Searcharxiv⌕ Search

arXiv subjects

Satyabrata Adhikari

Publications and source records attributed to Satyabrata Adhikari.

At least 19 recordsLinked to original sources
arXiv2026

Condition for the generation of the secret key in a BB84 like quantum key distribution protocol

Woodhead [Phys. Rev. A 88, 012331 (2013)] derived the lower bound of the secret key rate for a Bennett-Brassard (BB84) like quantum key distribution protocol under collective attacks. However, this lower bound does not always assure the generation of the secret key and thus the protocol may have to be aborted sometimes. Thus, we modify the Woodhead's lower bound of the secret key rate in such a way that the secret key is always generated in a BB84 like quantum key distribution protocol. We show the non-linear relationship between the lower bound of the secret key rate with the error rate and fidelity. Exploiting the obtained modified lower bound of the secret key rate, we analyze two state dependent quantum cloning machines such as (i) Wootters-Zurek QCM and (ii) Modified Buzek-Hillery QCM constructed by fixing the cloning machine parameters of Buzek Hillery quantum cloning machine (QCM), which may be used by the eavesdropper to extract information from the intercepted state. We, thereafter, show that it is possible for the communicating parties to distill a secret key, even in the presence of an eavesdropper. Moreover, we also discuss the effect of the efficiency of the QCM on the generation of the secret key for a successful key distribution protocol.

quant-ph↗
arXiv2026

Construction of a Non-Linear Entanglement Witness Operator in Arbitrary Dimension Using a Given Linear Witness Operator

Entanglement detection is one of the important problems in quantum information theory. To deal with this problem, many entanglement detection criteria have been proposed. Among the proposed criteria, the detection of entanglement through witness operator (also known as linear entanglement witness (LEW) operator) may be considered as the most practical. Although the witness operator approach to detect entanglement is experimentally friendly, the construction of these operators is not a very simple task. Even if we are able to construct a LEW operator, our problem is not solved as it may either detect a few entangled states or not a single entangled state from a given family of entangled states. Thus, we need a constructive approach in order to tackle this type of problem. In this work, we provide a few constructions of the non-linear entanglement witnesses (NLEW) for $d_1\otimes d_2$ dimensional system from any linear entanglement witness (LEW) operator. The advantage of these constructions is that, if a LEW is unable to detect any particular entangled state described by the density operator $ρ^{ent}$ then our construction of NLEW may detect the same entangled state $ρ^{ent}$. Further, we have constructed NLEW operator that may detect not only a class of bipartite negative partial transpose entangled state (NPTES), but also positive partial transpose entangled state (PPTES). Moreover, we have shown that the constructed NLEW operators may be decomposed in terms of the tensor product of local observables and hence may be realizable in an experiment.

quant-ph↗
arXiv2025

Combinatorial structures in quantum correlation: A new perspective

Graph-theoretic structures play a central role in the description and analysis of quantum systems. In this work, we introduce a new class of quantum states, called $A_α$-graph states, which are constructed from either unweighted or weighted graphs by taking the normalised convex combination of the degree matrix $D$ and the adjacency matrix $A_G$ of a graph $G$. The constructed states are different from the standard graph states arising from stabiliser formalism. Our approach is also different from the approach used by Braunstein et al. This class of states depend on a tunable mixing parameter $α\in (0,1]$. We first establish the conditions under which the associated operator $ρ_α^{A_G}$ is positive semidefinite and hence represents a valid quantum state. We then derive a positive partial transposition (PPT) condition for $A_α$-graph states in terms of graph parameters. This PPT condition involves only the Frobenius norm of the adjacency matrix of the graph, the degrees of the vertices and the total number of vertices. For simple graphs, we obtain the range of the parameter $α$ for which the $A_α$-graph states represent a class of entangled states. We then develop a graph-theoretic formulation of a moments-based entanglement detection criterion, focusing on the recently proposed $p_3$-PPT criterion, which relies on the second and third moments of the partial transposition. Since the estimation of these moments is experimentally accessible via randomised measurements, swap operations, and machine-learning-based protocols, our approach provides a physically relevant framework for detecting entanglement in structured quantum states derived from graphs. This work bridges graph theory and moments-based entanglement detection, offering a new perspective on the role of combinatorial structures in quantum correlations.

quant-ph↗
arXiv2025

Construction of PPT entangled state and its detection by using second-order moment of the partial transposition

We adopt a formalism by which we construct and detect a new family of positive partial transpose entangled states in $d_1\otimes d_2$ dimensional system. Our detection method is based on the second order moment $p_2(ρ^{T_B})$ as it is very easy to calculate and may be realizable in laboratory. We show that if the second order moment $p_2(ρ^{T_B})$ in $d_1\otimes d_2$ dimensional system satisfy $p_2(ρ^{T_B})\leq\frac{1}{d_1 d_2-1}$, then the state is a PPT state. We also derive an equivalent condition on the bloch vector. Then, we construct a quantum state by considering the mixture of a separable and an entangled state and obtain a condition on the mixing parameter for which the mixture represents a PPTES. Finally, applying our results, we have shown that the distillable key rate of the private state, prepared through our prescription, is positive. It suggests that our result also has potential applications in quantum cryptography.

quant-ph↗
arXiv2025

Geometric Discord of any arbitrary dimensional bipartite system and its application in quantum key distribution

Entangled quantum states are regarded as a key resource in quantum key distribution (QKD) protocols. However, quantum correlations, other than entanglement can also play a significant role in the QKD protocols. In this work, we will focus on one such measure of quantum correlation, known as geometric quantum discord (GQD). Firstly, we derive an analytical expression of GQD for two-qutrit quantum systems and further generalize it for $d_1\otimes d_2$ dimensional systems. Next, we apply the concept of GQD in studying QKD. In particular, if the shared resource state is an entangled state constructed with the linear combination of the tensor product of the Bell pair and the state $σ_i$'s, $i=0,1,2,3$, then we have shown that under some assumption on $σ_i$'s, the lower bound for a distillable secret key rate $K_D$ can be expressed in terms of GQD of $\frac{σ_0+σ_1}{2}$ and $\frac{σ_2+σ_3}{2}$. Thus, the distillable key rate depends upon the GQD of $\frac{σ_0+σ_1}{2}$ and $\frac{σ_2+σ_3}{2}$, when the communicating parties uses private states for generating a secret key in presence of an eavesdropper. Further, for a certain range of GQD of $\frac{σ_0+σ_1}{2}$ and $\frac{σ_2+σ_3}{2}$, we find that there exists some NPT entangled resource state for which the successful generation of the secret key may not be guaranteed. We, moreover study the behavior of distillable key rate when the geometric discord of $\frac{σ_0+σ_1}{2}$ and $\frac{σ_2+σ_3}{2}$ increases, decreases or remains constant, with the help of a few examples.

quant-ph↗
arXiv2025

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states

The Computable Cross Norm (CCN), or realignment criterion, is a widely used method for entanglement detection in quantum systems; however, it typically provides only a necessary condition. In this work, we advance the applicability of the realignment criterion by deriving a condition that is both necessary and sufficient for detecting entanglement in two-qubit. $X$-states derive their name from the characteristic 'X' shape of their density matrix, which contains seven independent matrix parameters. Notably, they incorporate several important subclasses of entangled states, including Bell states, Werner states, and maximally entangled mixed states. $X$-states have proven highly useful in entanglement studies due to their sparse structure and the ease with which entanglement-related quantities can be computed. This refined criterion improves the identification of entangled states that the standard CCN approach fails to detect, thereby extending the utility of the method.

quant-ph↗
arXiv2025

Quantum cloning transformation unlocks the potential of W class of states in a quantum secure direct communication protocol

In a controlled quantum secure direct communication (Controlled QSDC) protocol between three parties, the sender sends the encoded secured message to one of the two receivers, which can be decoded only when the other receiver agrees to cooperate. A lot of studies have been done on it using the three-qubit GHZ state, and only a few works have involved the W state. In this work, we introduce a controlled QSDC protocol exploiting a three-qubit W class of state shared between three parties, Alice (Sender), Bob (Controller), and Charlie (Receiver). In the proposed protocol, the shared state parameters and the secret are linked in such a way that it is very difficult to factor them. We will show that these parameters can be factored out easily if the receiver uses a quantum cloning machine (QCM) and thus can retrieve the secret. We find that the protocol is probabilistic and have calculated the probability of success of the protocol. Further, we establish the relation between the success probability and the efficiency of the QCM. In general, we find that the efficiency of the constructed QCM is greater than or equal to $\frac{1}{3}$, but we have shown that its efficiency can be enhanced when the parameters of the shared state are used as the parameters of the QCM. Moreover, we derived the linkage between the probability of success and the amount of entanglement in the shared W class of state. We analyzed the obtained result and found that even a less entangled W class of state can also play a vital role in the proposed controlled QSDC scheme.

quant-ph↗
arXiv2024

Modified Six State Cryptographic Protocol with Entangled Ancilla States

In a realistic situation, it is very difficult to communicate securely between two distant parties without introducing any disturbances. These disturbances might occur either due to external noise or may be due to the interference of an eavesdropper sitting in between the sender and the receiver. In this work, we probe here the existence of the possibility of the situation of generation of a secret key even if the eavesdropper is able to construct an entangled ancilla state in such a way that she can extract information from the intercepted qubit. To achieve this task, we consider and modify the six-state QKD protocol in which Eve can construct the unitary transformation that may make all ancilla components entangled at the output. Then, we calculate the mutual information between Alice and Bob and Alice and Eve, and identify the region where the secret key is generated even in the presence of Eve. We find that, in general, the mutual information of Alice and Eve depends not only on the disturbance D, but here we have shown that it also depends on the concurrence of the ancilla component states. We have further shown that it is possible to derive the disturbance-free mutual information of Alice and Eve, if Eve manipulates her entangled ancilla state in a particular manner. Thus, in this way, we are able to show that a secret key can be generated between Alice and Bob even if the disturbance is large enough. Moreover, we show that Bruss's six state QKD protocol failed to generate the secret key in the region where the modified six-state QKD protocol can generate the secret key.

quant-ph↗
arXiv2024

Theoretical proposal for the experimental realization of realignment operation

Realignment operation has a significant role in detecting bound as well as free entanglement. Just like partial transposition, it is also based on permutations of the matrix elements. However, the physical implementation of realignment operation is not known yet. In this letter, we address the problem of experimental realization of realignment operation and to achieve this aim, we propose a theoretical proposal for the same. We first show that after applying the realignment operation on a bipartite state, the resulting matrix can be expressed in terms of the partial transposition operation along with column interchange operations. We observed that these column interchange operations forms a permutation matrix which can be implemented via SWAP operator acting on the density matrix. This mathematical framework is used to exactly determine the first moment of the realignment matrix experimentally. This has been done by showing that the first moment of the realignment matrix can be expressed as the expectation value of a SWAP operator which indicates the possibility of its measurement. Further, we have provided an estimation of the higher order realigned moments in terms of the first realigned moment and thus pave a way to estimate the higher order moments experimentally. Next, we develop moments based entanglement detection criteria that detect positive partial transpose entangled states (PPTES) as well as negative partial transpose entangled states (NPTES). Moreover, we define a new matrix realignment operation for three-qubit states and have devised an entanglement criteria that is able to detect three-qubit fully entangled states. We have developed various methods and techniques in the detection of bipartite and tripartite entangled states that may be realized in the current technology.

quant-ph↗
arXiv2024

Entanglement detection in arbitrary dimensional bipartite quantum systems through partial realigned moments

Detection of entanglement through partial knowledge of the quantum state is a challenge to implement efficiently. Here we propose a separability criterion for detecting bipartite entanglement in arbitrary dimensional quantum states using partial moments of the realigned density matrix. Our approach enables detection of both distillable and bound entangled states through a common framework. We illustrate the efficiency of our method through examples of states belonging to both the above categories, which are not detectable using comparable other schemes relying on partial state information. The formalism of employing partial realigned moments proposed here is further shown to be effective for two-qubit systems too, with a slight modification of our separability criterion.

quant-ph↗
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.

quant-ph↗
arXiv2023

Physical realization of realignment criteria using structural physical approximation

Entanglement detection is an important problem in quantum information theory because quantum entanglement is a key resource in quantum information processing. Realignment criteria is a powerful tool for detection of entangled states in bipartite and multipartite quantum system. It is an important criteria for entanglement detection because it works well; not only for negative partial transpose entangled states (NPTES) but also for positive partial transpose entangled states (PPTES). Since the matrix corresponding to realignment map is indefinite so the experimental implementation of the map is an obscure task. In this work, firstly, we have approximated the realignment map to a positive map using the method of structural physical approximation (SPA) and then we have shown that the structural physical approximation of realignment map (SPA-R) is completely positive. Positivity of the constructed map is characterized using moments which can be physically measured. Next, we develop a separability criterion based on our SPA-R map in the form of an inequality and have shown that the developed criterion not only detect NPTES but also PPTES. We have provided some examples to support the results obtained. Moreover, we have analysed the error that may occur because of approximating the realignment map.

quant-ph↗
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 $ρ_{ABC}$ witness the genuine non-locality of $ρ_{ABC}$. 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.

quant-ph↗
arXiv2023

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.

quant-ph↗
arXiv2023

Detection and Classification of Three-qubit States Using $l_{1}$ Norm of Coherence

Entanglement is a purely quantum mechanical phenomenon and thus it has no classical analog. On the other hand, coherence is a well-known phenomenon in classical optics and in quantum mechanics. Recent research shows that quantum coherence may act as a useful resource in quantum information theory. We will employ here quantum coherence to detect and classify the entanglement property of three-qubit states. Moreover, we have shown that if any three-qubit state violates another necessary condition for the detection of a general biseparable state then the given three-qubit state cannot be a biseparable state. Since there are only three categories of states for the three-qubit system so if we detect that the state under probe is neither a separable nor a biseparable state then we can definitely conclude that the given three-qubit state is a genuine entangled state. We have illustrated our results with a few examples.

quant-ph↗
arXiv2023

Detection of $d_{1}\otimes d_{2}$ Dimensional Bipartite Entangled State: A Graph Theoretical Approach

Braunstein et. al. have started the study of entanglement properties of the quantum states through graph theoretical approach. Their idea was to start from a simple unweighted graph $G$ and then they have defined the quantum state from the Laplacian of the graph $G$. A lot of research had already been done using the similar idea. We ask here the opposite one i.e can we generate a graph from the density matrix? To investigate this question, we have constructed a unital map $ϕ$ such that $ϕ(ρ)=L_ρ+ρ$, where the quantum state is described by the density operator $ρ$. The entries of $L_ρ$ depends on the entries of the quantum state $ρ$ and the entries are taken in such a way that $L_ρ$ satisfies all the properties of the Laplacian. This make possible to design a simple connected weighted graph from the Laplacian $L_ρ$. We show that the constructed unital map $ϕ$ characterize the quantum state with respect to its purity by showing that if the determinant of the matrix $ϕ(ρ)-I$ is positive then the quantum state $ρ$ represent a mixed state. Moreover, we study the positive partial transpose (PPT) criterion in terms of the spectrum of the density matrix under investigation and the spectrum of the Laplacian associated with the given density matrix. Furthermore, we derive the inequality between the minimum eigenvalue of the density matrix and the weight of the edges of the connected subgraph of a simple weighted graph to detect the entanglement of $d_{1} \otimes d_{2}$ dimensional bipartite quantum states. Lastly, We have illustrated our results with few examples.

quant-ph↗
arXiv2022

Structured Negativity: A physically realizable measure of entanglement based on structural physical approximation

Quantification of entanglement is one of the most important problem in quantum information theory. In this work, we will study this problem by defining a physically realizable measure of entanglement for any arbitrary dimensional bipartite system $ρ$, which we named as structured negativity $(N_S(ρ))$. We have shown that the introduced measure satisfies the properties of a valid entanglement monotone. We also have established an inequality that relate negativity and the structured negativity. For $d\otimes d$ dimensional state, we conjecture from the result obtained in this work that negativity coincide with the structured negativity when the number of negative eigenvalues of the partially transposed matrix is equal to $\frac{d(d-1)}{2}$. Moreover, we proved that the structured negativity not only implementable in the laboratory but also a better measure of entanglement in comparison to negativity. In few cases, we obtain that structure negativity gives better result than the lower bound of the concurrence obtained by Albeverio [Phys. Rev. Lett. \textbf{95}, 040504 (2005)].

quant-ph↗
arXiv2022

Search for an efficient entanglement witness operator for bound entangled states in bipartite quantum systems

Entanglement detection problem is one of the important problem in quantum information theory. Gurvit showed that this problem is NP complete and thus this may be the possible reason that only one criterion is not sufficient to detect all entangled states. There are some powerful entanglement detection criterion such as partial transposition criterion, realignment criterion but it may not be possible to implement them successfully in the experiment. This situation can be avoided if the entanglement is detected through the construction of witness operator method. In this work, we take an analytical approach to construct a witness operator. To achieve this task, we first construct a linear map using partial transposition and realignment operation. Then we find some conditions on the parameters of the map for which the map represent a positive map. Further, we have constructed a Choi matrix corresponding to the map and have shown that it is not completely positive. We then construct an entanglement witness operator, which is based on the linear combination of the function of Choi matrix and the identity matrix and it can detect both NPTES and PPTES. Finally, we prove its efficiency by detecting several bipartite bound entangled states which were previously undetected by some well-known separability criteria. We also compared the detection power of our witness operator with three well-known powerful entanglement detection criteria, namely, dV criterion, CCNR criterion and the separability criteria based on correlation tensor (CT) proposed by Sarbicki et. al. and find that our witness operator detect more entangled states than these criterion.

quant-ph↗