arXiv subjects

Satyabrata Adhikari

Publications and source records attributed to Satyabrata Adhikari.

At least 37 records · Page 2Linked to original sources

arXiv2022

A few entanglement criterion for two-qubit and two-qudit system based on realignment operation

It is known that realignment crierion is necessary but not a sufficient criterion for lower as well as higher dimensional system. In this work, we first consider a two-qubit system and derived the necessary and sufficient condition based on realignment operation for a particular class of two-qubit system. Thus we solved the problem of if and only if condition partially for a particular class of two-qubit state. We have shown that the derived necessary and sufficient condition detects two-qubit entangled states, which are not detected by the realignment criterion. Next, we discuss the higher dimensional system and obtained the necessary condition on the minimum singular value of the realigned matrix of $d\otimes d$ dimensional separable states. Moreover, we provide the geometrical interpretation of the derived separability criterion for $d\otimes d$ dimensional system. Furthermore, we show that our criterion may also detect bound entangled state. The entanglement detection criterion studied here is beneficial in the sense that it requires to calculate only minimum singular value of the realigned matrix while on the other hand realignment criterion requires all singular values of the realigned matrix. Thus, our criterion has computational advantage over the realignment criterion.

quant-ph↗

arXiv2022

Lower Bound of $l_{1}$ Norm of Coherence of Bipartite Qubit-Qudit System and its Application in the Detection of Entangled Tripartite Qudit-Qubit-Qudit System

Quantum coherence and quantum entanglement are two strong pillars in quantum information theory. We study here for the possibility of any connection between these two important aspects of quantum mechanics while studying the entanglement detection problem for the detection of bipartite higher dimensional entangled states and multipartite entangled states. To achieve our goal, we derive the lower bound $L$ of $l_{1}$ norm of coherence of bipartite qubit-qudit system using the criterion that detect entanglement. Furthermore, we deduce the upper bound $U$ of $l_{1}$ norm of coherence of separable bipartite qubit-qudit system using the separability criterion. Thus, we find that if any $l_{1}$ norm of coherence of bipartite qubit-qudit system is greater than the upper bound $U$ then the given qubit-qudit state is entangled. Finally, we obtained the upper bound $U_{1}$ of $l_{1}$ norm of coherence of separable tripartite state lies either in $2 \otimes d \otimes d$ or $d \otimes 2 \otimes d$ or $d \otimes d \otimes 2$ dimensional Hilbert space using the upper bound $U$. We have shown that if the $l_{1}$ norm of coherence of any tripartite $qubit-qudit-qudit$ or $qudit-qubit-qudit$ or $qudit-qudit-qubit$ system is greater than the derived upper bound $U_{1}$ then the given tripartite system represent an entangled state.

quant-ph↗

arXiv2022

Structural physical approximation of partial transposition makes possible to distinguish SLOCC inequivalent classes of three-qubit system

Detection and classification of entanglement properties of a multi-qubit system is a topic of great interest. This topic has been studied extensively and thus we found different approaches for the detection and classification of multi-qubit entangled states. We have applied partial transposition operation on one of the qubit of the three-qubit system and then studied the entanglement properties of the three-qubit system, which is under investigation. Since the partial transposition operation is not a quantum operation so we have approximated partial transposition operation in such a way so that it represent a completely positive map. The approximated partial transposition operation is also known as structural physical approximation of partial transposition (SPA-PT). We have studied in detail the application of SPA-PT on a three qubit system and provided explicitly the matrix elements of the density matrix describing SPA-PT of a three qubit system. Moreover, we propose criterion to classify all possible stochastic local operations and classical communication(SLOCC) inequivalent classes of a pure as well as mixed three qubit state through SPA-PT map, which makes our criterion experimentally realizable. We have illustrated our criterion for detection and classification of three-qubit entangled states by considering few examples.

quant-ph↗

arXiv2021

Construction of a Family of Positive But Not Completely Positive Map For the Detection of Bound Entangled States

We construct a family of map which is shown to be positive when imposing certain condition on the parameters. Then we show that the constructed map can never be completely positive. After tuning the parameters, we found that the map still remain positive but it is not completely positive. We then use the positive but not completely positive map in the detection of bound entangled state and negative partial transpose entangled states.

quant-ph↗

arXiv2021

Classification witness operator for the classification of different subclasses of three-qubit GHZ class

It is well known that three-qubit system has two kind of inequivalent genuine entangled classes under stochastic local operation and classical communication (SLOCC). These classes are called as GHZ class and W class. GHZ class proved to be a very useful class for different quantum information processing task such as quantum teleportation, controlled quantum teleportation etc. In this work, we distribute pure three-qubit states from GHZ class into different subclasses denoted by $S_{1}$, $S_{2}$, $S_{3}$, $S_{4}$ and show that the three-qubit states either belong to $S_{2}$ or $S_{3}$ or $S_{4}$ may be more efficient than the three-qubit state belong to $S_{1}$. Thus, it is necessary to discriminate the states belong to $S_{i}, i=2,3,4$ and the state belong to $S_{1}$. To achieve this task, we have constructed different witness operators that can classify the subclasses $S_{i}, i=2,3,4$ from $S_{1}$. We have shown that the constructed witness operator can be decomposed into Pauli matrices and hence can be realized experimentally.

quant-ph↗

arXiv2021

Coherence based inequality for the discrimination of three-qubit GHZ and W class

Quantum coherence and entanglement orignate from the superposition principle. We derive a rigorous relation between the ${l_1}$-norm of coherence and concurrence, in that we show that the former is always greater than the latter. This result highlights the hierarchical relationship between coherence and concurrence, and proves coherence to be a fundamental and ubiquitous resource. We derive an analogous form of monogamy inequality which is based on the partial coherence of the reduced two-qubit and reduced single qubit of the particular class of three-qubit state. Moreover, we provide coherence based inequality for the classification of GHZ class and W class of three-qubit states. Finally, we provide theoretical discussion for the possible implementation of the scheme in an experiment.

quant-ph↗

arXiv2021

On a matrix equality involving partial transposition and its relation to the separability problem

In matrix theory, a well established relation $(AB)^{T}=B^{T}A^{T}$ holds for any two matrices $A$ and $B$ for which the product $AB$ is defined. Here $T$ denote the usual transposition. In this work, we explore the possibility of deriving the matrix equality $(AB)^Γ=A^ΓB^Γ$ for any $4 \times 4$ matrices $A$ and $B$, where $Γ$ denote the partial transposition. We found that, in general, $(AB)^Γ\neq A^ΓB^Γ$ holds for $4 \times 4$ matrices $A$ and $B$ but there exist particular set of $4 \times 4$ matrices for which $(AB)^Γ= A^ΓB^Γ$ holds. We have exploited this matrix equality to investigate the separability problem. Since it is possible to decompose the density matrices $ρ$ into two positive semi-definite matrices $A$ and $B$ so we are able to derive the separability condition for $ρ$ when $ρ^Γ=(AB)^Γ=A^ΓB^Γ$ holds. Due to the non-uniqueness property of the decomposition of the density matrix into two positive semi-definte matrices $A$ and $B$, there is a possibility to generalise the matrix equality for density matrices lives in higher dimension. These results may help in studying the separability problem for higher dimensional and multipartite system.

quant-ph↗

arXiv2021

Witness Operator Provides Better Estimate of the Lower Bound of Concurrence of Bipartite Bound Entangled States in $d_{1}\otimes d_{2}$ Dimensional System

It is known that the witness operator is useful in the detection and quantification of entangled states. This motivated us for the construction of the family of witness operators that can detect many mixed entangled states. This family of witness operators is then used to estimate the lower bound of concurrence of the detected mixed entangled states. Our method of construction of witness operator is important in the sense that it will estimate a better lower bound of concurrence of the entangled states in arbitrary $d_{1}\otimes d_{2} (d_{1}\leq d_{2})$ dimensional system compared to the lower bound of the concurrence given in \cite{kchen}. We have shown the significance of our constructed witness operator by detecting many bound entangled states that are not detected by the earlier methods and then we use the expectation value of the witness operator to estimate the lower bound of the concurrence of those bound entangled states.

quant-ph↗

arXiv2021

Constructing a ball of separable and absolutely separable states for $2\otimes d$ quantum system

Absolute separable states is a kind of separable state that remain separable under the action of any global unitary transformation. These states may or may not have quantum correlation and these correlations can be measured by quantum discord. We find that the absolute separable states are useful in quantum computation even if it contains infinitesimal quantum correlation in it. Thus to search for the class of two-qubit absolute separable states with zero discord, we have derived an upper bound for $Tr(\varrho^{2})$, where $\varrho$ denoting all zero discord states. In general, the upper bound depends on the state under consideration but if the state belong to some particular class of zero discord states then we found that the upper bound is state independent. Later, it is shown that among these particular classes of zero discord states, there exist sub-classes which are absolutely separable. Furthermore, we have derived necessary conditions for the separability of a given qubit-qudit states. Then we used the derived conditions to construct a ball for $2\otimes d$ quantum system described by $Tr(ρ^{2})\leq Tr(X^{2})+2Tr(XZ)+Tr(Z^{2})$, where the $2\otimes d$ quantum system is described by the density operator $ρ$ which can be expressed by block matrices $X,Y$ and $Z$ with $X,Z\geq 0$. In particular, for qubit-qubit system, we show that the newly constructed ball contain larger class of absolute separable states compared to the ball described by $Tr(ρ^{2})\leq \frac{1}{3}$. Lastly, we have derived the necessary condition in terms of purity for the absolute separability of a qubit-qudit system under investigation.

quant-ph↗

arXiv2021

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.

quant-ph↗

arXiv2019

Probabilistic Teleportation of a Single Qubit: Unearthing New W-Class of States

In this work, we propose a probabilistic teleportation protocol to teleport a single qubit via three-qubit W-states using two-qubit measurement basis. We show that for the proper choice of the state parameter of the resource state, it is possible to make success probability of the protocol very high. We deduce the condition for the successful execution of our teleportation protocol and this gives us new class of three-qubit W-states which act as a resource state. We have constructed operators that can be used to verify the condition of teleportation in experiment. This verification is necessary for the detection of whether the given three-qubit state is useful in our teleportation protocol or not. Further we quantify the amount of entanglement contained in the newly identified shared W-class of states. Moreover, we show that the W-class of shared state used in the teleportation protocol can be prepared using NMR set up.

quant-ph↗

arXiv2019

Detection of mixed bipartite entangled state in arbitrary dimension via structural physical approximation of partial transposition

It is very crucial to know that whether the quantum state generated in the experiment is entangled or not. In the literature, this topic was studied extensively and researchers proposed different approaches for the detection of mixed bipartite entangled state in arbitrary dimension. Proceeding in this line of research, we also propose three different criteria for the detection of mixed bipartite negative partial transpose (NPT) entangled state in arbitrary dimension. Our criteria is based on the method of structural physical approximation (SPA) of partial transposition (PT). We have shown that the proposed criteria for the detection of NPT entangled state can be realized experimentally. Two of the proposed criteria is given in terms of the concurrence of the given state in arbitrary dimension so it is essential to find out the concurrence. Thus, we provide new lower and upper bound of concurrence of the quantum state under investigation in terms of average fidelity of two quantum states and hence these bounds can be realized experimentally. Moreover, we have shown how to perform SPA map on qutrit-qubit system and then explicitly calculated the matrix elements of the density matrix describing the SPA-PT of the qutrit-qubit system. We then illustrate our criteria for the detection of entanglement by considering a class of qubit-qubit system and a class of qutrit-qubit system.

quant-ph↗

arXiv2019

Estimation of Entanglement Negativity of a Two-Qubit Quantum System With Two Measurements

Numerous work had been done to quantify the entanglement of a two-qubit quantum state, but it can be seen that previous works were based on joint measurements on two copies or more than two copies of a quantum state under consideration. In this work, we show that a single copy and two measurements are enough to estimate the entanglement quantifier like entanglement negativity and concurrence. To achieve our aim, we establish a relationship between the entanglement negativity and the minimum eigenvalue of structural physical approximation of partial transpose of an arbitrary two-qubit state. The derived relation make possible to estimate entanglement negativity experimentally by Hong-Ou-Mandel interferometry with only two detectors. Also, we derive the upper bound of the concurrence of an arbitrary two-qubit state and have shown that the upper bound can be realized in experiment. We will further show that the concurrence of (i) an arbitrary pure two-qubit states and (ii) a particular class of mixed states, namely, rank-2 quasi-distillable mixed states, can be exactly estimated with two measurements.

quant-ph↗

arXiv2018

Coherence and entanglement under three qubit cloning operations

Coherence and entanglement are the two most crucial resources for various quantum information processing tasks. Here, we study the interplay of coherence and entanglement under the action of different three qubit quantum cloning operations. Considering certain well-known quantum cloning machines (input state independent and dependent), we provide examples of coherent and incoherent operations performed by them. We show that both the output entanglement and coherence could vanish under incoherent cloning operations. Coherent cloning operations on the other hand, could be used to construct a universal and optimal coherence machine. It is also shown that under coherent cloning operations the output two qubit entanglement could be maximal even if the input coherence is negligible. Also it is possible to generate a fixed amount of entanglement independent of the nature of the input state.

quant-ph↗

arXiv2018

Proposal for Dimensionality Testing in Quantum Private Query

Recently, dimensionality testing of a quantum state has received extensive attention (Ac{í}n et al. Phys. Rev. Letts. 2006, Scarani et al. Phys. Rev. Letts. 2006). Security proofs of existing quantum information processing protocols rely on the assumption about the dimension of quantum states in which logical bits are encoded. However, removing such assumption may cause security loophole. In the present paper, we show that this is indeed the case. We choose two players' quantum private query protocol by Yang et al. (Quant. Inf. Process. 2014) as an example and show how one player can gain an unfair advantage by changing the dimension of subsystem of a shared quantum system. To resist such attack we propose dimensionality testing in a different way. Our proposal is based on CHSH like game. As we exploit CHSH like game, it can be used to test if the states are product states for which the protocol becomes completely vulnerable.

quant-ph↗

arXiv2018

Distinguishing different classes of entanglement of three-qubit pure states

Employing the Pauli matrices, we have constructed a set of operators, which can be used to distinguish six inequivalent classes of entanglement under SLOCC (stochastic local operation and classical communication) for three-qubit pure states. These operators have very simple structure and can be obtained from the Mermin's operator with suitable choice of directions. Moreover these operators may be implemented in an experiment to distinguish the types of entanglement present in a state. We show that the measurement of only one operator is sufficient to distinguish GHZ class from rest of the classes. It is also shown that it is possible to detect and classify other classes by performing a small number of measurements. We also show how to construct such observables in any basis. We also consider a few mixed states to investigate the usefulness of our operators. Furthermore, we consider the teleportation scheme of Lee et al. (Phys. Rev. A 72, 024302 (2005)) and show that the partial tangles and hence teleportation fidelity can be measured. We have also shown that these partial tangles can also be used to classify genuinely entangled state, biseparable state and separable state.

quant-ph↗

arXiv2018

Mutual Uncertainty, Conditional Uncertainty and Strong Sub-Additivity

We introduce a new concept called as the mutual uncertainty between two observables in a given quantum state which enjoys similar features like the mutual information for two random variables. Further, we define the conditional uncertainty as well as conditional variance and show that conditioning on more observable reduces the uncertainty. Given three observables, we prove a 'strong sub-additivity' relation for the conditional uncertainty under certain condition. As an application, we show that using the conditional variance one can detect bipartite higher dimensional entangled states. The efficacy of our detection method lies in the fact that it gives better detection criteria than most of the existing criteria based on geometry of the states. Interestingly, we find that for $N$-qubit product states, the mutual uncertainty is exactly equal to $N-\sqrt{N}$, and if it is other than this value, the state is entangled. We also show that using the mutual uncertainty between two observables, one can detect non-Gaussian steering where Reid's criteria fails to detect. Our results may open up a new direction of exploration in quantum theory and quantum information using the mutual uncertainty, conditional uncertainty and the strong sub-additivity for multiple observables.

quant-ph↗

arXiv2018

Structural Physical Approximation make possible to realize the optimal singlet fraction with two measurements

Structural physical approximation (SPA) has been exploited to approximate non-physical operation such as partial transpose. It has already been studied in the context of detection of entanglement and found that if the minimum eigenvalue of SPA to partial transpose is less than $\frac{2}{9}$ then the two-qubit state is entangled. We find application of SPA to partial transpose in the estimation of optimal singlet fraction. We show that optimal singlet fraction can be expressed in terms of minimum eigenvalue of SPA to partial transpose. We also show that optimal singlet fraction can be realized using Hong-Ou-Mandel interferometry with only two detectors. Further we have shown that the generated hybrid entangled state between a qubit and a binary coherent state can be used as a resource state in quantum teleportation.

quant-ph↗