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We investigate the quantum thermodynamic cycle of a quantum heat engine carrying out an Otto thermodynamic cycle. We use the thermal properties of a moving heat bath with relativistic velocity with respect to the cold bath. As a working medium, we use a two-level system and a harmonic oscillator that interact with a moving heat bath and a static cold bath. In the current work, the quantum heat engine is studied in the high and low temperatures regime. Using quantum thermodynamics and the theory of open quantum system we obtain the total produced work, the efficiency and the efficiency at maximum power. The maximum efficiency of the Otto quantum heat engine depends only on the ratio of the minimum and maximum energy gaps. On the contrary, the efficiency at maximum power and the extracted work decreases with the velocity since the motion of the heat bath has an energy cost for the quantum heat engine. Furthermore, the efficiency at maximum power depends on the nature of the working medium., 16 pages, 4 figures

Quantum private comparison (QPC) can tell us whether two users’ private data are equal or not by quantum technology without disclosing privacy to each other. There are many QPC protocols with diverse procedures and a wide variety of quantum resources. If two forms of quantum states or above are used in a QPC protocol, there will be a need of multiple devices or methods to generate these quantum states, which could bring about some lurking unfavourable effects such as inefficiency and high costs in application. In order to improve the QPC efficiency and reduce costs, a design principle to develop QPC protocols is put forward as a reference in this paper. Also, to take Bell states for example, a QPC protocol with a single Bell state as quantum resource is presented. The protocol is not only simple yet efficient and easy to apply but also of low costs. The analyses show its correctness so it could behave as an alternative way to exercise QPC.

We study the QSLT of the two-level system coupling to a single mode cavity which is driven by a laser field under the feedback control, and focus on the effect of the Rabi frequency and two types of the feedback on the QSLT. The results show that the QSLT is always less than the driving time, that is, the evolution speed of the two-level system can be accelerated. Whatever types of feedback we use, the QSLT varies with the initial time parameter, both the feedback and the classical field can change the acceleration in the evolution process.

Aiming at extending the classical strong mathematical morphology operations to quantum image processing field, in this paper, an quantum image edge detection method is designed based on the novel enhanced quantum representation of digital images (NEQR) and multi-directions Gray-scale morphology. Because NEQR is more convenient for gray operation of quantum image. In addition, based on multi-directional feature of image edges, the multi-directional structures are constructed by combining the mathematical morphology. Compared with the existing quantum image edge detection methods, this method can reach a better effect.

In this paper, we propose a two-party quantum private comparison (QPC) protocol using orthogonal product states. This protocol introduces a semi-honest third party who will faithfully execute the protocol and will not conspire with any of the participants. Every participant encodes the hash value of her (his) secret data into a quantum sequence of orthogonal product states. Each of these states comes from a locally indistinguishable set of product states. To ensure information security, each participant splits the quantum sequence of product states that she (he) generates into two single-particle sequences and transmits these two single-particle sequences separately. After the third party calculates and publishes the results, the two participants can know whether their secret information is equal by a simple calculation. Security and efficiency analyses show that our protocol is secure and efficient.

Optimal two-qubit operation is of significance to quantum information processing. An efficient scheme is proposed for realizing the shortcut to adiabatic two-qubit state swap in a superconducting circuit quantum electrodynamics (QED) via effective drivings. Two superconducting qutrits are coupled to a common cavity field and individual classical drivings. Based on two Gaussian-type Rabi drivings, two-qubit state swap can be adiabatically implemented within a reduced three-state system. To speed up the operation, these two original Rabi drivings are modified in the framework of shortcuts to adiabaticity, instead of adding an extra counterdiabatic driving. Moreover, owing to a shorter duration time, the decoherence effects on the accelerated quantum operation can be mitigated significantly. The strategy could offer an optimized method to construct fast and robust quantum operations on superconducting qubits experimentally.

In 2016, Li et al. [Int. J. Theor. Phys. 55, 1820–1823 (2016)] proposed schemes for quantum teleportation of certain class of three and four qubit states by utilizing four- and five- qubit cluster states, respectively, as the quantum channels. Moreover, their teleportation-schemes necessitates multi-qubit entangled states. In the present study, it has been demonstrated that these authors committed trivial errors while designing their teleportation schemes and, hence, quantum teleportation could not be perfectly achieved. It is seen that the tasks of teleporting aforementioned class of three and four qubit states can be accomplished by applying only a two-qubit maximally entangled states, i.e., single Bell state as the quantum channel. It is, therefore, an improvement on Li et al. teleportation-schemes is proposed, which not only reduces quantum resource consumption but also operation complexity.

In classical information processing, the windowed Fourier transform (WFT), or short-time Fourier transform, which is a variant of the Fourier transform by dividing a longer time signal into shorter segments of equal length and then computing the Fourier transform separately on each shorter segment, is proposed to provide a method of signal processing. Up to now the discrete Fourier transform has been successfully applied to the field of quantum information, but the related short-time discrete Fourier transform of this field has not been developed accordingly. To address this problem, we first introduce the concept of quantum window state, and further prove that the quantum Fourier transform of a quantum window state is also a quantum window state. Based on the definition of the quantum window state the local information of a quantum signal is extracted and the corresponding quantum circuits are also given. And then, by applying the quantum Fourier transform to the windowed quantum superposition states, we propose a novel concept called quantum windowed Fourier transform (QWFT). Finally, an application of quantum signal processing is given where QWFT is employed.

In this paper, inspired by Wang et al.’s deterministic secure quantum communication (DSQC) scheme (Commun. Theor. Phys. 60 (2013) 397–404), a novel quantum dialogue (QD) scheme is put forward also by using Bell states and single photons as quantum resource. The proposed scheme can effectively overcome the active attacks launched by an outside attacker, such the intercept-resend attack, the measure-resend attack, the entangle-measure attack, etc. The information-theoretical efficiency of the proposed scheme is as high as 66.67%.

In this paper, by using entanglement swapping of Bell states, an efficient quantum private comparison(QPC) protocol with a semi-honest party is proposed. The semi-honest third party (TP) is required to help two participants perform the comparison. She can record intermediate results and do some calculations in the whole process of the protocol execution, but she is not allowed to conspire with any participants. Moreover, TP cannot get two participants’ privacy information except the comparison results. The security analysis shows that the proposed protocol can resist both outsider attacks and insider attacks. Compared with other similar QPC protocols, the proposed one needs neither unitary operations nor the entanglement swapping of multiparticle quantum states, and it only needs the entanglement swapping of Bell states, which makes it more practical. Since three-bit classical information could be compared in each comparison, the proposed protocol has a good performance in its efficiency.

Combining the ideas of quantum state sharing and multi-party quantum remote control, a novel four-participant quantum rotation operation sharing protocol was proposed, which utilizes pre-shared entanglement and local operations. Concretely, using 4-qubit entanglement of Greenberger-Home-Zeilinger (GHZ) type state as quantum channel, the two senders of the protocol can remotely and independently implement various rotation operations on the target state of any site, which requires mutual cooperation between two agents. Moreover, by utilizing (M + N)-qubit GHZ type state as the entanglement channel, the above four-participant situation can be easily generalized to the scenario with M senders and N agents.

We consider a parametric oscillation driven by coherent light beams and coupled to a two-mode thermal reservoir. Applying the solutions of the quantum Langevin equations, we investigate the effect of decoherence and the driving coherent light beams on the squeezing and entanglement as well as statistical properties of the two-mode cavity radiation. We show that the two-mode thermal noise and the driving coherent light beams lead to an increase in the intensity of the cavity radiation. However, the driving coherent light beams do not have any effect on the squeezing and entanglement properties of the two-mode cavity radiation while the two-mode thermal noise leads to a decrease in the degree of squeezing and entanglement of the two-mode cavity radiation.

The interaction between two modes quantized field and asymmetric two atoms represents one of the important quantum models to study the nonclassical quantized phenomena. The two modes multiphoton processes and interacting asymmetric two two-level atoms are introduced in the proposed quantum system. The time dependent solution of the proposed quantum system is computed analytically for asymmetric and symmetric cases. This analytical solution depends on the eigenvalues and the eigenvectors of the coefficient matrix of the Schrodinger equation. The nonclassical features of the proposed quantum system are evaluated as the entanglement and the atomic populations. The entanglement between atom and field is measured via the von Neumann entropy while the entanglement between two atoms is measured by the concurrence. These quantized features are analyzed for variety of the detuning parameter, the atom-atom coupling constant, and the numbers of two photon modes. The most important observations are that: If the numbers of two photon modes are identical, the von Neumann entropy is strong most of the time, the periodic time of the entropy and atomic populations is double comparing with other cases, and the concurrence is non-existent for asymmetric case. In the presence the detuning parameter and the atom-atom coupling constant, the von Neumann entropy increases with time while the amplitude of the concurrence decreases with time for symmetric case. The fluctuations of the von Neumann entropy for symmetric case are stable and uniform more than its for asymmetric case. The concurrence is irregular for asymmetric case. Furthermore, there are other quantized effects of the proposed model which are discussed for symmetric and asymmetric cases.

With the development of quantum computation theory, some researchers further apply it to improve the efficiency of classical machine learning algorithms. Based on physical graph state, an efficient quantum version of classifier is proposed in this paper. Different from existing classical methods, realizing the proposed scheme is an entangling-subgraphs process of physical system to build the classifier by using the graph states. Resort to the efficiency of graph state, the quantum algorithm is more efficient to big data than the classical ones.

Distributed quantum system is a well-known method to overcome the problems of designing and manufacturing large quantum systems to achieve higher processing power in the world of quantum processing. In distributed quantum computing, a number of limited-capacity quantum circuits communicating with each other through communication channels operate as a large quantum circuit. The most essential step in designing a distributed quantum system is to optimize the communication between the components to reduce the overhead cost of communications. In this study, based on the commuting of quantum gates, an efficient method is proposed to reduce the number of teleportations required to perform distributed quantum circuits (DQCs). The results obtained from the evaluation of our method on benchmark circuits indicate an impressive decrease in the number of teleportations and a significant reduction in the execution time compared to the present methods.

We first propose a three-party semi-quantum summation protocol with an almost-dishonest third party (TP) using single photons. TP who has full quantum power helps three classical users compute the summation of their private bit strings while the privacy of their inputs is preserved. For a particle from TP, three users’ operations are limited either to (1) reflect the particle without disturbance back to TP or to (2) measure the particle in the Z basis and resend the measured particle back to TP. We also show that our protocol is secure against both outside and participant attacks.

Most games in the real world are asymmetric, and participants can have different conditions or strategies, depending on the available resources. In this work, the quantum prisoner’s dilemma with two dilemma strength parameters is studied. Two examples of asymmetric strategy spaces are considered. We show that, most of the obtained Nash equilibria are not Pareto optimal. Therefore, the classical dilemma can still exist in the quantum regime with asymmetric strategy spaces. These results can be applied to real-world situations, when global issues requiring the interaction of agents from different environments exist.

In this paper, a controlled quantum dialogue protocol is designed based on five-qubit entangled states. One five-qubit entangled state can be used to exchange one communicant’s two private bits with the other communicant’s two private bits under the control of an honest supervisor. Security analysis turns out that it can overcome the information leakage problem and can resist the active attacks from an outside attacker. The designed protocol only needs single-particle measurements and Bell state measurements, both of which can be realized with current technologies.

In secure multiparty quantum computation (SMQC), the multiplication is one of the fundamental operations that can be used to assemble the complex quantum protocols. The existing protocols have the approach of either (n, n) threshold or (t, n) threshold, with high cost and low security. In this paper, we propose a secret sharing based quantum protocol for (t, n) threshold secure multiparty multiplication, where t out of n players can compute the multiplication efficiently with low cost. In this protocol, the multiparty quantum multiplication can be performed if the number of secrets are more than the number of players as the secrets are shared using the linear secret sharing. Further, the security analysis shows that it is more secure against the intercept, entangle-measure, collusion, collective, and coherent attacks as compared to the existing protocols.

Quantum entanglement is one of the key methods in quantum information processing, but it is difficult to prepare quantum entanglement. Quantum walk is widely used in quantum computation and quantum simulation, it can be applied to the preparation of quantum entangled states. In this paper, a controllable quantum network coding scheme based on quantum walk is proposed. With the help of quantum walk, the scheme preliminary realized the entanglement distribution of butterfly network, reduced entanglement resources and enhanced scalability. According to the existing technology, it is feasible to implement the quantum network coding scheme proposed in this paper.

In the present work, a novel approach was proposed to optimize the teleportation cost in Distributed Quantum Circuits (DQCs) by applying a new approach. To overcome the difficulty with keeping a large number of qubits next to each other, DQCs, as a well-known solution, have always been employed. In a distributed quantum system, qubits are transferred from a subsystem to another subsystem by a quantum protocol such as teleportation. First, we proposed a heuristic approach through which we could replace the equivalent circuits in the initial quantum circuit. Then, we used a genetic algorithm to partition the placement of qubits so that the number of teleportations could be optimized for the communications of a DQC. Finally, results showed that the proposed approach could impressively work.

Gram matrices arise naturally in the consideration of pair-wise overlap of a family of vectors or quantum pure states, and play an important role in synthesizing information of a family of pure states. Since a quantum ensemble in general consists of mixed states, it is desirable to extend the concept of Gram matrix to the case of mixed states. By employing two prominent notions of overlap between mixed states, i.e., quantum affinity and quantum fidelity, one can readily extend the concept of Gram matrices of pure-state ensembles to that of mixed-state ensembles. We study these two extended versions of Gram matrices and reveal their fundamental properties. It is remarkable that while Gram matrix based on quantum affinity is non-negative definite (and thus can be regarded as a quantum state in a fictious system), the one based on quantum fidelity may fail to be non-negative definite. As applications of Gram matrices of mixed-state ensembles, we introduce two quantifiers of quantumness of ensembles via coherence of the corresponding Gram matrices, investigate their properties, and illustrate them in the qubit case.

Using the thermal-entangled state representations, we obtain the analytical evolution of quantum states simultaneously undergoing two kinds of quantum noises that can be represented as the infinitive Kraus operator-sum representation. We also prove the normalization and trace preservation of Kraus operators. Besides, we obtain the evolutions of Wigner distribution and photon number distribution of any quantum state when simultaneously passing through two kinds of quantum noises.

The quantum Fisher information defined via the symmetric logarithmic derivative and the skew information are two different aspects describing the information contents of quantum mechanical density operators. They are considered as natural generalizations of the classical Fisher information and constitute key ingredients in the emerging field of quantum metrology. In this paper, we give the analytical expression of quantum Fisher information and skew information for two-qubit system prepared in a two-qubit state of X type.

Under the actions of different Hamiltonians on the different two-qubit input states by using the quantum Yang-Baxterization approach, we investigate the behaviors of the fidelity and the trace distance as measures of 'closeness' and distinguishability of two quantum states. The results show that the fidelity that is the main figure of merit for any communication and computing process can be kept to high values depending on the choice of the initial states and the Hamiltonians constructed by the Yang-Baxter equation. On the other hand, by choosing the initial states and Yang-Baxter systems which are the various extensions of the Yang-Baxter equations for several matrices, these quantifiers can be adjusted as desired to achieve many quantum computing and computational tasks. Furthermore, to quantify the performance of quantum teleportation we examine the teleportation fidelity for the outputs that correspond to the different two-qubit X-type states under the actions of the different Hamiltonians. It is possible to obtain high fidelity to use the quantum teleportation process.

Blind quantum computation (BQC) allows quantum-limited clients to delegate their quantum-computing tasks to a remote quantum server while keep their inputs, outputs, and algorithms private during the computation. Secure multi-party computation aims to solve the problem of collaborative calculations among a group of distrustful participants. Although BQC has been used to solve the problem of secure two-party quantum computation, the case of multiple clients carrying out collaborative calculations has not been considered. In this paper, a quantum secure three-party computation protocol is proposed based on BQC, and the protocol is further extended to a quantum secure multi-party computation protocol. Using the blindness of BQC, the problem of privacy of clients’ data in quantum secure multi-party computation is solved. Moreover, in the preparation stage of the protocols, the initial states only need to be encrypted once, which is simpler than previous protocols.

Quantum logic gates are the foundation of circuit-based quantum computation and quantum simulation. Multi-qubit quantum controlled gates are of vital importance when large-scale quantum circuits are concerned. Here, assisted by diamond nitrogen-vacancy (NV) centers inside single-sided optical cavities, we first introduce the single-photon quantum routing operation, with which a single-photon polarization qubit can be coherently routed to the superposition of two spatial modes according to the state of the other polarization qubit. On this basis, we propose two schemes for the implementation of universal three-qubit quantum Fredkin- and Toffoli-gate operations on single-photon polarization qubits. Moreover, we show that a general multi-qubit controlled-unitary gate can be realized using the same strategy. Compared to other NV-cavity-based schemes, our schemes utilize photonic polarization, spatial, and temporal degrees of freedom (DOFs) simultaneously, so that the quantum circuits are simplified and the required quantum resources are reduced, making our schemes more resource-efficient and highly scalable. Our calculations show that the schemes can posses near-deterministic efficiency and near-unity fidelity with current or near-future techniques, which guarantees the experimental feasibility. Our schemes can therefore provide a new recipe for the construction of multi-qubit quantum gates and for efficient processing of multi-photon states.

The security of quantum cryptography is based on microscopic quantum properties, which is much higher than that of classical cryptography. In this paper, we combine the proxy threshold multiple signature with quantum signature in classical cryptography, which not only retains the agent property, threshold property, multiplicity and forward property of the original scheme, but also makes the scheme have the security of quantum signature. So it is a secure and practical signature scheme.

Two-qubit X-state is a large class of quantum states which plays an important role in the quantification and dynamical study of quantum correlations. However, the corresponding quantification of quantum discord is still missing for bona fide discord measures, like original quantum discord, Bures distance of discord, and relative entropy of discord. In this paper, we consider the calculation of Bures distance of discord, which is a kind of correlations satisfying all criteria of a discord measure, for two-qubit X-states. Firstly, we derive explicit expression for Bures distance of discord for a kind of five-parameters family of states. Moreover, for general two-qubit X-states, we not only calculate the Bures distance of discord for a subset of two-qubit X-states by classifying and analyzing the optimal local measurements and the optimal projection operators, but also provide an analytic upper bound for entirety.

In this paper, we use exact matrix diagonalization to research property of the many-body localization (MBL) in the disordered Heisenberg XXX model with periodic driving. We get the periodic time-dependent external field by trigonometric function, which is added to periodically drive this model. It is demonstrated that the fidelity of eigenstate is able to capture quantum criticality underlying many-body physics (Zhou et al. Phys. Rev. Lett. 100, 080601, 2008, Zhou and Barjaktarevi J. Phys. A: Math. Theor. 41, 412001 2008), which can be used to characterize the many-body localization transition in this closed spin system (Zanardi and Paunkovic Phys. Rev. E 74, 031123, 2006). We obtain the fidelity for high-energy many-body eigenstates, namely, the excited state fidelity, which shows the phase transition of periodically driven Heisenberg XXX chain with different disordered external field strengths and different system sizes. It is demonstrated that when Heisenberg XXX system is in a very small disorder, periodic driving can cause the occurrence of a transition from ergodic phase to MBL phase. In contrast to the HS model which has global two-body interaction, which we have studied recently with the same situation, there is no MBL phase transition when we drive the HS model in ergodic phase with periodic driving. It also shows that for the strong disordered Heisenberg XXX system, there will exist a critical driving period Tc, when driving period T is higher than Tc, the system will undergo a transition from localized phase to ergodic phase and the MBL phase will be broken. Furthermore, we discover that the size of the system and the strength of disorder will affect the critical point of driving period and the magnitude of the phase change. For the same system, the critical point increases as the strength of disorder increases. We also explore the non-disorder system of HS model with the same driving to explore the properties of MBL, it shows that under periodic driving, the non-disordered HS system has the quantum phase transition rather than MBL phase transition. This illustrates the important role of disorder on MBL.

We propose a bidirectional controlled teleportation scheme using two pairs of Bell states as quantum channels. This solution uses Charlie as the controlled party. After two Bell state measurements, while Alice sends any single particle state to Bob, Bob can also send any single particle state to Alice, thus successfully completing the bidirectional controlled teleportation. Our plan is also compared with several other protocols from five aspects to illustrate that the plan has certain advantages. This makes our scheme relatively simpler and easier to implement and more maneuverable.

We explore quantum multi-parameter estimation, based on quantum Fisher information matrix (QFIM), in an extended anisotropic XY spin chain associated with non-trivial topological characterization driven by varying system parameters (i.e., magnetic field λ, the anisotropic of the nearest-neighbor interaction γ, the next-nearest-neighbor interaction α and its anisotropy δ). The results show that QFIM can provide us a useful tool to detect the topological critical points in this model. Furthermore, we find that the behavior of QFIM associated with variance of estimators are driving parameters dependent at different topological quantum phase transition points. Meanwhile, the choice of estimators $\hat {\theta }$ also take a prominent role on the behavior of QFIM.

We extend the standard solid-state quantum mechanical Hamiltonian containing only Coulomb interactions between the charged particles by inclusion of the (transverse) current-current diamagnetic interaction starting from the non-relativistic QED restricted to the states without photons and neglecting the retardation in the photon propagator. This derivation is supplemented with a derivation of an analogous result along the non-rigorous old classical Darwin-Landau-Lifshitz argumentation within the physical Coulomb gauge.

Quantum image scaling is an important branch of quantum image processing and has been extensively studied in recent years. A quantum image scaling algorithm based on bilinear interpolation is proposed in this paper. This algorithm can scale the image of any floating point number scale. Quantum arithmetics for floating point numbers are proposed, and quantum algorithms for quantum image scaling up and down are presented. Moreover, the quantum circuits of quantum image scaling are designed and their network complexity is analyzed. With the results of simulation experiment on the classical computer MATLAB software, it is demonstrated that the proposed quantum image scaling algorithms have the good effect.

The analog multicolor optomechanically induced transparency (OMIT) of distant optomechanical system is studied. The two charged mechanical oscillators couple to each other via Coulomb interaction, and the atomic ensemble is introduced into the hybrid system. We focus on the width of OMIT windows which is manipulated by some interference effects of the system components. The research shows that five transparency windows can be observed from the output field at the probe frequency. In the absence of some internal interactions, the number of transparent windows will reduce. Furthermore, the width and the number of the transparent windows are affected by the coupling strength between the optical mode and the mechanical mode, between the optical mode and atoms and the Rabi frequency, between the two optical modes, as well as the Coulomb coupling between the two charged oscillators. It is feasible for our approach to manipulate multiple optomechanically induced transparency, which provides potential applications in quantum information processing and quantum net works.

In this paper, we study cyclic codes over a finite non-chain ring $\mathbb {F}_{p^{m}}+v\mathbb {F}_{p^{m}}$ with v2 = 1 and find new and better quantum error-correcting codes than previously known quantum error correcting codes over $\mathbb {F}_{p^{m}}$ . Therewith, we characterize the LCD codes and obtain many new LCD codes. Also, we prove that the Gray map of an LCD code of length n over $\mathbb {F}_{p^{m}}+v\mathbb {F}_{p^{m}}$ is an LCD code of length 2n over $\mathbb {F}_{p^{m}}$ .

Quantum enhancement of the optical behavior for V −type open atomic system is examined analytically. With consideration of the system which contain N number of atoms, it is derived that the evolution of the atomic variable evolution with respect to time. At steady state, the optical properties of the system have been analyzed. The phase between the upper doublet levels is influencing the optical parameters change in the system. It is observed that for small values of the phase between the upper doublet energy states, the better refractive index of the atomic medium. The refractive index gets the peak value near to the resonance frequency of the probe field. The properties of the re-emitted light from ensemble of three-level atoms have been analyzed in details. In this regard, it is observed that the height of the power spectrum increased while the number of atoms are large in the sample.

Different from traditional signature schemes, the paper gives a novel protocol which uses quantum logic gates to perform operations on quantum states, and it realizes the quantum state representation of two classical information and uses mixed entangled states to measure information. The binary measurement results of the protocol are converted into blocks of a certain length, and these blocks are encrypted by quantum Fourier transform and transmitted through N-dimensional quantum states. In the proposed protocol, the quantum channel uses N-dimensional quantum states, which is more efficient than the currently proposed two-dimensional information carrier channel protocol. The security analysis of this article shows that the program is anti-counterfeit, undeniable and blind. In addition, compared with other existing efficiency analysis schemes, this scheme has higher signature efficiency.

We study the effect of unentangled states with nonzero discord on Quantum Stackelberg duopoly game (QSD). We show that the initial state parameter and quantum discord will cause remarkable change in the Nash equilibrium of the QSD game and the profits of the two players. We also find that under certain conditions there is a ‘specific point’ of the initial state parameter and quantum discord. The two players have the same moves and payoffs at the ‘specific point’. The QSD game can switch between the first-mover advantage game and the follower-mover advantage game when the initial state parameter and quantum discord varies from the left-hand-side regime of the ‘specific point’ to the right-hand-side regime.

In this paper, we investigate the entanglement of a quantum system containing two subsystems characterized by the angular momenta j1 and j2, in the framework of the superposition of spin coherent states. We formulate the measure of the entanglement in terms of the amplitudes of the spin coherent states as well as their spins j1 and j2. We extend this investigation to rank-two bipartite mixed states involving spin-j coherent states by using a simplified expression of concurrence. We show that the bipartite entanglement of mixed states is strongly dependent on the spin ji of each subsystem and the probabilities associated with it.

We study the interatomic energy and force of two ground-state atoms in interaction with the fluctuating quantum massless scalar field in vacuum with two different approaches, i.e. the stationary perturbation theory and the DDC formalism [the formalism proposed by Dalibard, Dupont-Roc and Cohen-Tannoudji]. With the DDC formalism, we calculate the interatomic energy in terms of the contributions of vacuum fluctuations and the contributions of the atomic radiation reaction. We find that, in the near region, the contributions of vacuum fluctuations is less important than the contributions of the atomic radiation reaction, and as a result, the interatomic force is attractive and proportional to L− 3. While in the far zone, the contributions of vacuum fluctuations and those of the atomic radiation reaction become equally important, and the interatomic force is attractive and proportional to L− 4. The interatomic energy and force derived with these two different approaches are accurately the same. We comment that the two different approaches deal with the interatomic interaction from different perspectives and have their own advantages.

Private set intersection(PSI) allows two parties to get all common elements of their private sets without leaking any information about their sets. In this paper, we present a novel PSI protocol which is based on quantum Fourier transform. Correctness analysis shows that our protocol can get the result correctly. And the security of our protocol is also analyzed, it can resist most of outside attacks, such as Trojan horse attack, intercept-resend attack, entanglement-and-measure attack, man-in-the-middle attack and so on. And it also can overcome participant attacks.

The exploration of quantum entanglement in multipartite quantum systems is of great significance to the study of quantum entanglement, maximally multi-qubit entangled state is one of the research objects. Recently, Che et al. presented a recurrence relation of multi-qubit state. According to this inspiration, we present the recurrence relation of maximally multi-qubit pure states of N-qubits for N = 6, 7, 8. Further, some new forms of the seven- and eight-qubit maximally entangled states are found with the recurrence relation.

Hardy’s paradox can demonstrate the conflict between quantum mechanics and local realism. Experimental testing of Hardy’s paradox has been carried out, but it involved only a few qubits. We propose a simple but novel approach to verify the generalized Hardy’s paradox and Hardy’s inequality using quantum programming. By designing scalable quantum circuits, we write quantum programs in Q# and corresponding classical controls in C# using Visual Studio. Our quantum simulation results are consistent with the original theoretical values; moreover, they can be easily extended to multiqubit systems. This provides an effective means for investigating multipartite entanglement question using quantum programming.

Due to many classical numerical methods have not yet mature quantum counterparts, the quantum circuits design for quantum image processing is very important. In this paper, using the novel enhanced quantum image representation (NEQR) model and the crossing number (CN) minutiae detection method, quantum circuits for fingerprint minutiae extraction are designed, which is focus on extracting ridge endings and ridge bifurcations from thinned binary fingerprint image. In order to improve the performance of the whole system, the quantum circuits for detection and elimination the false minutiae among the extracted minutiae are also constructed.

Quantum coherence, coming from quantum superposition, occupies a significant position in the field of physics. We put forward a lower bound of the robustness of multilevel coherence mathematically by optimizing the coherence witnesses via semi-definite programming, which can be direct and easy to evaluate and experimentally accessible. A numerical example is supplemented to illustrate the efficiency of the presented bound.

We consider entangled state production utilizing a full optomechanical arrangement, based on which we create entanglement between two far three-level V-type atoms using a quantum repeater protocol. At first, we consider eight identical atoms (1; 2;...; 8), while adjacent pairs (i; i + 1) with i = 1; 3; 5; 7 have been prepared in entangled states and the atoms 1, 8 are the two target atoms. The three-level atoms (1,2,3,4) and (5,6,7,8) distinctly become entangled with the system including optical and mechanical modes by performing the interaction in optomechanical cavities between atoms (2,3) and (6,7), respectively. Then, by operating appropriate measurements, instead of Bell state measurement which is a hard task in practical works, the entangled states of atoms (1,4) and (5,8) are achieved. Next, via interacting atoms (4,5) of the pairs (1,4) and (5,8) and operating proper measurement, the entangled state of target atoms (1,8) is obtained. In the continuation, entropy and success probability of the produced entangled state are then evaluated. It is observed that the time period of entropy is increased by increasing the mechanical frequency and by decreasing optomechanical coupling strength to the field modes. Also, in most cases, the maximum of success probability is increased by decreasing G and via decreasing.