We investigate the issue of finding common entanglement witness for certain class of states and extend this study to the case of Schmidt number witnesses. We also introduce the notion of common decomposable and non-decomposable witness operators which is specially useful for constructing a common witness where one of the entangled states is with a positive partial transpose. Our approach is illustrated with the help of suitable examples of qutrit systems.

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arXiv2011

Deletion, Bell's Inequality, Teleportation

In this letter we analyze the efficacy of the entangled output of Pati-Braunstein deletion machine [3] as a teleportation channel. We analyze the possibility of it violating the Bell's inequality. Interestingly we find that for all values of the input parameter$α$ the state does not violate the Bell's inequality but when used as a teleportation channel can give a fidelity higher than the classical optimum (i.e 2/3).

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arXiv2011

Witness for an entangled state with positive partial transpose

In this letter we have analyzed an entangled state in $C^{3} \bigotimes C^{3}$ having a positive partial transposition and have shown that it is an edge state. Further we have constructed explicitly a witness operator $W$ which detects the entanglement.

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