arXiv subjects

Anuma Garg

Publications and source records attributed to Anuma Garg.

4 recordsLinked to original sources

arXiv2023

Estimation of Power in the Controlled Quantum Teleportation through the Witness Operator

Controlled quantum teleportation (CQT) can be considered as a variant of quantum teleportation in which three parties are involved where one party acts as the controller. The usability of the CQT scheme depends on two types of fidelities viz. conditioned fidelity and non-conditioned fidelity. The difference between these fidelities may be termed as power of the controller and it plays a vital role in the CQT scheme. Thus, our aim is to estimate the power of the controller in such a way so that its estimated value can be obtained in an experiment. To achieve our goal, we have constructed a witness operator and have shown that its expected value may be used in the estimation of the lower bound of the power of the controller. Furthermore, we have shown that it is possible to make the standard W state useful in the CQT scheme if one of its qubits either passes through the amplitude damping channel or the phase damping channel. We have also shown that the phase damping channel performs better than the amplitude damping channel in the sense of generating more power of the controller in the CQT scheme.

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arXiv2023

Detection of the genuine non-locality of any three-qubit state

It is known that the violation of Svetlichny inequality by any three-qubit state described by the density operator $\rho_{ABC}$ witness the genuine non-locality of $\rho_{ABC}$. But it is not an easy task as the problem of showing the genuine non-locality of any three-qubit state reduces to the problem of a complicated optimization problem. Thus, the detection of genuine non-locality of any three-qubit state may be considered a challenging task. Therefore, we have taken a different approach and derived the lower and upper bound of the expectation value of the Svetlichny operator with respect to any three-qubit state to study this problem. The expression of the obtained bounds depends on whether the reduced two-qubit entangled state is detected by the CHSH witness operator or not. It may be expressed in terms of the following quantities such as (i) the eigenvalues of the product of the given three-qubit state and the composite system of single qubit maximally mixed state and reduced two-qubit state and (ii) the non-locality of reduced two-qubit state. We then achieve the inequality whose violation may detect the genuine non-locality of any three-qubit state. A few examples are cited to support our obtained results. Lastly, we discuss its possible implementation in the laboratory.

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arXiv2022

Strength of the nonlocality of two-qubit entangled state and its applications

Non-locality is a feature of quantum mechanics that cannot be explained by local realistic theory. It can be detected by the violation of Bell's inequality. In this work, we have considered the evaluation of Bell's inequality with the help of the XOR game. In the XOR game, a two-qubit entangled state is shared between the two distant players. It may generate a non-local correlation between the players which contributes to the maximum probability of winning of the game. We have aimed to determine the strength of the non-locality through XOR game. Thus, we have defined a quantity $S_{NL}$ called the strength of non-locality, purely on the basis of the maximum probability of winning of the XOR game. We have also derived the relation between the introduced quantity $S_{NL}$ and the quantity $M$ introduced in \cite{horo3}, to study the non-locality of a two-qubit entangled state problem in depth. The quantity $M$ may be defined as the sum of the two largest eigenvalues of the correlation matrix of the given entangled state and it determines whether the given entangled state under probe is non-local. Further, we have explored the non-locality of any two-qubit entangled state, whose non-locality cannot be detected by the CHSH inequality. Interestingly, we have found that the newly defined quantity $S_{NL}$ fails to detect non-locality for the entangled state, when the witness operator corresponding to $CHSH$ operator cannot detect the entangled state. To overcome this problem, we have modified the definition of the strength of non-locality and have shown that the modified definition may detect the non-locality of such entangled states, which were earlier undetected by $S_{NL}$. Furthermore, we have also provided two applications of the strength $S_{NL}$ of the non-locality in controlled quantum teleportation and linkage of non-locality of three qubit state to two-qubit state.

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arXiv2019

Teleportation criteria based on maximum eigenvalue of the shared $d\otimes d$ dimenional mixed state: Beyond Singlet Fraction

We derive a criteria for the detection of $d\otimes d$ dimensional negative partial transpose (NPT) entangled state useful for teleportation. The newly derived criteria are based on the maximum eigenvalue of the NPT entangled state, which is easier to determine experimentally than to completely reconstruct the state via tomography. We then illustrate our criteria by considering a class of qubit-qubit system and qutrit-qutrit system.

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