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The enumeration of multipartite entanglement is an essential, yet challenging task in quantum information processing. A new measure for calculating genuine tripartite entanglement, called the concurrence fill (CF), has been added to the list of entanglement measures. In this article, we employ the CF to calculate the extent of entanglement present in the three-mode continuous variable states, such as the quasi-GHZ state and quasi-W state. The above mentioned states mimic their respective discrete variable states for moderate coherent strength, while for lower coherent strength, the states are far from possessing maximum entanglement. The photon addition in these states at the single mode and three-mode levels results in the states reaching their respective maximum amount of entanglement even for the lower coherent amplitude. In continuation, a nonlocal tripartite photon addition is implemented on a product three-mode coherent state, and the resultant state is shown to have W-type entanglement. [ABSTRACT FROM AUTHOR]

The W-type entangled states are very useful in quantum computing and quantum communication. Many works have been devoted to preparing non-hybrid W states (i.e., all qubits with the same encoding) in various physical systems. On the other hand, hybrid W entangled states are key ingredients for hybrid quantum computing and quantum communication. In this work, we propose to create a hybrid W entangled state of three photonic qubits each with a different encoding. The hybrid W state is prepared by employing three microwave cavities coupled to a superconducting flux qutrit (i.e., a three-level quantum system). This proposal requires only a single qutrit to couple the three cavities, thus the system architecture is greatly simplified. Since there is no need of making any measurement, the W state is created deterministically. As an example, our numerical simulation demonstrates that within current experimental technology, the proposed hybrid W state can be created with a high fidelity. This proposal is universal and can be applied to create the proposed hybrid W state, by using three microwave or optical cavities coupled to a three-level natural or artificial atom. [ABSTRACT FROM AUTHOR]

Quantum state synthesis typically aims to convert an initial direct-product state into a highly entangled target state. As a benchmark problem, we consider the task of spreading one excitation among N two-level atoms or qubits. Starting from an initial state where one qubit is excited, we seek a target state where all qubits have the same excitation amplitude—a generalized-W state. This target is to be reached by suitably chosen pairwise exchange interactions. For example, we may have a setup where any pair of qubits can be brought into proximity for a controllable period of time. We describe three protocols that accomplish this task, each with N - 1 tightly constrained steps. In the first, one atom acts as a flying qubit that sequentially interacts with all others. In the second, qubits interact pairwise in sequential order. In these two cases, the required interaction times follow a pattern with an elegant geometric interpretation. They correspond to angles within the spiral of Theodorus—a construction known for more than two millennia. The third protocol follows a divide-and-conquer approach—dividing equally between two qubits at each step. For large N, the flying-qubit protocol yields a total interaction time that scales as N , while the sequential approach scales linearly with N. For the divide-and-conquer approach, the time has a lower bound that scales as log N —achievable when multiple exchange interactions can take place in parallel. We argue that this is the optimal solution that requires the least time. For any protocol that achieves this task, the phase differences in the final state cannot be independently controlled. As an example, we show that a W state (where all phases are equal) cannot be generated by pairwise exchange. [ABSTRACT FROM AUTHOR]

The three-particle W state is used as a quantum resource in this research. The sender’s unitary operator works on the Bell state via the Pauli and controlled Z gates and encodes the unitary operations. Subsequently, the receiver measures the joint Bell state. Next, the receiver identifies the sender’s unitary process and decodes the secret message for its retrieval. Finally, two quantum secure direct communication protocols are developed under collective noise channels. These protocols use different logical Bell states to resolve two different types of noise in the transmission channel. The protocol compensates for the weaknesses of three-particle W state quantum secure direct communication in resisting the collective noise. Moreover, the logical W state is applied to protect the quantum state, which increases its fidelity and improves the information transmission rate. In addition, the security of this study’s protocols is demonstrated using a rigorous security analysis of diverse attacks. [ABSTRACT FROM AUTHOR]

The goal of this paper is to study controlled quantum teleportation (CQT for short) of an unknown single-qubit state by using a three-qubit W state as the quantum channel. The tripartite scheme is first introduced in an ideal environment, and its detailed implementation is described via the transformation of the quantum system. Then, this scheme is analyzed under two successive uses of Pauli noisy channels with memory. We give general formula quantifying the fidelity under the correlated Pauli channels. For each type of noise, the average fidelity of single-qubit CQT is calculated as a function of memory and noise parameters in the case of teleportation through a three-qubit W state in which the sender’s and receiver’s entangled qubits are interacted to environment during the process of entanglement distribution. The results demonstrate that the performance of the scheme is reduced in the correlated Pauli channel with partial memory, which means that the memory in this kind of noise channels will significantly weaken the communication efficiency of CQT. [ABSTRACT FROM AUTHOR]

As an important practical cryptographic protocol, quantum key distribution (QKD)-based quantum private query (QPQ) has gained widespread attention in the past few decades. However, many of these protocols require classical post-processing, and the number of transmitted qubits is often much larger than the size of the database. Recently, Zhou et al. proposed a QPQ protocol that uses the W state and relies on a third party, which only requires qubits of the same size as the database [37]. Unfortunately, we have discovered a potential attack strategy against this protocol. By using fake entangled photons, a dishonest third party may be able to compromise the privacy of both the database owner and the user. To address this security vulnerability, we propose an improved QPQ protocol. [ABSTRACT FROM AUTHOR]

Anonymous conference key agreement (ACKA), also known as multiparty key distribution, is a cryptographic task in which multiple parties hope to establish a common key. Different from the pioneering works, we propose an anonymous quantum conference key protocol based on the W state, which takes advantage of multipartite entanglement to establish a conference key. In contrast with the existing protocols that use GHZ state, the application of the W state is even more effective. If one of the particles is labeled, the others remain entangled. And the purpose of this study is to demonstrate that states other than the GHZ state can be utilized in the design of anonymous quantum conference key protocols. During the design process, four sub-protocols are developed, including the quantum anonymous collision detection protocol and the quantum notification protocol. Moreover, the entire anonymous conference key agreement protocol has been constructed, which includes the anonymous multiparty entanglement protocol and the verification process. Finally, we analyze the correctness and security of the proposed anonymous quantum conference key agreement protocol. [ABSTRACT FROM AUTHOR]

In 2019, Wen et al. proposed authenticated semi-quantum key distribution (ASQKD) for identity and message using the teleportation of W states and GHZ-like states without pre-shared keys. However, the ASQKD protocol presents a vital issue in the teleportation of W states owing to its inappropriate design. Bob recovers the teleported W states without obtaining the position of the corresponding photons and then returns the recovered photons back to Alice. Hence, the teleportation of W states in Wen et al.'s ASQKD protocol was malfunctioning. Moreover, Wen et al.'s ASQKD protocol requires quantum memory, which strongly disobeys the definition of semi-quantum proposed by Boyer et al. Therefore, in this study, we discover the flaws of Wen et al.'s ASQKD protocol and propose an authenticated semi-quantum key distribution protocol. When compared to Wen et al.'s ASQKD protocol, the proposed ASQKD protocol has the following advantages: legal semi-quantum environment (i.e., does not require quantum memory), reduced quantum hardware requirement (i.e., based only on W states), does not involve classical cryptography (i.e., the hash function), and provided 1.6 times higher qubit efficiency. [ABSTRACT FROM AUTHOR]

Large-scale entangled states are important physical resources, which can be generated from small-scale ones via quantum state fusion. Measurement in fusion operation will cause particle and efficiency loss, so a fusion scheme without qubit loss is expected to be the most efficient one, but counter-intuitively it is not the case. So in this paper we reveal the essence of the fusion mechanism, and answer this counter-intuitive question. The results show that any fusion mechanism is basically a generalized measurement (POVM), and the POVM essence shows why the qubit-loss-free fusion scheme for standard W state is not the most efficient one. A more efficient fusion mechanism targeting at large-scale W state is proposed, where two unequally-weighted W states are fed into the fusion mechanism, and it beats all the current fusion schemes. The universality of the POVM essence of the fusion mechanism makes it applicable to any multipartite entangled state. • The essence of quantum state fusion mechanism was revealed: generalized measurement. • The mechanism is applicable to any kind of multipartite entangled states. • Reveal why the qubit-loss scheme is more efficient than the qubit-loss-free one. • More efficient fusion schemes for generating large-scale W/W-like states. • Beat all the current fusion schemes by a huge margin in the resource cost. [ABSTRACT FROM AUTHOR]

Entanglement witnesses are fundamental tools for detecting entanglement. We prove the necessary and sufficient conditions via two entanglement witnesses for the full separability of system of the four-qubit GHZ and W mixed states in white noise in some parameter regions. The witnesses lead to the necessary conditions. For the sufficiency of the system, we generate three types of optimal product states. Then we show how to combine optimal product states to construct the four-qubit fully separable GHZ and W mixed states in white noise. [ABSTRACT FROM AUTHOR]

Quantum fisher information of a parameter characterizing the sensitivity of a state with respect to parameter changes. In this paper, we study the quantum fisher information of the W state for four, five, six and seven particles in decoherence channels, such as amplitude damping, phase damping and depolarizing channel. Using Krauss operators for decoherence channels components, we investigate the quantum fisher information quite analytically. We observe that for the W state, the amount of the quantum fisher information and consequently, the amount of entanglement are reduced by applying the quantum noises, which affect each particle in the same way. In some cases, a relative increase appears in the quantum fisher information for certain values of the decay strength p. We also show that the phase damping channel vanishes the value of the quantum fisher information for the W state.

We propose three schemes to generate polarization W-states of size n + m , n + m + t , and n + m + t + z without qubit loss, i.e., large-sized W n + m ( W n + m + t and W n + m + t + z ) is generated from one W n and one W m (one W n , one W m , and one W t , and one W n , one W m , one W t , and one W z ). The qubit-loss-free fusion mechanism increases the size of the fusion W states essentially, i.e., reduces the fusion steps, which makes the implementations of the schemes possible within current technology. Ancillary photons, controlled-NOT, Toffoli, Fredkin, and partial-SWAP gates are not required in our schemes. In addition, the number of the coherence states is reduced from 3 to 2, and path couplers are not employed. There is no complete failure output, and all garbage states are recyclable in the W n + m fusion scheme. [ABSTRACT FROM AUTHOR]

With the rapid development of computer-related technology, how to realize privacy query between both parties becomes very important. In this paper, we propose a quantum privacy query protocol based on W state, compared with the GHZ state, the W state is more robust and easier to prepare, the quantum circuit for preparing W state is also given. The protocol makes use of the correlation after entangled state measurement, and enables the querying party to obtain only one secret key information with the assistance of a third party, thus compared with existing schemes, this scheme eliminates the need for classic post-processing operations and can resist joint measurement attacks. In addition, the proposed protocol has two security checks, which can well resist ancilla particle attacks and entanglement measurement attacks by third parties and external intruders participating in the protocol. Therefore, the proposal of this protocol is very necessary. [ABSTRACT FROM AUTHOR]

In 2019, Wen et al. proposed authenticated semi-quantum key distribution (ASQKD) for identity and message using the teleportation of W states and GHZ-like states without pre-shared keys. However, the ASQKD protocol presents a vital issue in the teleportation of W states owing to its inappropriate design. Bob recovers the teleported W states without obtaining the position of the corresponding photons and then returns the recovered photons back to Alice. Hence, the teleportation of W states in Wen et al.’s ASQKD protocol was malfunctioning. Moreover, Wen et al.’s ASQKD protocol requires quantum memory, which strongly disobeys the definition of semi-quantum proposed by Boyer et al. Therefore, in this study, we discover the flaws of Wen et al.’s ASQKD protocol and propose an authenticated semi-quantum key distribution protocol. When compared to Wen et al.’s ASQKD protocol, the proposed ASQKD protocol has the following advantages: legal semi-quantum environment (i.e., does not require quantum memory), reduced quantum hardware requirement (i.e., based only on W states), does not involve classical cryptography (i.e., the hash function), and provided 1.6 times higher qubit efficiency.

An efficient scheme to generate multiparticle W state based on transitionless quantum driving (TQD) with trapped ions is proposed. In the TQD scheme, the effective Hamiltonian can be obtained with the help of quantum Zeno dynamics and large off‐resonance condition, and the multiparticle W state can be generated with high fidelity. The influence of decoherence induced by the ionic spontaneous emission and the ambient heating, and the sensitivity of the TQD scheme to some experimental errors are discussed by numerical simulation. The result demonstrates that the TQD scheme is faster than that only via the fractional stimulated Raman adiabatic passage and robust against decoherence and operation imperfection. [ABSTRACT FROM AUTHOR]

Based on the polarization-dependent beam splitter (PDBS), we propose an optical scheme to fuse small-size polarization entangled W states into a large-scale W states. With the present scheme, two W m + n + t - 2 states can be created from an n-qubit W state, an m-qubit W state and a t-qubit W state, and two W m + n + t + q - 3 states can be generated from W m , W n , W t and W q states. In the previous fusion schemes, only one particle from each initial W state is allowed to enter the fusion mechanism, but with the progress of experimental technology, two particles can be extracted. In this case, the W states fusion of our scheme will be realized without any ancillary particles and controlled quantum gate. In addition, compared with the one target W state obtained in previous preparation schemes, our scheme can generate two large-scale W states, which effectively improve the success rate of generating target W state. The ability to generate two target W states makes our scheme have a distinct advantage in preparing W states with larger particle numbers. This preparation mechanism also can be generalized to the case of fusing more different or same particles W states. [ABSTRACT FROM AUTHOR]

Using a three-particle W state as the quantum channel, we investigate the teleportation of an arbitrary single-qubit state in noisy environments. The influence of different noises on the process of teleporation of an arbitrary single-qubit state with a three-particle W state is considered by analytically derivation and calculations of the fidelities of the teleportation. The single-qubit teleportation fidelity was derived and computed numberically in the case of teleportation through a triparticle W state in which the sender's entangled qubit is interacted to environment during the process of entanglement distribution and the receiver's entangled particle is rotated to optimize the teleportation fidelity. It is shown that the fidelity of single-qubit teleportation through a strong bit flipping or bit-phase flipping environment can be enhanced by rotating the entangled particle about x-axis or y-axis. While such effect does not appear in quantum teleportation when rotating an entangled particle of Bell state under a strong bit-phase flipping environment. [ABSTRACT FROM AUTHOR]

Entanglement detection is one of the important topics in quantum information theory. Wootters formula can be seen as a high level criterion for entanglement detection or entanglement quantification. However, it is restricted to two-qubit system, and its generalization is also limited. Based on a thorough study of a three-qubit Greenberger-Horne-Zeilinger (GHZ) state mixed with a W state and white noise, we find a connection between Wootters formula and the matched entanglement witness. Further study shows that for a four-qubit GHZ state mixed with a Dicke state and white noise, there is a new kind of Wootters formula. [ABSTRACT FROM AUTHOR]

In this paper we are going to calculate the correlation function and Bell'sinequality for three qubit W state under the Lorentz transformations. This survey is basedon the introduction of two different expressions of spin observable were presented byLee-Young and Kim-Son.

In quantum information theory, fidelity is a measure of the closeness of the two quantum states. In this work we consider the fidelity for W state in several noisy channels and calculate this parameter for these noisy channels. We showed that the fidelity is approximately equivalent in Pauli channels σz, σx(σy) and fidelity for Pauli channels σx and Pauli channels σy, are the same. But in depolarizing channel, the fidelity decreases faster than those three channels (Pauli channels σx, σy, σz). Also, if the system does not interact with the environment, the fidelity stays fixed and at all times is equal to one(1). If the interaction between the system and the environment is strong, all the diagrams of fidelity slow down quickly with increasing time. [ABSTRACT FROM AUTHOR]

A semi-quantum bi-signature scheme based on W states is designed, in which two signers sign the same message. The unconditional security of the new semi-quantum bi-signature scheme is guaranteed with the teleportation of W states and semi-quantum key distribution (SQKD) protocol. From the aspects of hardware requirement and efficiency, the proposed semi-quantum bi-signature scheme is more efficient and convenient than many typical quantum signature schemes. [ABSTRACT FROM AUTHOR]

We propose a scheme to create a 4-atom W state by Lyapunov control with the help of quantum Zeno effect. The effective Hamiltonian to describe quantum Zeno dynamics can be obtained in an invariant Zeno subspace and the 4-atom W state can be achieved through modulating the system parameters. Numerical simulation shows that the present scheme is robust against both cavity decay and the atom spontaneous emission. Furthermore, we present a proposal for W state conversion by the same principle, which provides theoretically a novel way for multi-qubits entanglement preparation. [ABSTRACT FROM AUTHOR]

We propose a scheme to prepare entangled states between solid-state nitrogen-vacancy (NV) centers. In our scheme, NV centers are coupled to the whispering-gallery modes of microtoroidal resonators (MTRs). With a protocaled polarized photon input and measurement of single-photon detector, NV centers will be projected on entangled states with the assistance of the special input-output process of polarized photon in MTRs. More importantly, both Bell and W state can be generated with our optical system. This scheme provides a physical feasibility for entangling NV centers, and maybe pave the way towards NV center-based quantum information processing (QIP). [ABSTRACT FROM AUTHOR]

A new quantum bi-signature scheme based on GHZ states and W states is proposed. In the proposed scheme, Alice and Bob sign one same message and send their signatures to Charlie. Different from some typical quantum signature schemes, the new quantum bi-signature scheme firstly sets up a secure channel and the three parties verify each other with the correlation of GHZ states. Then Alice, Bob and Charlie utilize the measurement outcomes of W states to implement signature and verification. The proposed scheme without any key converts the message with quantum one-way function to improve the security. The new quantum bi-signature scheme can solve the most issues of two-way choice in real life, and analysis results show that the proposed scheme is secure and efficient. Furthermore, the proposed scheme can be implemented with the existing physical technologies. [ABSTRACT FROM AUTHOR]

We explore the simulation of three-qubit Heisenberg XY chain with nearest-neighbour interaction in a system of superconducting charge qubits ultrastrongly coupled to a LC resonator. By resorting to parametric modulation of external magnetic fields, the derived effective Hamiltonian is just the required Heisenberg XY chain with nearest-neighbour interaction. This effective Hamiltonian can be utilized to create two/three-qubit entangled states at the time scale of nanoseconds with high fidelity. Since the entangled states have been widely used in different quantum protocols as valuable resource states, the enhanced fast generation of those states reduces errors at the level of resource states. [ABSTRACT FROM AUTHOR]

We propose a scheme to prepare W state for three atoms in a cavity via adiabatic passage and quantum Zeno dynamics. Appropriate Rabi frequencies of the classical fields are selected to realize the present scheme. Numerical analysis is showed, which indicates that the scheme is robust against the floating of the pulse delay and laser intensity, and the atomic spontaneous radiation and the cavity decay are efficiently suppressed by engineering adiabatic passage. Moreover, the scheme is more achievable in experiment than other existing schemes. Based on the current experimental technology, this scheme for generation of high-fidelity W state for three atoms can be achieved. [ABSTRACT FROM AUTHOR]

Based on four-qubit symmetric W state, the delayed measurement, decoy photos method, block transmission technique and the dense coding method, a multi-party quantum key agreement protocol is proposed. By utilizing the delayed measurement and decoy photos method, the fairness and security of the protocol are ensured. That is, the final generation key can be got fairly by m participants and the outside eavesdropper (includes Trojan-horse attacks, Measure-resend attack, Intercept-resend attack and Entangle-measure attack) and the dishonest participants attacks can be resisted in this protocol. By utilizing block transmission technique and the dense coding method, the efficiency of the protocol is improved. The efficiency analysis shows that the proposed protocol is more efficient than other multi-party QKA protocols. [ABSTRACT FROM AUTHOR]

We show that the tensor rank of tensor product of two three-qubit W states is not less than eight. Combining this result with the recent result of M. Christandl, A.K. Jensen, and J. Zuiddam that the tensor rank of tensor product of two three-qubit W states is at most eight, we deduce that the tensor rank of tensor product of two three-qubit W states is eight. We also construct the upper bound of the tensor rank of tensor product of many three-qubit W states. [ABSTRACT FROM AUTHOR]

Quantum teleportation is important in quantum communication networks. Considering that quantum state information is also transmitted between two distant nodes, intermediated nodes are employed and two multi-hop teleportation protocols based on W state are proposed. One is hop-by-hop teleportation protocol and the other is the improved multi-hop teleportation protocol with centralized unitary transformation. In hop-by-hop protocol, the transmitted quantum state needs to be recovered at every node on the route. In improved multi-hop teleportation protocol with centralized unitary transformation, intermediate nodes need not to recover the transmitted quantum state. Compared to the hop-by-hop protocol, the improved protocol can reduce the transmission delay and improve the transmission efficiency. [ABSTRACT FROM AUTHOR]

Motivated by the concept of quantum finite-state machines, we have investigated their relation with matrix product state of quantum spin systems. Matrix product states play a crucial role in the context of quantum information processing and are considered as a valuable asset for quantum information and communication purpose. It is an effective way to represent states of entangled systems. In this paper, we have designed quantum finite-state machines of one-dimensional matrix product state representations for quantum spin systems. [ABSTRACT FROM AUTHOR]

We propose two schemes for preparing GHZ-type and W-type entangled squeezed vacuum states of electromagnetical fields based on dispersive cavity QED. The GHZ-type and W-type entangled squeezed vacuum states in n separate cavities can be effectively obtained after detecting the final states of the atoms. We also discuss the influences of cavity decay on two schemes. [ABSTRACT FROM AUTHOR]

In this paper, we present an alternative scheme to generate W state of three superconducting qubits in three spatially separated coplanar waveguide resonators with the quantum Zeno dynamics and the dressed states. When a set of dressed states is suitably chosen, a scheme can be designed for accelerating the adiabatic passage without additional couplings. What is more, the populations of the intermediate states of the system can be restricted by choosing suitable control parameters. We discuss the influence of dissipation and operational imperfection by numerical analysis and the results show that the scheme is robust against various decoherence processes. In addition, we hope the scheme can provide a theoretical basis for the manipulation of the multi-qubit quantum state. [ABSTRACT FROM AUTHOR]

We present su±cient criteria for the entanglement of three-qubit states. For some special families of states, the criteria are also necessary for the entanglement. They are formulated as simple sets of inequalities for the mean values of certain observables defined as tensor products of Pauli matrices. The criteria are good indicators of the entanglement in the vicinity of three-qubit GHZ and W states and enjoy the capability of detecting the entangled states with positive partial transpositions. Furthermore, they improve the best known result for the case of W state mixed with the white noise. The e±ciency of the criteria is illustrated through several examples. [ABSTRACT FROM AUTHOR]

Quantum Fisher Information (QFI) is a very useful concept for analyzing situations that require phase sensitivity. It become a popular topic especially in Quantum Metrology domain. In this work, we study the changes in quantum Fisher information (QFI) values for one relative arbitrary phased quantum system consisting of a superposition of N Qubits W and GHZ states. In a recent work (Ozaydin et al. Int. J. Theor. Phys. 52, 2977, 2013), QFI values of this mentioned system for N qubits were studied. In this work, we extend this problem for the changes of QFI values in some noisy channels for the studied system. We show the changes in QFI depending on noise parameters. We report interesting results for different type of decoherence channels. We show the general case results for this problem. [ABSTRACT FROM AUTHOR]

Group signature scheme is a method of allowing a member of a group to sign a message anonymously on behalf of the group. The group administrator is in charge of adding group members and has the ability to reveal the original signer in the event of disputes. Based on controlled quantum teleportation with three-particle entangled W states, we propose a new quantum group signature scheme with designated receiver. Security analysis proves that the proposed scheme possesses the characteristics of group signature and resists the usual attacks. Compared with previous proposed schemes, this scheme follows security definition of group signature fully and meets its basic requirements. [ABSTRACT FROM AUTHOR]

We propose a scheme to generate W states based on transitionless-based shortcuts technique in cavity quantum electrodynamics (QED) system. In light of quantum Zeno dynamics, we first effectively design a system whose effective Hamiltonian is equivalent to the counter-diabatic driving Hamiltonian constructed by transitionless quantum driving, then, realize the W states' generation within this framework. For the sake of clearness, we describe two stale schemes for W states' generation via traditional methods: the adiabatic dark-state evolution and the quantum Zeno dynamics. The comparison among these three schemes shows the shortcut scheme is closely related to the other two but better than them. That is, numerical investigation demonstrates that the shortcut scheme is faster than the adiabatic one, and more robust against operational imperfection than the Zeno one. What is more, the present scheme is also robust against decoherence caused by spontaneous emission and photon loss. [ABSTRACT FROM AUTHOR]

In this article, the robustness of tripartite Greenberger-Horne-Zeilinger (GHZ) and W states is investigated against Dzyaloshinskii-Moriya (i.e. DM) interaction. We consider a closed system of three qubits and an environmental qubit. The environmental qubit interacts with any one of the three qubits through DM interaction. The tripartite system is initially prepared in GHZ and W states, respectively. The composite four qubits system evolve with unitary dynamics. We detach the environmental qubit by tracing out from four qubits, and profound impact of DM interaction is studied on the initial entanglement of the system. As a result, we find that the bipartite partitions of W states suffer from entanglement sudden death (i.e. ESD), while tripartite entanglement does not. On the other hand, bipartite partitions and tripartite entanglement in GHZ states do not feel any influence of DM interaction. So, we find that GHZ states have robust character than W states. In this work, we consider generalised GHZ and W states, and three $$\pi $$ is used as an entanglement measure. This study can be useful in quantum information processing where unwanted DM interaction takes place. [ABSTRACT FROM AUTHOR]