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We realize the second Hopf fibration for a two-qubit system without using the quaternionic language. In this respect, we explore the geometrical features emerging from this Hopf fibration. Further, we investigate the metric tensor and the SO(4) non-abelian gauge field defined on the $$S^4$$ -base in terms of the entanglement quantified by the Wootters concurrence on the associated Hopf bundle. Finally, by transforming an entangled two-qubit state in the Schmidt form, we examine the different quantum phases acquired by this state under $$U(2) \times U(2)$$ local unitary operations in relation to the entanglement as well as the geometry of the corresponding state manifold.

The four-qubit cluster state has a more robust entanglement property than other four-particle states. Empowered by the 4-qubit cluster state and Bell state entanglement, two quantum secret sharing (QSS) protocols are proposed in this paper. The first protocol is with the quantum users who can perform Bell measurement. The second protocol is with classical users who only can perform Z basis measurement and is also known as semi-quantum secret sharing (SQSS). Moreover, the security analysis shows the proposed QSS and SQSS protocols can achieve full security and resist some common eavesdropping attacks, such as interception attack, measure-resend attack, entanglement-measure attack, and Trojan horse attack. Meanwhile, the efficiency comparison shows that the proposed protocols are also efficient than other similar protocols with relate to the qubit efficiency.

Quantum game theory is a rapidly evolving subject that extends beyond physics. In this research work, a schematic picture of quantum game theory has been provided with the help of the famous game Prisoners' Dilemma. It has been considered that the shared qubits of the prisoners may interact with the environment which is a bath of simple harmonic oscillators. This interaction introduces decoherence and this model has been compared with phase damping. Calculation of the decoherence factor shows that decoherence reduces the payoff of the prisoners. The factor has been calculated based on whether the decoherence occurred once or twice. A comparative discussion establishes that the process of decoherence is faster for the case when it occurs twice. It needs to be mentioned here that the total time of decoherence is the same in both cases., Comment: 7 pages, 4 figures

Quantum teleportation protocols are widely employed for secure transfer of quantum states to away part. In this paper, we present a new scheme for teleporting a N-qubit entangled state via a ( $$N+1$$ )-qubit cluster state as quantum channel. In this scheme, the sender (Alice) performs a von Neumann measurement on her basis and announces the result to the receiver (Bob), let him to recover the original state by affecting unitary operator on his state. Here, firstly, we present our general scheme for teleportation of a N-qubit entangled state by using a ( $$N+1$$ )-qubit cluster state; then, the proposed scheme is examined by a simple example in which a 6-qubit entangled state is teleported by employing the proposed scheme. Finally, we analyze the efficiency of the scheme and indicate its advantages.

Blind quantum machine learning (BQML) is a novel secure quantum computation protocol that enables a client (Alice), who has limited quantum technology at her disposal, to delegate her quantum machine learning to a remote quantum server (Bob) who owns a fully-fledged quantum computer and promises to execute the learning task honestly, in such a way that Bob cannot obtain Alice’s private information. In this paper, we first propose the concept of BQML that combines blind quantum computation and quantum machine learning and we devise two BQML protocols based on quantum circuit model in which Alice can classify vectors of any dimension to different clusters. The first protocol is half-blind, while the second is blind. It means Alice’s privacy can be protected. On the other hand, Alice is only required to possess a quantum random access memory (QRAM), apply the Pauli operators (X and Z), store, send, receive qubits and perform measurements in our protocols. Finally, we analyze the security, blindness and correctness of our protocols, and give a brief conclusion.

Semi-quantum private comparison protocol permits two classical participants to compare the equality of their private information with the help of a semi-honest third party without disclosing privacy. An innovative semi-quantum private comparison protocol based on maximally entangled Greenberger–Horne–Zeilinger-type states has been discussed. The proposed protocol is efficient and without the pre-shared keys. Next, the security analysis guarantees the presented protocol is asymptotically secure against the outsider and the insider attacks. Moreover, the qubit efficiency of the presented protocol is 3.125%. The efficiency comparison shows that it improves the efficiency by 125% for the literature without pre-shared keys.

We design a quantum circuit to generate a class of partially entangled quantum states. Using this kind of quantum state as quantum channel, we put forward deterministic schemes for controlled joint remote state preparation of arbitrary two- and three-qubit states and extend them to prepare arbitrary multi-qubit states. For each case, we give the concrete construction methods of multi-qubit measurement basis and unitary transformations to recover the initial original state. Unlike most previous works, where the parameters of the quantum channel are given to the receiver who can accomplish the task only probabilistically by consuming auxiliary resource, operation and measurement, here we give them to the supervisor. Thanks to the knowledge of quantum channel parameters, the supervisor can perform appropriate complete projection measurement. Combined with the feed-forward strategy adapted by the preparers, the measurement not only much simplifies the receiver’s operation but also yields unit success probability. Amazingly, our protocols do not depend on the entanglement degree of the shared quantum channel, and they are within the reach realization of current quantum technologies.

Quantum secret sharing plays an important role in quantum cryptography. In this paper, we propose a new general quantum secret sharing scheme based on access structure and monotone span program. In our scheme, the secret distributor first distributes the secret share according to the access structure, and then each participant in the authorization set hides their secret share in the qubits, and then transmits each qubit safely performed on unitary transformation. Compared with the existing quantum secret sharing schemes, our scheme is more flexible, general and less computational cost in practical applications.

The type of environments to which a quantum system is exposed has a significant impact on the quantum system’s entanglement and coherence protection. In this regard, we investigate the time evolution of tripartite entanglement and coherence in GHZ-like state when subject to independent classical environments. In particular, we focus on local environments with the same and mixed disorders, resulting in various Gaussian noisy conditions, namely pure power-law noise, pure fractional Gaussian noise, power-law noise maximized, and fractional Gaussian noise maximized configurations. We show that the environments with mixed disorders are more detrimental than those having single kind of disorder for entanglement and coherence preservation using time-dependent quantum negativity, entanglement witnesses, purity, and decoherence metrics. Besides, there is no ultimate solution for avoiding the negative consequences of fractional Gaussian noise-assisted classical environments in both pure and mixed noise conditions. Not only the noise, but also the number of qubits driven by a certain noise, has been discovered to strongly influence the amount, nature of the decay, and preservation intervals. We also show that the GHZ-like states can be modelled in classical channels driven by pure power-law noise for extended quantum correlations, coherence, and quantum information preservation. In addition, we compare the entanglement measurement efficiency between entanglement witness and negativity measures.

We propose here a new idea for quantum teleportation of superposed coherent state which is not only almost perfect, in principle, but also feasible experimentally. We use entangled resource $\sim |\alpha,\frac{\alpha}{\sqrt{2}}\rangle-|-\alpha,-\frac{\alpha}{\sqrt{2}}\rangle$ in contrast with the usual $\sim |\alpha,\alpha\rangle-|-\alpha,-\alpha \rangle$ (both states unnormalized). Bob receives state which is then superposition of the states $|\pm \frac{\alpha}{\sqrt{2}}\rangle$ . Bob mixes these with even or odd coherent states involving superposition of states $|\pm \frac{\alpha}{\sqrt{2}}\rangle$ to obtain a two-mode state which is one of $\sim |I,0\rangle \pm |0,I\rangle$, $|I\rangle$ being the information state. Bob then obtains the teleported information by using interaction of one of these modes in two cavities with resonant two-level atoms. This scheme results in average fidelity of $\simeq 0.95$ for $|\alpha|^2 \simeq 10$, which increases with $|\alpha|^2$ and tends to 1 asymptotically, varying as $1-\frac{\pi^2}{16|\alpha|^2}+\frac{\pi^2(\pi^2+8)}{256|\alpha|^4}$ for large values of $|\alpha|^2$., Comment: 12 pages, 5 figures

Emerging quantum technologies represent a promising alternative for solving hard combinatorial problems in the post-Moore’s law era. For practical purposes, however, the current number of qubits limits the direct applicability to larger real-world instances in the near-term future. Therefore, a promising strategy to overcome this issue is represented by hybrid quantum classical algorithms which leverage classical as well as quantum devices. One prominent example of a hard computational problem is the community detection problem: a partition of a graph into distinct communities such that the ratio between intra-community and inter-community connectivity is maximized. In this paper, we explore the current potential of quantum annealing and gate-based quantum technologies to solve the community detection problem for an arbitrary number of communities. For this purpose, existing algorithms are (re-)implemented and new hybrid algorithms, that can be run on gate-model devices, are proposed. Their performance on standardized benchmark graphs has been evaluated and compared to the one of a state-of-the-art classical heuristic algorithm. Although no quantum speed-up has been achieved, the existing quantum annealing-based methods as well as the novel hybrid algorithms for gate-based quantum computers yield modularity values, which are similar to those of the classical heuristic. However, the modular architecture of the used algorithms allows for fast utilization of more powerful quantum technologies once they become available.Reproducibility:Our code and data are publicly available (Github in Quantum Modularization.https://github.com/jku-win se/quantum_modularization2021).

The quantum state discrimination problem is to distinguish between non-orthogonal quantum states. This problem has many applications in quantum information theory, quantum communication and quantum cryptography. In this paper, a quantum algorithm using weak measurement and partial negation will be proposed to solve the quantum state discrimination problem using a single copy of an unknown qubit. The usage of weak measurement makes it possible to reconstruct the qubit after measurement since the superposition will not be destroyed due to measurement. The proposed algorithm will be able to determine, with high probability of success, the state of the unknown qubit and whether it is encoded in the Hadamard or the computational basis by counting the outcome of the successive measurements on an auxiliary qubit.

Blind quantum computing (BQC) allows a client with limited quantum technology to delegate her quantum computational tasks to a server who can perform universal quantum computation while retaining the client’s secret information. Firstly, in qubits transmission between the server and the client, the loss of qubits is inevitable due to the channel noise. Thus, we propose a fault-tolerant framework for blind quantum computing using logical GHZ states over depolarization channels. In our protocol, an encoded GHZ state by 7-qubit Calderbank–Shor–Steane code is sent by the quantum channel as a medium of quantum teleportation. The client only makes a single-qubit measurement on the third qubit of the logical GHZ state, and the remaining Bell state is shared between the client and the server. After decoding logical Bell state, the client and the server perform the measurement-based blind quantum computing protocol. Secondly, there are two classes of collective noises in the channel, which will affect the blind quantum computing. We modify our BQC protocol to overcome the collective-dephasing noise and the collective-rotating noise with logical states $$|H_{dp}\rangle $$ , $$|V_{dp}\rangle $$ , $$|H_{r}\rangle $$ and $$|V_{r}\rangle $$ . Our protocol is robust against channel noise and qubits loss.

Quantum computing is a field of study aimed at developing technologies based on the principles of quantum theory. In this research area, enormous theoretical progress has been made, but at the current state, few quantum algorithms have been developed. It is very hard to efficiently construct new ones. The complexity is due to the non-intuitive nature of quantum operations. To overcome this obstacle, we opt for the integration of an automatic design approach. In this paper, we propose an adapted version of BackTracking algorithm allowing complete but optimal exploration of the quantum circuits space. For a given problem, the test of possible quantum gate sequences is optimized by using a constraint making it possible to ignore all unnecessary calculation in an efficient manner. In addition, solutions are generated automatically without resorting to mathematical formulas. Our approach allowed us to generate two new versions of controlled quantum teleportation. In the first version, the controller can switch the teleported Qubit between two possible distant receivers, while in the second version, this controller can choose between two different transmitters.

The research of quantum network will promote the application of quantum image to be more universal and widespread. Quantum image representation model is the basis of quantum image processing. Therefore, we propose a multimode quantum image representation (MQIR) and its preparation. In this representation, the image size can be arbitrary and the color can be in one of several color models, such as Gray, RGB, Lab, HSL. This improves the universality of quantum image applications, and our MQIR requires fewer qubits than other quantum image representations. Furthermore, an MQIR image encryption scheme is presented, which is based on three-dimensional non-equilateral Arnold transformation. We give the MQIR transformation (inverse transformation) algorithm and quantum circuits. Some of the transformation times and the parameters in the scrambling process can be used as the keys in the proposed encryption. Finally, we conduct some simulation experiments on the classical computer to analyze the performance such as histogram analysis, peak signal-to-noise ratio and the correlation coefficients of adjacent pixels between original images and encrypted images. Simulation results show that the proposed quantum image encryption scheme is efficient.

We investigate the preservation of quantum coherence and entanglement carried by the three non-interacting qubits during their evolution in the presence of an external fluctuating field characterized by a classical Gaussian noise. Initially, the three non-interacting qubits are considered in two different maximally entangled states, namely Greenberger–Horne–Zeilinger ( $$\mathcal {X}_{G}$$ ) and Werner $$(\mathcal {X}_{W})$$ state. Besides this, we study the time evolution of the two states in three different schemes, namely: common, mixed, and independent system–environment couplings. By deploying different measures, we show that the system–environment coupling and the Gaussian noise greatly affected the quantum correlation and coherence. We also found that the non-local correlation and coherence remain more dominant and robust in common system–environment coupling for the $$\mathcal {X_G}$$ state under the Gaussian noise. Hence, this kind of feature of the $$\mathcal {X}_{G}$$ state is a vital resource for the transmission of quantum information with reduced loss.

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., 9 pages, 1 figure, 1 table, Accepted in Quantum Information Processing(2021)

The Schwinger effect on the entanglement of a hybrid state is studied in this paper. We consider a system composed of a qubit and a bosonic mode. We show that when only the bosonic mode is coupled with a constant electric field, entanglement depends on the strength of the electric field. The results show that the entanglement between the qubit and the bosonic particle decreases with increasing the value of the electric field. Furthermore, applying the electric field creates entanglement between the qubit and antiparticle mode where initially there is no entanglement between them. Moreover, we analyze the variation of entanglement with respect to other parameters such as the mass of the particles and the parameter of hybrid state, $$\alpha $$ .

We develop a theory of linear witnesses for detecting non-Markovianity, based on the geometric structure of the set of Choi states for all Markovian evolutions having Lindblad-type generators. We show that the set of all such Markovian Choi states form a convex and compact set under the small time interval approximation. Invoking geometric Hahn–Banach theorem, we construct linear witnesses to separate a given non-Markovian Choi state from the set of Markovian Choi states. We present examples of such witnesses for dephasing channel and Pauli channel in case of qubits. Furthermore, we have devised another method of detection NM of various qubit channels, by using projective measurements in the Bell basis. This can be done without the knowledge of what specific kind of channel we are dealing with. This gives us a huge operational advantage for NM detection. We further investigate the geometric structure of the Markovian Choi states to find that they do not form a polytope. This presents a platform to consider nonlinear improvement of non-Markovianity witnesses.

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.

We study the dynamic creation of two different geometric quantum discords (GQDs) defined, respectively, via the Hilbert–Schmidt norm (GQD-2) and trace norm (GQD-1) between the two qubits, which are prepared initially in a zero discord two-qubit X-shape state, and subject to a two layers environment that consists of a lossy cavity coupled to the W-coupled lossy cavities. We find that the GQD-2 and GQD-1 exhibit oscillatory behavior in the regime of the strong coupling between the qubit and first-layer cavity environment. And in both the weak and strong coupling regimes, for the greater the number of cavities in the second-layer environment, the GQDs reach their peak value in a larger time and go to zero more slowly. But in the qubit–cavity coupling, the coupling between two nearest neighbor cavities and the decay rate of cavities in the second-layer environment have the opposite effect on the GQDs. Furthermore, the maximum value of GQDs remains unchanged and the steady value increases, or they both decrease, depending on the threshold value of coupling between the two layers environment. Finally, we propose an effective strategy to improve the GQD-2 and GQD-1 by using local filtering operation.

Hierarchical remote preparation of an arbitrary two-qubit state has not been investigated by the previous work. We first put forward two deterministic schemes to realize the task among three agents by using two five-qubit cluster states as the quantum channel. To design these schemes, some useful and general measurement bases are constructed for the sender. Then, the two schemes are extended to multiparty with the aid of the symmetry of cluster state. There exists a hierarchy among the agents in terms of their ability to reconstruct the target state. The upper-grade agent requires the help of all the remaining upper-grade agents and anyone of the lower-grade agents. While the lower-grade agent needs the assistance of all the other agents. Finally, we consider the effect of two important decoherence noises: the amplitude-damping noise and phase-damping noise.

In distributed quantum computation, quantum remote-controlled gates are used frequently and applied on separate nodes or subsystems of a network. One of the universal and well-known controlled gates is the n-qubit controlled-NOT gate, especially Toffoli gate for the case of three qubits, which are frequently used to synthesize quantum circuits. In this paper, we considered a more general case, an n-qubit controlled-U gate, and present a general protocol for implementing these gates remotely with minimum required resources. Then, the proposed method is applied to implement a Toffoli gate in bipartite and tripartite systems. In this method, we considered cases in which a group of qubits belongs to one subsystem of the network. Then, we improved its consumption resources.

Semi-quantum private comparison (SQPC) aims to compare the equality of the classical participants’ secrets with the help of a semi-honest TP, in which TP has full quantum capability while the classical participants’ quantum capability is limited. In the existing SQPC protocols, the entanglement resource (e.g., entangled state preparation and entangled state measurement) and pre-shared key are usually required. Besides, the qubit efficiency is relatively low. In this paper, we propose an efficient SQPC protocol based on single-particle states, in which the entanglement resource and pre-shared key are unnecessary. The qubit efficiency of our protocol is far greater than that of all existing SQPC protocols due to the use of single-particle states and circular transmission mode. Moreover, our protocol can be extended to the multi-party case, which can accomplish arbitrary pair’s comparison of equality among $$n(n\ge 2)$$ classical participants. Finally, various kinds of attacks have been analyzed, which show that the proposed protocol is secure against the outside and inside attacks.

We present a scheme for implementing deterministic joint remote preparation of the Knill–Laflamme–Milburn state with two GHZ states as the quantum channel. Assuming that four of the six involved qubits collectively suffer the same type of noise, we first investigate the effects of four typical types of noises on the protocol by means of Kraus operators. It is shown that the bit-flip and amplitude damping noise are the severe noises for decoherence rate $$\chi 0.5$$ in bit-flip and phase-flip noise channel. Afterward, we investigate the dynamics of deterministic joint remote state preparation for dissipative environments. Analytical and numerical calculations show that the quality of our scheme can be enhanced by adjusting the system detuning no matter whether the non-Markovian effect is applicable or not.

As quantum computation grows, the number of qubits involved in a given quantum computer increases. But due to the physical limitations in the number of qubits of a single quantum device, the computation should be performed in a distributed system. In this paper, a new model of quantum computation based on the matrix representation of quantum circuits is proposed. Then, using this model, we propose a novel approach for reducing the number of teleportations in a distributed quantum circuit. The proposed method consists of two phases: the pre-processing phase and the optimization phase. In the pre-processing phase, it considers the bi-partitioning of quantum circuits by Non-Dominated Sorting Genetic Algorithm (NSGA-III) to minimize the number of global gates and to distribute the quantum circuit into two balanced parts with equal number of qubits and minimum number of global gates. In the optimization phase, two heuristics named Heuristic I and Heuristic II are proposed to optimize the number of teleportations according to the partitioning obtained from the pre-processing phase. Finally, the proposed approach is evaluated on many benchmark quantum circuits. The results of these evaluations show an average of 22.16% improvement in the teleportation cost of the proposed approach compared to the existing works in the literature.

In this paper, we propose a theoretical scheme to study the dynamics of the geometric measure of quantum discord (GMQD) between two non-interacting qubits in a dissipative optomechanical system composed of two Fabry–Perot cavities. In this system, each cavity contains a single-mode quantized radiation field which, in the rotating wave approximation, interacts with both mechanical resonator and two-level atom. In addition, the effects of dissipation are taken into account by considering cavity decay, losses of cavity mirror, and spontaneous emission from the atom. We start with the master equation approach and under some circumstances, we find a non-Hermitian Hamiltonian. Adopting this procedure yields the problem with an acceptable analytical solution. This means that all enough information in the study of the considered open quantum system is exactly obtained. Thereupon, we study the quantum correlations between the atoms with the help of the GMQD. It can be seen that the GMQD between two atoms can be controlled by the optomechanical coupling coefficient, the atom-field coupling strength and the dissipation parameters. Moreover, decreasing the coefficient of optomechanical coupling as well as reducing the strength of atom-field coupling improves the GMQD between two atoms. It is also mentioned that, taking the dissipation effects into account, we see that, as the time proceeds, the GMQD approaches to a stable value. In addition, eliminating the effect of spontaneous emission leads to a diminution in the amount of GMQD. Consequently, the quantum correlations between two atoms can be enhanced by considering the effect of spontaneous emission.

The correlation signals generated by pairs of entangled qubits in CHSH scenarios are studied using the multi-resolution analysis (MRA). When a classical version of the MRA is applied, the correlation functions of the partially synthesized signals do not violate the CHSH inequality until the signals have been fully reconstructed. Later, we apply a variant of the MRA, inserting the detail signals in inverse order. Surprisingly, what we obtain is that the partially synthesized signals violate the CHSH inequality after the second insertion, thus revealing a nonlocal component even long before the synthesis is complete. This results in signals that are up to $$25\%$$ shorter than the original ones but conserving their entangled and nonlocal character.

We analytically obtain the maximum probability of converting a finite number of copies of an arbitrary two-qubit pure state to a single copy of a maximally entangled two-qubit pure state via entanglement-assisted local operations and classical communications using a two-qubit catalyst state, which may be destroyed when the conversion fails. We show that the optimal catalyst for this transformation is always more entangled than the initial state but any two-qubit state can act as a (non-optimal) catalyst. Interestingly, the entanglement of the optimal two-qubit catalyst state is shown to decrease with that of the initial state. The unitaries and measurements required for catalytic entanglement concentration are presented.

Quantum secret sharing (QSS) allows a trusted party to distribute the secret keys to a group of participates, who can only access the secret cooperatively. The semi-quantum secret sharing (SQSS) takes fewer quantum resources and has higher efficiency than the QSS protocol. However, in the existing SQSS protocols, the shared secrets are generated according to the random operations of Bob and Charlie, which are inefficient and uncertain. An efficient semi-quantum secret sharing protocol based on Bell states was proposed, where Alice can share the specific secrets with Bob and Charlie, by encoding her secrets on the two different Bell states. Then, the security analysis shows that this scheme is secure against intercept–resend attack, entangle–measure attack and Trojan horse attack. Compared with similar studies, the proposed scheme is more flexible and practical, and the qubit efficiency is increased by about $$100\%$$ .

There has been an extensive development in the use of multi-partite entanglement as a resource for various quantum information processing tasks. In this paper, we focus on preparing arbitrary spin eigenstates whose subset contains important entangled resources like Dicke states. Leveraging on the symmetry of these states, we consider uniform pairwise exchange coupling between every pair of qubits. Starting from a product state of a given spin eigenstate with a single-qubit state, another spin eigenstate can be prepared using simple time evolutions. This expansion paves a deterministic approach to prepare arbitrary Dicke states in linear steps. We discuss an improvement in this cost, building up on a previous work on deterministic preparation of W states in logarithmic circuit depth (Sharma and Tulapurkar in Phys Rev A 101:062330, 2020). The modified algorithm requires several iterations of pumping spin angular momentum into the system and is akin to the amplitude amplification in Grover’s search. To demonstrate the proposed scheme, we choose a system of non-interacting static spin qubits connected to a ferromagnetic reservoir. The flying qubits emerging from the reservoir locally interact with static qubits successively, mediating an in-direct exchange interaction between all the pairs.

We explore nonlocality of three-qubit pure symmetric states shared between Alice, Bob and Charlie using the Clauser-Horne-Shimony-Holt (CHSH) inequality. We make use of the elegant parametrization in the canonical form of these states, proposed by Meill and Meyer (Phys. Rev. A, 96, 062310 (2017)) based on Majorana geometric representation. The reduced two-qubit states, extracted from an arbitrary pure entangled symmetric three-qubit state do not violate the CHSH inequality and hence they are CHSH-local. However, when Alice and Bob perform a CHSH test, after conditioning over measurement results of Charlie, nonlocality of the state is revealed. We have also shown that two different families of three-qubit pure symmetric states, consisting of two and three distinct spinors (qubits) respectively, can be distinguished based on the strength of violation in the conditional CHSH nonlocality test. Furthermore, we identify six of the 46 classes of tight Bell inequalities in the three-party, two-setting, two-outcome i.e., (3,2,2) scenario (Phys. Rev. A 94, 062121 (2016)). Among the two inequivalent families of three-qubit pure symmetric states, only the states belonging to three distinct spinor class show maximum violations of these six tight Bell inequalities., 11 pages, 9 figures, revised version

This paper takes advantage of the quantum mechanics to present two efficient circular controlled quantum communication schemes. The proposed protocols utilize ten qubits for transmitting the information qubits to five partners circularly, under the permission of a controller. The first protocol is a circular controlled quantum teleportation, which teleports unknown quantum states. The second protocol is a circular controlled quantum broadcast scheme which sends quantum states to two dispersed recipients, circularly. In this paper, the effects of quantum noises on these protocols are analyzed, and the fidelity of the quantum states is calculated too. We will see that, in the circular controlled quantum teleportation protocol, the impact of the noise on input qubits is less than its impact on channel qubits.

We consider the following scenario: a bipartite quantum state is prepared in one of the four Bell-type states. Each qubit is possessed by the spatially separated party, and the parties wish to distinguish between the four Bell-type states. To date, it is not possible to distinguish between the four orthonormal Bell-type states without entanglement-assisted discrimination by means of local operations and classical communication (LOCC). In this paper, we demonstrate the distinguishability of orthonormal Bell-type states with certainty by using LOCC, but no particle is exchanged between the two parties. We start with the local distinguishability of the orthogonal Bell-type states and generalize it for non-orthogonal Bell-type states with nonzero fidelity.

We theoretically analyze the Bell’s inequalities by continuously monitoring a system comprising two-coupled superconducting qubits. The weak probing could measure the observables accurately after sufficient runs. While for the strong measurement, due to the measurement backaction, the system will collapse to the basis state corresponding to the eigenvalue measured with a higher probability. Interestingly, for system in the maximal two-qubit entanglement state, the measurement backaction from strong probe could be compensated by a parity measurement. Under the imperfect detection, a correction term could help yield a result which is compatible with the correct value of the observables. Furthermore, we investigate the Bell’s inequalities during the dynamical evolution of the coupled two-qubit system and demonstrate that the more the two-qubit entangle, the larger violation of Bell’s inequality will present with the upper bound $$2\sqrt{2}$$ .