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Satyabrata Adhikari

Publications and source records attributed to Satyabrata Adhikari.

At least 55 records · Page 3Linked to original sources
arXiv2017

Laplacian matrices of weighted digraphs represented as quantum states

Representing graphs as quantum states is becoming an increasingly important approach to study entanglement of mixed states, alternate to the standard linear algebraic density matrix-based approach of study. In this paper, we propose a general weighted directed graph framework for investigating properties of a large class of quantum states which are defined by three types of Laplacian matrices associated with such graphs. We generalize the standard framework of defining density matrices from simple connected graphs to density matrices using both combinatorial and signless Laplacian matrices associated with weighted directed graphs with complex edge weights and with/without self-loops. We also introduce a new notion of Laplacian matrix, which we call signed Laplacian matrix associated with such graphs. We produce necessary and/or sufficient conditions for such graphs to correspond to pure and mixed quantum states. Using these criteria, we finally determine the graphs whose corresponding density matrices represent entangled pure states which are well known and important for quantum computation applications. We observe that all these entangled pure states share a common combinatorial structure.

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arXiv2016

Usefulness of Multiqubit W-type States in Quantum Information Processing Task

We analyze the efficacy of multiqubit W-type states as resources for quantum information. For this, we identify and generalize four-qubit W-type states. Our results show that the states can be used as resources for deterministic quantum information processing. The utility of results, however, is limited by the availability of experimental setups to perform and distinguish multiqubit measurements. We, therefore, emphasize on another protocol where two users want to establish an optimal bipartite entanglement using the partially entangled W-type states. We found that for such practical purposes, four-qubit W states can be a better resource in comparison to three-qubit W-type states. For dense coding protocol, our states can be used deterministically to send two bits of classical message by locally manipulating a single qubit.

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arXiv2016

Teleportation via maximally and non-maximally entangled mixed states

We study the efficacy of two-qubit mixed entangled states as resources for quantum teleportation. We first consider two maximally entangled mixed states, viz., the Werner state\cite{werner}, and a class of states introduced by Munro {\it et al.} \cite{munro}. We show that the Werner state when used as teleportation channel, gives rise to better average teleportation fidelity compared to the latter class of states for any finite value of mixedness. We then introduce a non-maximally entangled mixed state obtained as a convex combination of a two-qubit entangled mixed state and a two-qubit separable mixed state. It is shown that such a teleportation channel can outperform another non-maximally entangled channed, viz., the Werner derivative for a certain range of mixedness. Further, there exists a range of parameter values where the former state satisfies a Bell-CHSH type inequality and still performs better as a teleportation channel compared to the Werner derivative even though the latter violates the inequality.

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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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arXiv2016

An analytical condition for the violation of Mermin's inequality by any three qubit state

Mermin's inequality is the generalization of the Bell-CHSH inequality for three qubit states. The violation of the Mermin inequality guarantees the fact that there exists quantum non-locality either between two or three qubits in a three qubit system. In the absence of an analytical result to this effect, in order to check for the violation of Mermin's inequality one has to perform a numerical optimization procedure for even three qubit pure states. Here we derive an analytical formula for the maximum value of the expectation of the Mermin operator in terms of eigenvalues of symmetric matrices, that gives the maximal violation of the Mermin inequality for all three qubit pure and mixed states.

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arXiv2015

More Communication with Less Entanglement

We exhibit the intriguing phenomena of "Less is More" using a set of multipartite entangled states. We consider the quantum communication protocols for the {\em exact} teleportation, superdense coding, and quantum key distribution. We find that sometimes {\em less} entanglement is {\em more} useful. To understand this phenomena we obtain a condition that a resource state must satisfy to communicate a $n$-qubit pure state with $m$ terms. We find that the an appropriate partition of the resource state should have a von-Neumann entropy of ${\rm log}_{2} m$. Furthermore, it is shown that some states may be suitable for exact superdense coding, but not for exact teleportation.

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arXiv2015

Feed-forward control scheme generate Bell states and three-qubit W-type states when qubits passes through decoherence channel

It is known that maximally entangled Bell state and three-qubit W-type states are very useful in various quantum information processing task. Thus the problem of preparation of these type of states is very important in quantum information theory. But the factor which prohibit the generation of the above mentioned pure states shared between two and three distant partners is decoherence. When we send one qubit, from a two qubit state, through decoherence channel like amplitude damping channel, the purity of the qubit is lost and it ends up with a mixed state. Therefore it is very difficult to keep the pure maximally entangled state in a maximally entangled pure state or in an entangled state with high entanglement. In this work we have provided a method by which one can generate experimentally a maximally entangled Bell states shared between distant parties with a non-zero probability when a qubit, from a two qubit general state, passes through decoherence channel. Therefore, despite of the fact that qubit is interacting with the noisy channel, we are able to generate Bell state shared between two distant partners. Further, we have shown that it is possible to generate pure three-qubit W-type states shared between three distant partners using economical quantum cloning machine and weak-measurement based feed-forward control scheme, even though the second and third qubit is interacting with the noisy channel. Lastly, we have shown that the generated three-qubit W-type states can be used in teleporting one of the two non-orthogonal states.

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arXiv2014

A New Method of Classification of Pure Tripartite Quantum States

The classification of the multipartite entanglement is an important problem in quantum information theory. We propose a class of two qubit mixed states $σ_{AB}= p|χ_{1}\rangle\langleχ_{1}|\otimesρ_{1}+(1-p)|χ_{2}\rangle\langleχ_{2}|\otimesρ_{2}$, where $|χ_{1}\rangle=α|0\rangle+β|1\rangle$, $|χ_{2}\rangle=β|0\rangle+(-1)^{n}α|1\rangle$. We have shown that the state $σ_{AB}$ represent a classical state when $n$ is odd while it represent a non-classical state when $n$ is even. The purification of the state $σ_{AB}$ is studied and found that the purification is possible if the spectral decomposition of the density matrices $ρ_{1}$ and $ρ_{2}$ represent pure states. We have established a relationship between three tangle, which measures the amount of entanglement in three qubit system and the quantity $\langleχ_{1}|χ_{2}\rangle$, which identifies whether the two qubit mixed state is classical or non-classical. The three qubit purified state is then classified as a separable or biseparable or W-type or GHZ-type state using the quantum correlation, measured by geometric discord, of its reduced two qubit density matrix.

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arXiv2014

Upper Bound on Singlet Fraction of Two Qubit Mixed Entangled States

We demonstrate the possibility of achieving the maximum possible singlet fraction using a entangled mixed two-qubit state as a resource. For this, we establish a tight upper bound on singlet fraction and show that the maximal singlet fraction obtained in \cite{Verstraete} does not attain the obtained upper bound on the singlet fraction. Interestingly, we found that the required upper bound can in fact be achieved using local filtering operations.

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arXiv2014

Quantification of Entanglement of Teleportation in Arbitrary Dimensions

We study bipartite entangled states in arbitrary dimensions and obtain different bounds for the entanglement measures in terms of teleportation fidelity. We find that there is a simple relation between negativity and teleportation fidelity for pure states but for mixed states, an upper bound is obtained for negativity in terms of teleportation fidelity using convex-roof extension negativity (CREN). However, with this it is not clear how to distinguish betweeen states useful for teleportation and positive partial transpose (PPT) entangled states. Further, there exists a strong conjecture in the literature that all PPT entangled states, in 3 \times 3 systems, have Schmidt rank two. This motivates us to develop measures capable of identifying states useful for teleportation and dependent on the Schmidt number. We thus establish various relations between teleportation fidelity and entanglement measures depending upon Schmidt rank of the states. These relations and bounds help us to determine the amount of entanglement required for teleportation, which we call the ``Entanglement of Teleportation''. These bounds are used to determine the teleportation fidelity as well as the entanglement required for teleportation of states modeled by a two qutrit mixed system, as well as two qubit open quantum systems.

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arXiv2014

Controlled Secret Sharing Protocol using a Quantum Cloning Circuit

We demonstrate the possibility of controlling the success probability of a secret sharing protocol using a quantum cloning circuit. The cloning circuit is used to clone the qubits containing the encoded information and {\em en route} to the intended receipients. The success probability of the protocol depends on the cloning parameters used to clone the qubits. We also establish a relation between the concurrence of initially prepared state, entanglement of the mixed state received by the receivers after cloning scheme and the cloning parameters of cloning machine.

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arXiv2013

Entanglement in the Grover's Search Algorithm

Quantum Algorithms have long captured the imagination of computer scientists and physicists primarily because of the speed up achieved by them over their classical counterparts using principles of quantum mechanics. Entanglement is believed to be the primary phenomena behind this speed up. However their precise role in quantum algorithms is yet unclear. In this article, we explore the nature of entanglement in the Grover's search algorithm. This algorithm enables searching of elements from an unstructured database quadratically faster than the best known classical algorithm. Geometric measure of entanglement has been used to quantify and analyse entanglement across iterations of the algorithm. We reveal how the entanglement varies with increase in the number of qubits and also with the number of marked or solution states. Numerically, it is seen that the behaviour of the maximum value of entanglement is monotonous with the number of qubits. Also, for a given value of the number of qubits, a change in the marked states alters the amount of entanglement. The amount of entanglement in the final state of the algorithm has been shown to depend solely on the nature of the marked states. Explicit analytical expressions are given showing the variation of entanglement with the number of iterations and the global maximum value of entanglement attained across all iterations of the algorithm.

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arXiv2013

Non-classical Correlations in the Quantum Search Algorithm

Entanglement lies at the heart of quantum mechanics and has no classical analogue. It is central to the speed up achieved by quantum algorithms over their classical counterparts. The Grover's search algorithm is one such algorithm which enables us to achieve a quadratic speed up over any known classical algorithm that searches for an element in an unstructured database. Here, we analyse and quantify the effects of entanglement in the generalized version of this algorithm for two qubits. By 'generalized', it is meant that the use of any arbitrary single qubit unitary gate is permitted to create superposed states. Our analysis has been firstly on a noise free environment and secondly in the presence of noise. In the absence of noise, we establish a relation between the concurrence and the amplitude of the final state thereby showing the explicit effects of entanglement on the same. Moreover, the effects of noisy channels, namely amplitude and phase damping channels are studied. We investigate the amount of quantum correlation in the states obtained after the phase inversion stage of the algorithm followed by interaction of those states with the noisy environment. The quantum correlations are quantified by geometric discord. It has been revealed that the states generated after the effect of amplitude damping on the phase inverted states of the quantum search algorithm possess non-zero quantum correlation even when entanglement is absent. However, this is absent in the phase damping scenario.

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arXiv2013

Generalized form of optimal teleportation witnesses

We propose a generalized form of optimal teleportation witness to demonstrate their importance in experimental detection of the larger set of entangled states useful for teleportation in higher dimensional systems. The interesting properties of our witness reveal that teleportation witness can be used to characterize mixed state entanglement using Schmidt numbers. Our results show that while every teleportation witness is also a entanglement witness, the converse is not true. Also, we show that a hermitian operator is a teleportation witness iff it is a decomposable entanglement witness. In addition, we analyze the practical significance of our study by decomposing our teleportation witness in terms of Pauli and Gell-Mann matrices, which are experimentally measurable quantities.

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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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arXiv2012

An Operational Meaning of Discord in terms of Teleportation Fidelity

Quantum discord is a prominent measure of quantum correlations, playing an important role in expanding its horizon beyond entanglement. Here we provide an operational meaning of (geometric) discord, which quantifies the amount of non-classical correlation of an arbitrary quantum system in terms of its minimal distance from the set of classical states, in terms of teleportation fidelity for general two qubit and $d \otimes d$ dimensional isotropic and Werner states. A critical value of the discord is found beyond which the two qubit state must violate the Bell inequality. This is illustrated by an open system model of a dissipative two qubit. For the $d \otimes d$ dimensional states the lower bound of discord is shown to be obtainable from an experimentally measurable witness operator.

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arXiv2011

Probabilistic Secret Sharing Through Noisy Quantum Channels

In a realistic situation, the secret sharing of classical or quantum information will involve the transmission of this information through noisy channels. We consider a three qubit pure state. This state becomes a mixed-state when the qubits are distributed over noisy channels. We focus on a specific noisy channel, the phase-damping channel. We propose a protocol for secret sharing of classical information with this and related noisy channels. This protocol can also be thought of as cooperative superdense coding. We also discuss other noisy channels to examine the possibility of secret sharing of classical information.

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